Download a changing cosmos - Whittier Union High School District

Global Systems Science
University of California, Berkeley
Lawrence Hall of Science
http://lawrencehallofscience.org/gss
A CHANGING
COSMOS
Global Systems Science
based on Hands-On Universe Units by TERC
Edited by Alan Gould
Telescope Images by Vivian Hoette
A Changing Cosmos
2009 Edition
1
Global Systems Science (GSS) and
Hands-On Universe (HOU) are
projects of the Lawrence Hall
of Science (LHS), University of
California, Berkeley.
GSS is also an activity of the
Museum of Science in Boston,
Massachusetts, which provides
assistance in revising and
disseminating the program.
Global Systems Science (GSS) is an integrated,
interdisciplinary course for schools, grades 9–12. GSS
consists of 10 student books (see back cover), teacher
guides, and Image Analysis software. Each GSS book
deals with a societal issue that requires science for
full understanding. GSS may be used in designing an
integrated interdisciplinary science course or serve as
supplementary materials for existing biology, physics,
chemistry, Earth science, or social studies courses. To
obtain latest revised editions of GSS books through
University of California, Lawrence Hall of Science,
please visit the GSS website:
http://lhs.berkeley.edu/gss/
Hands-On Universe (HOU; http://www.handsonuniverse.org)
is an educational program that enables students to investigate
the Universe while applying tools and concepts from science,
math, and technology. Using the Internet, HOU participants
around the world request observations from observatories,
download images from a large image archive, and analyze
them with user-friendly image processing software.
Sources of Support
NIGEC. Development and publication of the Global Systems Science series was funded by
the U.S. Department of Energy’s (DOE) National Institute for Global Environmental Change
(NIGEC) through the NIGEC Western Regional Center (WESTGEC) at the University of
California, Davis (DOE Cooperative Agreement No. DE-FC03-90ER61010). Noreen Dowling,
Joseph Knox, Linda Ono, and Thomas Suchanek provided assistance to this project on
behalf of NIGEC and WESTGEC.
NSF. The opportunity to involve high school teachers in the development of this project was
made possible by a grant from the Teacher Enhancement Program of the National Science
Foundation (Grant #TPE 9155393). This grant enabled us to invite 125 teachers to test
these materials with their students, then come to Berkeley for three weeks, where they
reported on trial test results, suggested improvements in the printed materials, and
developed new laboratory activities. We are indebted to Larry G. Enochs and Wayne
Sukow, Program Directors of the National Science Foundation, as well as to many teachers
and students whose insights, ideas, and hard work have helped bring the GSS series to
fruition.
NASA. Support from NASA’s Earth Science Enterprise (ESE) has included printing and
distribution of the GSS Books under a Memorandum of Understanding between NASA and
the University of California at Berkeley. Nahid Khazenie provided assistance on behalf of
NASA/ESE. NASA ESE also funded the enhancement of GSS to make it part of the Digital
Library for Earth System Education (http://www.dlese.org/)
Major portions of this book are adaptations of Hands-On Universe high school modules
developed by Jodi Asbell-Clark and Tim Barclay © 1995-2000 by TERC.
Financial support does not constitute an endorsement by DOE, NSF, or NASA of the views
expressed in this book.
2
© 2007 by The Regents of the University of California. All rights reserved. Printed in
the United States of America. This work may not be reproduced by mechanical or
electronic means without written permission from the Lawrence Hall of Science,
except for pages to be used in classroom activities and teacher workshops. For
permission to copy portions of this material for other purposes, please write to:
Global Systems Science, Lawrence Hall of Science, University of California, Berkeley, CA
Global
Systems
Science
A Changing Cosmos
94720-5200 or
e-mail
[email protected].
Based on Hands-On Universe Units by TERC
(Jodi Asbell-Clarke, Tim Barclay)
edited by Alan Gould
HOU Telescope Images by Vivian Hoette, Yerkes Observatory
Contents
1. Cosmic Cataclysms....................................................................... 2
2. Astronomers' Tools........................................................................ 8
3. Cosmic Engines.......................................................................... 22
4. Fathoming Huge Distances ........................................................ 30
5. Color, Temperature, and Age....................................................... 42
6. Dramatic Change in Stars........................................................... 60
7. Planet-Star Systems.................................................................... 72
8. Search for Habitable Planets....................................................... 86
9. Cosmos Begins...and Ends?....................................................... 90
List of Investigations........................................................................ 96
References...................................................................................... 97
Acknowledgments........................................................................... 98
News and updates are available at the GSS website
http://www.lhs.berkeley.edu/GSS/ through the
"Staying Up To Date” section.
Global Systems Science
A Changing Cosmos
1
Chapter 1
1. Cosmic Cataclysms
Asteroid Collision
We normally think of things in space as remote
and not really able to affect things around us much. But
there are some types of events in our changing cosmos
that could really mess things up badly for us. In fossil
records, there are many instances of species going
extinct—apparently unable to cope with some change
in environment. At certain times in Earth's history, not
just one species has died off, but lots of species have
died off, in mass extinctions.
The latest such mass extinction happened 65
million years ago, when the Age of Reptiles ended and
the Age of Mammals began. The question, “What caused
the mass extinction at the end of the dinosaur age?”
made scientists disagree and squabble for quite a while.
The candidates for the cause of the extinction were:
a. The theory of gradual change — mass
extinctions took place over thousands or
maybe millions of years, possibly due to
long term climate change. Fossil evidence
indicates that prior to sixty-five million years
ago the dinosaurs were beginning to decline
and many dinosaur species had already
become extinct.
b. The impact theory — set forth by Geologist
Walter Alvarez from the University of California
at Berkeley. He was studying a thin layer of clay
between rock layers of the Cretaceous Period
(Age of Reptiles) and the Tertiary Period (containing no dinosaurs
fossils). The clay layer contained very large amounts of the rare
element iridium, which is common in meteorites but uncommon
in the Earth’s crust. This suggested a sudden large influx—perhaps
one really huge meteor struck the Earth at about that time. An
underground crater found near Chixulub (pronounced Chi’-shooloob), Mexico, was found to be about 65 million years old. The
clay layer contained tiny pieces of minerals (shocked quartz)
and glassy rocks (tektites), which are found at nuclear test
sites and large meteor impact sites, as well as soot—indicative
of continent-sized forest fires. An asteroid in the 10 kilometer
diameter size range could have caused the event.
2
Global Systems Science
The Chixulub Crater
is buried underground,
so it cannot be directly
photographed. This is a 3-D
graph made with equipment
normally used to search for
oil. It shows gravitational
attraction of underground
structures. Photo courtesy
of Virgil L. Sharpton,
Center for Advanced Space
Studies, Houston, Texas,
USA
A Changing Cosmos Chapter 1: Cosmic Cataclysms
c. The volcanic eruption theory—A huge
series of lava flows in India, named the
Deccan Traps, which covers 10,000 square
kilometers and is in some places more than
2 kilometers thick, is evidence of a period
of volcanic activity that spanned about
half a million years—including the period
of the mass extinction at the end of the
Cretaceous Period. The volcanic eruption
theory is in agreement with paleontologists’
original idea that the extinction of species
was gradual, or at least occurred in several
steps, over hundreds of thousands of
years.
When a 10 km-sized asteroid strikes the
ground, it buries itself in the Earth and coverts its
tremendous energy of motion into heat in a period
of only seconds. It opens a crater that reaches a
diameter of 100 miles and a depth of fifteen miles.
Red hot rock debris streams outward, forming a
plume heading into the sky. The plume can go so
high it sends hot debris into orbit that eventually
rain back all over Earth. On the ground, you would
feel an effect very similar to an oven on broil for
about an hour. As a result of this thermal radiation,
even green vegetation would dry out and begin to
burst into flames spontaneously, causing global forest
fires.
The Deccan Traps are extensive lava flows in India.
Source: © Dr. Keith G. Cox, University of Oxford,
Oxford, England.
Which Theory is Right?
Will Earth be Hit by a Large Asteroid?
It may well be that we will never know for
sure if either a large impact or massive volcanism
caused the death of the dinosaurs.
Eventually, it is likely. But the odds of one
hitting tomorrow, or next week, or in the next
few thousand years are quite low. Of course tons
of smaller bodies (sand grain size) enter Earth’s
atmosphere every day. But the larger the body,
the rarer it is.
The Barringer Meteor Crater near Winslow,
Arizona, is as deep as a 60 story building and more
than a kilometer across. It was created about 30,000
years ago by a rocky object about 30 meters in diameter
traveling at 40,000 miles per hour. The impact had an
explosive energy
equivalent to
over a million
tons of TNT. It
is 1/100 the size
of the crater
in Chixulub,
Mexico.
Source: Yerkes
Observatory.
Chapter 1: Cosmic Cataclysms
Asteroids are not the only menace. Evidence
of comets crashing into planets was dramatically
seen in 1994 when the large comet ShoemakerLevy 9 fragmented and created huge explosions
when it struck the planet Jupiter at more than
20 different sites. We’ll find out more about this
event at the end of Chapter 3.
It would behoove us to seek advance warning
of such an approaching body. An asteroid could
come in quickly, but it may be technically possible
to deflect an asteroid from an Earth impact course
if there is enough advance warning.
Hands-On Universe
3
The Search for Near Earth Asteroids (NEOs)
Asteroids must be discovered and their orbits tracked. At this point in time
North American Aerospace Defense Command (NORAD) has a limited number
of people monitoring the skies for
asteroids. There is also a project called
Space Guard which is an international
network of telescopes and people
working together to discover and track
asteroids, with the idea of providing
lots of advance warning if an asteroid
is found to be on a collision course
with Earth, so that an effort could
be made to divert it. Currently, NASA
carries out the “Spaceguard Survey”
to find NEOs greater than 140 meters
in diameter, and this program was
budgeted at $4.1 million per year for
FY 2006 through FY 2012.
In chapter 7, we'll learn more
about asteroids, as well as other
bodies in the solar system.
Supernova
It is in the darkness before dawn on July 4,
1054 A.D. Chinese astronomers are greatly excited
by the appearance of a “guest star”—a new star in
the sky, never seen before. As the Earth spins, half
a day later on July 5, it is predawn in Navajo lands
of what is now northern Arizona. The Anasazi, the
“ancient ones” of this region, have spotted that
same new star and are equally excited. The legacy
of that “guest star” continues to this day.
Each culture records the event in its own
way. Anasazi etch a rock drawing—a petroglyph—
on a rock overhang, depicting a circle next to
a crescent Moon as it appeared to them that
morning. Petroglyphs in Navaho Canyon and White
Mesa, Arizona, as well as in the Chaco Canyon
National Park of New Mexico are lasting records
left by those Anasazi skywatchers. Mimbres Indian
ceramic art from New Mexico also apparently
depicted the supernova.
Japanese and Chinese astronomers record
that the “guest star” shone at least as bright as
4
Global Systems Science
the maximum brightness of planet Venus. Some
said it was about four times brighter than Venus,
which was nearly a hundred times brighter than
the brightest stars in the sky (aside from the Sun).
It was visible in broad daylight for 23 days, and in
the night sky it shone for 653 days to the naked
eye. Its location was in a part of the sky that we
now call the constellation Taurus.
Six hundred and seventy seven years later,
in 1731, a nebulous cloud was spotted in the
constellation Taurus by John Bevis through his
telescope. Charles Messier observed the nebula
again through a telescope on August 28, 1758, and
first thought it was a comet. He recorded it in a
catalog he was compiling to help him distinguish
comets which he eagerly sought to discover from
“comet impostors” which stayed always in the
same places in the sky. In 1844, the 3rd Earl of
Rosse, at Birr Castle in Ireland, examined and
made a detailed drawing of the nebula using his
giant 6 foot diameter, 56 foot long telescope. The
drawing of the nebula resembled a "Crab" which
A Changing Cosmos Chapter 1: Cosmic Cataclysms
has been the name of the nebula ever since.
The Crab Nebula, or M1 in Charles Messier’s
catalog of “comet impostors,” is in the exact same
spot as the recorded position of the “guest star” of
1054. But it wasn’t until 1928 that Edwin Hubble
measured the rate of expansion of the Crab
nebula which led him to conclude that it had been
expanding for about 900 years. The connection
with the “guest star” of 1054 was clear. The
“guest star” was actually a supernova—exploding
star— and the Crab nebula, the supernova
remnant, consists of the material ejected in the
supernova explosion which has been spread over
a volume approximately 10 light years in diameter
and is still expanding at the very high velocity of
about 1,800 km/sec.
A supernova is an unimaginably powerful
explosive event. It occurs when a very large star,
over eight times the Sun's mass, has burned most
of its nuclear fuel. When such a star's central fires
go out, its core collapses releasing a huge amount
of gravitational energy. A blast wave ejects the
star's outer layers into space. The Crab nebula
supernova remnant is incredibly bright, even
though it looks quite dim at our distance from
it—6,300 light-years. If we were to observe it from
much closer, we would find that it puts out 1000
times as much visible light as our Sun. In 1948,
the Crab nebula was found to be an even stronger
source of radio wave radiation, and in 1964,
observations with a high-altitude rocket showed
that the energy emitted in X-rays by the Crab
nebula is about 100 times more than that emitted
in visual light. Taking into account all energies
of radiation, the Crab nebula is putting out over
100,000 times more energy than our Sun.
Another indication of the violence of a
supernova explosion is that in some cases all that
is left is a neutron star, which is an extremely
dense object. It is denser than an atomic nucleus,
concentrating more than the entire mass of the
Sun in a volume only 30 kilometers (20 miles)
across. On November 9, 1968, a pulsating radio
source was discovered in the Crab nebula by
astronomers using a 300-meter radio telescope in
Arecibo, Puerto Rico. It pulses about 30 times per
second! It’s that neutron star (pulsar) rotating 30
times per second and putting out 100,000 times
more energy than our Sun.
Chapter 1: Cosmic Cataclysms
Image of M1, the Crab Nebula, the aftermath of a
supernova explosion. From the Grasslands Observatory
near Tucson, Arizona.
If the Crab nebula pulsar is pumping out that
much energy now, over 900 years after the supernova
explosion, how much energy did the supernova release
at its peak? At its brightest, a supernova can put out
the energy of 10 billion suns!
Could Our Sun Become a Supernova?
Not a chance! Our Sun is not large enough to
become a supernova of any sort. Besides, it will
take another 5 billion years before our Sun's supply
of hydrogen is depleted. At that time it will begin its
dying process and eventually become a white dwarf
with a surrounding shell of material much like the Ring
Nebula (M57) in the constellation of Lyra!
Can a Nearby Supernova Affect Us on Earth?
Yes, if it’s near enough, within several dozen
light-years. The intense influx of radiation could kill all
life on Earth, sterilizing the planet. However, the odds
of this happening are extremely small, especially in
the short life-span of us humans. The most important
effects of more distant supernovae are extreme
excitement among astronomers who study supernovae
to understand cosmology—the history and fate of the
Universe.
We will be learning a great deal more about
supernova in chapter 3.
Hands-On Universe
5
The Sun Engulfs the Earth
If you have read the book or seen the
movie “The Time Machine” by H.G. Wells,
you may know of the eerie landscape that
the Time Traveller (Alexander Hartdegen)
saw near the end of his time travels. The
passage here is from Chapter 11 of H.G.
Wells’s The Time Machine as serialized in
the New Review, cut from the book, but
later published as a short story, “The Grey
Man.”
“I have already told you of the sickness and
confusion that comes with time travelling.
...when I brought myself to look at the dials again
I was amazed to find where I had arrived. One
dial records days, another thousands of days,
another millions of days, and another thousands
of millions. ...the thousands hand was sweeping
round as fast as the seconds hand of a watch—
into futurity.
"...I stopped. ...The time was midday, the orange
sun, shorn of its effulgence, brooding near the
meridian in a sky of drabby grey.
"...I rose to my feet, and stared at this grotesque
monster. I can only describe it by comparing
it to a centipede. It stood about three feet high,
and had a long segmented body, perhaps thirty
feet long, with curiously overlapping greenishblack plates. It seemed to crawl upon a multitude of feet,
looping its body as it advanced. Its blunt round head
with a polygonal arrangement of black eye spots, carried
two flexible, writhing, horn-like antennae. It was coming
along, I should judge, at a pace of about eight or ten miles
an hour, and it left me little time for thinking.
"...When I gained the machine the monster was scarce fifty
yards away. It was certainly not a vertebrated animal.
"...But I did not care for a nearer view.
"...As I drove on, a peculiar change crept over the
appearance of things. The unwonted greyness grew
lighter; then—though I was travelling with prodigious
velocity—the blinking succession of day and night, which
was usually indicative of a slower pace, returned, and
grew more and more marked. This puzzled me very much
at first. The alternations of night and day grew slower and
slower, and so did the passage of the sun across the sky,
until they seemed to stretch through centuries.
6
Global Systems Science
"At last a steady twilight brooded over the earth, a twilight
only broken now and then when a comet glared across the
darkling sky. The band of light that had indicated the sun
had long since disappeared; for the sun had ceased to set—it
simply rose and fell in the west, and grew ever broader and
more red. All trace of the moon had vanished. The circling
of the stars, growing slower and slower, had given place to
creeping points of light.
"At last, some time before I stopped, the sun, red and very
large, halted motionless upon the horizon, a vast dome
glowing with a dull heat, and now and then suffering a
momentary extinction. At one time it had for a little while
glowed more brilliantly again, but it speedily reverted to its
sullen red-heat. I perceived by this slowing down of its rising
and setting that the work of the tidal drag was done. The earth
had come to rest with one face to the sun, even as in our own
time the moon faces the earth.”
Wells described how our Sun might appear not
after thousands of years, or even millions of years,
but after a few billion years. Current theories
for progression of the Sun in its lifetime predict
that when the nuclear furnace at its core runs
out of fuel, it will begin a stage of expansion and
surface cooling that will make it huge and its
A Changing Cosmos Chapter 1: Cosmic Cataclysms
surface red—a red giant star. The surface could swell up big enough
to engulf the current orbit of Earth. Even if the gravitational pull of
the Sun will have weakened by then from loss of mass, so that Earth
migrates to a larger orbit, Earth still will get hot enough for the oceans
to evaporate to space, and our biosphere will be destroyed.
The good news is the enormous time span before this particular fate
occurs. Humans may not even be recognizable as humans by then, in
terms of species adaptations.
Understanding, Helplessness, and
Empowerment
Understanding the three ways that life on Earth is threatened
can invoke various reactions. In the case of the threat of the Sun
in its red giant stage, we are pretty much helpless for now, but not
too many people are worrying a whole lot in any practical terms
about what will be happening in 5 billion years. In the case of a
nearby supernova explosion, we are also pretty much helpless, since
protecting the Earth from a huge influx of planet-wide radiation is a
bit much to contemplate in practical terms. However, we can learn
about what the probabilities are for such a scenario, and for the
time being, the likelihood of that kind of disaster is exceedingly low,
almost vanishingly so.
The likelihood of Earth being hit by a large
body, such as an asteroid, is much, much higher
than our being saturated by radiation from a
supernova. It is nearly inevitable—only a matter
of time, though we do not know if it will be today,
tomorrow, or in many millions of years. But in this
scenario, we certainly are not helpless. If we are
able to detect a body that is hurtling towards
Earth with enough advance warning, there are a
number of strategies proposed to avert disaster.
It's tempting to try blowing the thing up with
nuclear weapons, a typical video game-style
mentality, that unfortunately, at best, would
create a number of smaller bodies that would still
continue on their trajectories and impact Earth
with devastating effect. Other ideas are mostly
different ways of nudging the asteroid to deflect
it into a path that will not strike Earth.
This book is devoted to better understanding
various astronomical ideas, many of which
relate directly or indirectly with the challenge
of early detection of "near Earth asteroids," as
well as other intriguing aspects of our "changing
cosmos."
Chapter 1: Cosmic Cataclysms
Find late breaking news and information about
Cosmic Cataclysms at the Staying Up To Date
pages for A Changing Cosmos:
http://lhs.berkeley.edu/gss/uptodate/10acc
Hands-On Universe
7
Chapter 2
2. Astronomers'
Tools
Astronomers are very limited in ability to
actually visit and explore their objects of interest.
Humans have personally visited only one other
body in the cosmos other than Earth: the Moon.
We have sent spacecraft to most of the planets
in our own solar system and received treasure
troves of data and information about those
places, including their moons, some asteroids,
and comets. But when it comes down to more
distant objects—and most of the Universe—we
basically have only the light we receive from
those objects and our imagination and ingenuity
to analyze and interpret that light. Fortunately,
we are not restricted to visible light only. We
have detectors for all types of electromagnetic
radiation: infrared light, ultraviolet light, x-rays,
gamma rays, and radio waves.
Mapping Space and Time
One of the simplest tools of astronomy is
something to help find things in the sky: a star
map. There are a wide variety of these, ranging
from those ideal for beginning stargazers to
highly detailed maps and computer programs for
advanced amateur or professional astronomers.
One kind of star map, the planisphere, is
adjustable to show what the sky looks like any
time of night and any time of year.
Caution—it’s common and easy to confuse
these terms:
Rotate—think of something spinning on its
own axis.
Revolve—think of something orbiting (going
around) something else.
These terms are verbs, but similarly, people
often confuse the corresponding nouns:
rotation and revolution.
8
Global Systems Science
Kyle Cudworth controlling the Yerkes Observatory 40"
telescope—the largest refractor telescope in the world.
Motion Defines Time
Time often seems so subjective—while
listening to a boring lecture, it seems like time
drags on endlessly. When spending an enjoyable or
exciting evening with friends, time flies. When we
need to actually measure time, the sky is a great
reference—it seems to move “like clockwork” with
the different ways that the Earth is moving:
Rotation—Earth spinning on its axis makes the
sky seem to move from east to west.
Revolution—Earth orbiting around the Sun
makes the sky seem to shift each day so that
the part of the sky is visible to us without
the Sun blocking it in daytime
Precession—the wobbling of the Earth’s
rotation axis, so the direction that Earth's
axis points in the sky slowly drifts over
thousands of years— 26,000 years for one
complete wobble. Earth’s axis currently
points to within a degree of the star Polaris
(North Star). In about 10,000 years it will
point closer to the very bright star Vega, in
the constellation Lyra.
A Changing Cosmos Chapter 2: Astronomers’ Tools
In the investigation on the next page, Star Maps, you can construct
your own star map and use it not only to find things in the sky, but to
show how the sky changes with time.
Coordinates For Earth and Sky
To roughly locate things in the sky, we can identify groups of stars,
called constellations. But to specify exactly where an object is in the
sky, we use celestial coordinates. Celestial coordinates are to the sky,
as geographical coordinates (latitude and longitude) are to the Earth.
Review of Geographical Coordinates
The Earth’s spin determines special locations on Earth. The spin
axis goes through the North and South Poles, and midway between
them, is the equator.
Latitude—To indicate how far north or south we are on Earth, we use
degrees (°) of latitude. The equator is neither north nor south and is
0° latitude. Latitude lines range between 90°S, which is the latitude
of the South pole, and 90°North, the latitude of the North Pole.
Longitude—To indicate how far east or west we are, we use longitude in
degrees. Longitude lines are perpendicular to the latitude lines and
go from the North Pole to the South Pole. As Earth spins, longitude
lines swing under the Sun “like clock-work.” A zero longitude line
was arbitrarily chosen to go through Greenwich, England. Longitude
lines are numbered to 180 degrees east of Greenwich and 180 degrees
west of Greenwich.
For telling more precise locations, each degree of latitude or
longitude is subdivided into 60 minutes, often called minutes of arc
(measure of angle, not time). Each minute is further divided into 60
seconds of arc. An apostrophe (') is the symbol for minutes of arc,
and a quote mark (") is the symbol for seconds of arc. Example: San
Francisco, California is 122° 26' west of Greenwich and 37°46' north
of the equator. These geographical coordinates are abbreviated
37°46' N 122°26' W.
Celestial Coordinates
Long ago, people believed that there was a giant sphere
to which the stars were attached—the celestial sphere. Imagine
extending the Earth’s axis infinitely into space, north and south.
It would pierce that sphere in two places: the celestial north pole
and the celestial south pole. If Earth’s equator were extended
infinitely outward to the celestial sphere, it would become the
celestial equator.
Even though we know there is no physical sphere
out there holding up the stars, we still find it convenient
to think of an imaginary celestial sphere to specifying
locations of things in the sky. The “celestial latitude
lines” are called declination. As with latitude on Earth,
declination in the sky increases from 0°at the celestial
equator to 90° at the celestial North or South pole.
As with latitude on Earth, each degree has 60 minute
divisions (') and each minute is further divided into 60
seconds (").
Chapter 2: Astronomers' Tools
Right Ascension is the name of the celestial
coordinate that corresponds to longitude on Earth. Unlike
longitude, which is measured in degrees and minutes,
right ascension is measured in hours and minutes. There
are 24 hours of right ascension corresponding to the full
sweep of 360 degrees around the celestial equator. Simple
division will tell you that each hour of right ascension
must be equivalent to 15 degrees of arc. As you might
expect by now, each hour has 60 minute divisions (') and
each minute is further divided into 60 seconds (").
Hands-On Universe
9
Investigation
Using Star Maps
Standing here on Earth which is rotating, we
see everything in the sky wheeling around us once
every 24 hours. Each object in the sky appears to
move 15° westward every hour as Earth rotates.
(15°/hr = 360°/24 hrs)
Make “Uncle Al's HOU Sky
Wheel” to demonstrate this motion.
[Print the "Coordinate Sky Wheel" and "Sky Wheel
Holder" from http://lhs.berkeley.edu/starclock/
skywheel.html.] Follow the instructions on the
printed starwheel sheet, and when it is cut out and
assembled, set the Sky Wheel for near the end of
the school year, June 1, at shortly after sunset, say
9 p.m.
Notice the Big Dipper is high in the sky and the
tip of the handle is near Right Ascension 14 hours,
which in turn points close to the word “Southern” in
“Southern Horizon” on the Star Wheel Holder. The
times on the Star Wheel Holder are always standard
time, so you may need to take that into account if
your clock is set to daylight savings time.
Rotate the Star Wheel FORWARD 2 hours
(to 11 p.m. standard time on June 1).
2.1 What Right Ascension line now points
to the word “Southern” in Southern
Horizon?
2.2 What constellation just rose, almost
due east?
2.3 What constellation is setting in the
northwest?
2.4 What constellation is closest to the
zenith (highest place in the sky; center
of the map)?
Rotate the Star Wheel FORWARD by another 2
hours (to 1 am standard time on June 1).
2.5 What Right Ascension line now points to
the “Southern” in Southern Horizon?
2.6 What constellation is closest to the
zenith?
2.7 What constellation is rising, almost due
east?
2.8 What constellation is setting in the
west?
Rotate the Star Wheel FORWARD another 2
hours (to 3 am standard time, June 1).
2.9 What Right Ascension line now points to
10
Global Systems Science
the "S" in Southern Horizon?
2.10 What constellation is closest to the
zenith?
2.11 What constellation is rising in the
northeast?
2.12 What constellation is setting in the
northwest?
Notice that there is one star in the sky which
does not seem to change its position ever. It's at
the tip of the handle of the Little Dipper, (Ursa
Minor) and is called Polaris, or the North Star.
Now some more questions to test your Star
Wheel driving skill:
2.13 What constellation is near the zenith on
New Year's Eve at 11 p.m.?
2.14 In what month is the Big Dipper (Ursa
Major) highest in the sky at midnight?
2.15 About what time is Leo setting (in the
northwest) on the summer solstice
(about June 21)?
A Changing Cosmos Chapter 2: Astronomers’ Tools
Earth Rotating on Its Axis and Revolving Around the Sun
Rotating the Star Wheel can represent both rotation (spinning)
of Earth and revolution (orbiting) of Earth around the Sun. To imagine
Earth’s rotation, keep your attention focused on one date and watch
the hours go by that date as you turn the wheel. To imagine Earth
revolving around the Sun, keep your attention focused on a particular
hour of the night and imagine that you are coming out each night
to see that sky at that particular hour of night. You can then watch
the days and months go by from the perspective of that particular
time of night. The Sun appears to creep Eastward in the sky each
day by approximately one degree, or about 30 degrees (2 hours right
ascension) per month.
2.16 How many degrees does the sky shift in one month?
The Trifid Nebula, the 20th entry
in Charles Messier’s catalog,
commonly referred to as M20.
Photo courtesy Richard Bennion,
Ewell Observatory, Belmont, CA.
http://www.ewellobservatory.com
Find Messier Objects
Charles Messier, a French comet hunter,
created a catalog of interesting sky objects that
might look a little like comets, but are not. They
are actually a variety of objects including star
clusters, galaxies, and nebulae (clouds of gas).
If you find a table that has the coordinates of
the Messier objects, you can mark them on your
own star map. For example, the Owl Nebula
is a Planetary Nebula 1630LY from us, whose
coordinates are RA 11h14.8m; DEC +55°01'
2.17 In which constellation is the Owl Nebula?
You can download the HOU Messier
Object Excel spreadsheets at http://www.
handsonuniverse.org/activities/uncleal. You
might choose to mark the BRIGHTEST Messier
objects on your Coordinate Star Wheel, or perhaps
the CLOSEST Messier objects.
2.18 Get image(s) of Messier object(s). In
book(s) or searching the worldwide web, find
Messier objects of the following types: nebulae
(gas clouds), globular star clusters, open star
clusters, galaxies. Print one for wall decoration
or save for a computer screen display.
Moving Planets, Asteroids, and Comets
Most things we see in the solar system—
planets, asteroids, and comets—generally move
across the sky through the night along with the
“fixed” stars. However, most of them very slowly
drift relative to stars from west to east as they
orbit the Sun. The movements of the planets range
from Mercury’s fast orbit motion (as much as 2
degrees per day eastward in the sky) to Pluto’s
slow orbit motion (about 1.5 degree per year
eastward against the background stars).
August 2007: Google announced the
roll-out of its Google Sky software
for exploring celestial objects.
best if you make those marks in pencil so you can
erase and update their positions as needed.
Good ways to find planets include:
•
Get a “planetarium program” that computes celestial
coordinates of planets. See
http://astro.nineplanets.org/astrosoftware.html
• Que Tal in the Current Sky -- http://currentsky.com
• Magazines: Sky & Telescope or Astronomy magazine
• Observers Handbook (Royal Astronomical Society of Canada)
• Guy Ottwell's Astronomical Calendar (Dept. of Physics, Furman
University, Greenville, S.C.)
You can also get an ephemeris of the
Planet's Coordinates which is a table of celestial
coordinates pinpointing the object's location at
specific time intervals as it moves in the sky. You
can find an Ephemeris generator at the NASA Jet
Propulsion Lab (JPL) website, http://ssd.jpl.nasa.
gov/horizons.cgi.
You can mark the positions of planets on your
Coordinate Star Wheel, but since they change, it’s
Chapter 2: Astronomers' Tools
Hands-On Universe
11
Telescopes
Since astronomical objects are so far
away, detecting light from those objects is
one of the most important ways we have to
learn anything at all about them. For the most
part, we can’t physically go out there and get
samples of material or poke around.
The first telescopes were built in the
time of Galileo, in 1608, by Jan Lippershey,
an eyeglass maker in an area of Europe that is
now Holland. Two key functions of a telescope
are (1) to gather light from dim objects and
(2) to make things look bigger. These are
two powers of a telescope: light-gathering
power to make dim objects look brighter, and
magnifying power to make distant objects
look bigger. Generally speaking there are
two types of telescopes: one type, called a
refractor telescope, depends on a large lens
of curved glass to gather light and focus the
light towards a smaller lens (or system of
lenses) called the eyepiece. The other type
of telescope, called a reflector, depends on a
large curved mirror to gather light and focus it
towards the eyepiece. Today there are many
types of telescopes, but most of the largest
ones are reflectors—they depend on mirrors
for light-gathering.
Galileo Galilei, in 1609, was
the first person to do serious
observations of sky objects with a
telescope.
Galileo’s telescope was very
simple: two lenses, one at each
end of a tube. It was one of the
first refractor telescopes.
Telescope Timeline
1608 - Invention of the refracting telescope
1609 - Galileo Galilei builds his first refracting telescope
1668 - Isaac Newton constructs the first reflecting telescope
1672 - Laurent Cassegrain designs the Cassegrain reflecting
telescope
1757 - John Dollond invents the achromatic lens
1789 - William Herschel builds a 49-inch (1.2-meter) optical reflecting
telescope, located in Slough, England
1840 - Invention of astronomical photography — J.W. Draper
photographs the Moon
1845 - Lord Rosse finishes the Birr Castle 72-inch optical reflecting
telescope, located in Parsonstown, Ireland
1859 - Invention of spectroscopy (Kirchoff and Bunsen)
1872 - Henry Draper invents astronomical spectral photography and
photographs the spectrum of Vega
1897 - Alvan Clark finishes the Yerkes 40-inch optical refracting
telescope, located in Williams Bay, Wisconsin
1917 - Mount Wilson 100-inch optical reflecting telescope begins
operation, located in Mount Wilson, California
1934 - Bernhard Schmidt finishes the first 14-inch Schmidt optical
reflecting telescope
Sir Isaac Newton and a replica
of his reflector telescope
1941 - Dmitri Maksutov invents the Maksutov telescope
1949 - Palomar 200-inch optical reflecting telescope (Hale telescope)
begins regular operation, located in Palomar, California
1979 - NASA Infrared Telescope Facility[1] 120-inch infrared reflecting
telescope begins operation, located at Mauna Kea, Hawaii
1993 - Keck 10-meter optical/infrared reflecting telescope begins
operation, located at Mauna Kea, Hawaii
1996 - Keck 2 10-meter optical/infrared reflecting telescope begins
operation, located at Mauna Kea, Hawaii
2005 - First light at SALT, the largest optical telescope in the southern
hemisphere, with a primary mirror diameter of 11 meters.
12
Global Systems Science
A Changing Cosmos Chapter 2: Astronomers’ Tools
Cameras and Detectors
For about 400 years, people have been putting their eyes
up close to the eyepieces of telescopes and enjoying magnificent
views of heavenly objects. In 1727, Johann Heinrich Schulze
discovered that silver nitrate darkened upon exposure to light—
laying the groundwork for the invention of photography. In 1840,
John William Draper started the discipline of astrophotography
and made the first photograph of the Moon. Chemical reactions
on photographic film are much more sensitive than the human
eye, largely because many many photons can be collected from
very faint objects in a photographic exposure of many minutes.
Astrophotography can capture faint details that the eye cannot
detect.
Electronic photography was ushered in after the CCD
(charge coupled device) was invented in 1969 by Willard
Boyle and George E. Smith at AT&T Bell Labs. CCDs
have the ability to transfer electric charge along
the surface of a semiconductor and can
receive charge by converting light energy to
electrical energy through the photoelectric
effect. In this way electronic images are
created.
The Keck
Observatory
has two telescopes,
each with a 10 meter
diameter primary mirror to
collect light.
The mirrors
are each
made of 36
hexagonal
segments, each
1.8 meters
wide. Courtesy
W. M. Keck
Observatory.
Computers and Software
With the advent of digital images of sky objects
captured by CCD cameras on telescopes, the opportunity to
use computers and image processing software is irresistible
and in modern astronomy, indispensable.
CCD chip being prepared for the NASA
Kepler mission photometer.
Chapter 2: Astronomers' Tools
To study astronomical objects, we really have little
more than the light from those objects to reveal their
qualities and their essence. The light is made of up tiny
packets we call photons, and in a CCD, each photon that
strikes the CCD is converted into an electrical pulse that
is stored and recorded in computer memory. The CCD is
made up of rows and columns of tiny sensors that capture
each tiny element of the picture. These picture elements
are called pixels.
Hands-On Universe
13
Investigation
CCD Image Color Coding
The images from the HOU telescopes are generated using a
CCD camera. This kind of camera uses an electronic chip rather
than the photosensitive chemical films used by regular cameras.
The electronic chip is divided into many small areas that collect and
record light. Each pixel on the screen is then given a number based
on the amount of light from that particular area of the CCD chip.
The more light at a pixel, the larger the number. The computer
assigns a shade of gray or a color (when using a false color palette)
at each pixel to produce the image you view on the screen.
Below is a grid that simulates a CCD image with each pixel
assigned a number between 0 and 9 to represent the amount of light
at that pixel. Using only four different colored markers, develop a
color coding scale for the ten different brightness values, 0 to 9.
Indicate your color code in the Key at the bottom of the screen.
Using your color scale, color each pixel with its proper color.
Tape your sheet on the wall with everyone else’s and compare
the result of using different color scales to represent the same
data.
Color Key
Brightness Key
<--- Make a copy of this grid
1. What is different and what is the
same as you look at the collection
of grids?
2. How does this activity relate to
Min/Max settings in the image
processing program?
3. Did anyone simulate a log scale
in his or her color coding scale? If
so, what difference did it make?
If not, what difference do you
believe it would have made?
4. Each coding scale can be thought
of as a different color palette.
Compare the grid images in terms
of the pros and cons of using
different palettes.
14
Global Systems Science
A Changing Cosmos Chapter 2: Astronomers’ Tools
Investigation
Browsing the Universe
There is a myriad variety of celestial objects.
Astronomers delight in describing, classifying, and naming
them, but also grapple with trying to explain why they look
the way they do.
Materials
• HOU Image Processing (IP 2.0) software*
• Images: browser1 through browser7; galaxy1 through galaxy8
• Pencil and paper for worksheet(s)
* There are differences between old HOU IP and HOU IP 2.0.
For details see http://www.handsonuniverse.org/ip/
Part I: Browse
2.19. Using each of the files, browser1 through browser7, use and
familiarize yourself with the following HOU IP functions:
See diagram of “HOU Image
Processing Screen at the
bottom of this page.
• Open the image (file folder icon or “Open” in File menu).
• Use Zoom Factor (in the View menu) or Zoom icon (in Tools
Palette on left of screen) to enlarge the image.
• Use Color Palette to change colors.
• Drag the sliders.
• Adjust Min/Max settings to change contrast,
brightness and improve the appearance of the image.
• Enter new values in the boxes
at either side.
• Try the Log scaling function (View
menu).
a. Get or create worksheets on which to write
a detailed description of the appearance of
each object. See sample worksheets on next
page.
b. For each object, make a hypothesis about
what type it is and why it looks the way it
does. The following are a few questions to
think about. They may not all apply to each
object, and you may choose other questions
to explore.
Min/Max values can be changed
two ways:
Is it solid or gaseous?
Why is it dark or bright in certain areas?
Are we looking at it from a side view or
top down view?
c. Pick your favorite of the images, select the
best color palette for the image, adjust with
the Min and Max tool, and set Log Scaling. Then
record your settings for the best display of this
image. Optional: Print out or save your image
(both options are under the File menu). If your
printer is a black and white one, you probably
HOU Image Processing Screen
should use the grey or igrey palettes.
Zoom
Open
Sliders for Min-Max
Min-Max
Log Indicator
Color Palette
Image displayed here.
This one is “browser3.fts”
Chapter 2: Astronomers' Tools
Hands-On Universe
15
2. My h
Date: ______________
ypothe
it looks sis on what ty
p
the wa
y it doe e each objec
browse
t might
s.
r1:
be
Name: ____________________________
Worksheet: Browser’s Guide to the Universe
1. Detailed description of the appearance of each object.
and wh
y
browse
r2:
browser1:
browse
r3:
s
t
e
e
h
s
k
le Wor
browser2:
browser3:
browser4:
browse
r4:
Samp
browse
r5:
browse
r6:
browser5:
browse
r7:
browser6:
3. Sett
browser7:
ings fo
r my fa
vorite
image:
Image
file nam
e: ____
______
Min/Ma
_____
x: ____
Color p
______
alette:
_____
______
Log sca
______
ling:
____
yes
no
Part II: Galaxy Features
If you are fortunate enough to view the sky
from a place far from city lights—the mountains,
desert, or a remote area—you may see the largest
and most beautiful sky object visible without a
telescope: a large cloud-like band where there
are many more stars than anywhere else in the
sky. It is called the Milky Way, and astronomers
have studied it, concluding that we live in a
galaxy—a huge collection of billions of stars—that
we call the Milky Way Galaxy. If we could go
outside our galaxy, , it would look like this:
In the 20th century, astronomers discovered
other galaxies than our own, some larger than
our Milky Way Galaxy, many smaller. There are
different types of galaxies. Our own looks like a
spiral galaxy. Spiral galaxies have a lot of dust
and gas with stars forming in them. The famous
Orion Nebula is a star-forming region in our
own galaxy. Galaxies NGC 4636 and NGC 4697
Side View
Top View
16
Global Systems Science
These two images are really not the Milky Way—
noone could have taken pictures like that of our galaxy
because we live inside it. The right image is galaxy
NGC 4565 and the left one is galaxy NGC 6946. Both
photos courtesy Richard Bennion, Ewell Observatory,
Belmont, CA. http://www.ewellobservatory.com
A Changing Cosmos Chapter 2: Astronomers’ Tools
in the “Galaxy Atlas” on the next page are not like spirals. They are
simply a lot of stars clumped into the same region of space with no
measurable interstellar dust or gas and no new stars forming now.
They look like ellipses, so astronomers call them elliptical galaxies.
Finally, there are peculiar galaxies. They are not spiral or elliptical.
Sometimes galaxies crash into each other. The two peculiar galaxies
in this unit, NGC 2146 and NGC 3034, are interesting because they
have an enormous amount of dust and gas, so many stars are being
born in them right now.
2.20. Describe and categorize eight galaxies. Get or create a
worksheet like the sample on the page after the Galaxy Atlas. With
your computer, open images galaxy1, galaxy2, etc. one at a time.
[All images came from the Leuschner Observatory which is operated
by the Astronomy Department of the University of California at
Berkeley.]. On your worksheet, draw a quick sketch of the galaxy
and compare it to the ones in the Galaxy Atlas. Decide whether it is
a spiral galaxy, an elliptical galaxy, or a peculiar galaxy and record
that on the worksheet. Then identify different features—see if any
of the ones described below are present. Change the Min, Max, and
Log settings to better bring out its features. Sometimes selecting Log
and moving the ‘Min’ up a little is best with galaxy images. Changing
color palettes is often very helpful, too.
1. Galaxy nucleus: Almost all galaxies have a nucleus. It
is the bright central part of the galaxy. Galaxy nuclei
are made of millions of stars and tons of dust and gas (if
available). There is reason to believe there might even
be enormous black holes in the center of galaxy nuclei.
2. Foreground Stars: You know what stars look like. They
are the bright points of light in your image. Foreground
stars are ones inside our own galaxy that lie between
us and other galaxies. They are not part of the galaxy
in the image. We have so many stars in our Milky Way
galaxy that all of the images in our collection include
foreground stars.
3. Spiral Arms: These are the features that give spiral
galaxies their name. Only spiral galaxies have them. They
are spiral shaped regions of dust, gas, and stars where
star formation is occurring.
4. Bar: An interesting feature in many spiral galaxies is a bar
running through the middle of the galaxy nucleus. While
there are many theories about why this feature forms,
astronomers are not completely sure why they do. There
are many things in astronomy that are not known.
5. Ring: Similar to the bar, except that this looks like a ring around
the galaxy nucleus in some spiral galaxies. Like galaxy bars,
astronomers are not 100% sure why the rings form or why they
form in some galaxies and not in others.
6. H II Regions (pronounced “H 2 Regions”): Areas of star
formation. Young, hot stars heat the dust and gas around them,
causing the dust and gas to radiate light. These appear as
faint balls of light. Elliptical galaxies do not have H II regions
because there is little dust and gas in these galaxies. HII
Regions are made up of ionized hydrogen, the nuclei without
its electron.
7. Dust Lanes: Dark bands of dust that block the light from a
galaxy. If you look closely at the two peculiar galaxies, you
will see that both have dust lanes.
8. Companion Galaxies: A galaxy that orbits around another
galaxy the way the Earth orbits the Sun. These galaxies can
interact with their parent galaxy and change the parent galaxy’s
appearance.
Galaxy Nucleus
HII Regions
Spiral
Arm
Bar
Chapter 2: Astronomers' Tools
Hands-On Universe
17
GALAXY ATLAS
Spiral
Galaxies:
NGC 4321
(M100)
N.A. Sharp/
NOAO/
AURA/NSF
NGC 3351
(M95)
NOAO/
AURA/NSF
NGC 2841
NGC 5194
(M51)
T.A. Rector and
Monica Ramirez/
NOAO/AURA/
NSF
Elliptical
Galaxies:
NGC 4636
Courtesy
Digital Sky
Survey
M 82
Peculiar
Galaxies:
NGC 2146
NOAO/
AURA/NSF
18
NGC 4697
Daniel
Verschatse Observatorio
Antilhue
Global Systems Science
Mark
Westmoquette
(University
College London),
Jay Gallagher
(University
of WisconsinMadison), Linda
Smith (University
College London),
WIYN//NSF,
NASA/ESA
A Changing Cosmos Chapter 2: Astronomers’ Tools
ets
Galaxy
Date: ______________
Name: __________________
5: Disp
Sample
Worksh
e
Answer Sheet
lay: M
in: ___
Name (s
Max: _
ee Gala
__ LogGalaxy Features Unit
xy Atla
s): ___
Feature
______
s used
Rough Min: ___ Max: ___ Log ______Galaxy 1: Display:
Sketch
to iden
_____
:
tify gala
______
______
xy: ___
______
______Name (see Galaxy Atlas): ____________________
______
_____
Galaxy
______
Type:_
______ Features used to identify galaxy: ______________
______
_____
______
Spiral A
______
rms B
______ _________________________________________
ar _____
Dust La
Ring
ne H
Galaxy Type:______________________________
II Regio
ns
Compa
nion G
Spiral Arms Bar Ring
alaxy
Foregro
Dust Lane
HII Regions
und Sta
rs
Companion Galaxy Foreground Stars
Galaxy
6: Disp
lay: M
in: ___
Name (s
Max: _
ee Gala
Galaxy 2: Display: Min: ___ Max: ___ Log __ Log
xy Atla
s): ___
Feature
______
s used
ugh SGalaxy
NameRo(see
______
to iden
ketch:Atlas): ____________________
_____
tify gala
______
______
xy: ___
Features used to identify galaxy: ______________
______
______
______
_____
Galaxy
______
Type:_
______
______
_____ _________________________________________
______
Spiral A
______
rms B
______
Galaxy Type:______________________________
ar _____
Dust La
Ring
ne H
Spiral Arms Bar Ring
II Regio
ns
Compa
nion G
alaxy
Dust Lane
HII Regions
Foregro
und Sta
Companion Galaxy Foreground Stars
rs
Galaxy
7: Disp
lay: M
in
: ___ M
Name (s
ax: ___
ee Gala
Galaxy 3: Display: Min: ___ Max: ___ Log xy Atla
Log s): ___
Feature
______
s used
Rough
______
to iden
NameSk(see
Atlas): ____________________
etchGalaxy
_____
:
tify gala
______
______
xy: ___
______
______
Features
used
to
identify
galaxy: ______________
_
_
______
____
Galaxy
______
Type:_
______
______
_________________________________________
____
______
Spiral A
______
rms B
______
ar Galaxy Type:______________________________
_____
Dust La
Ring
ne H
II Regio
Spiral Arms Bar Ring
ns
Compa
nion G
alaxy
Dust Lane
HII Regions
Foregro
und Sta
Companion Galaxy Foreground Stars
rs
Galaxy
8: Disp
lay: M
in: ___
Name (s
Max: _
ee Gala
__ Log
xy Atla
s): ___
Feature
______
s used
______
to iden
_____
ti
______
fy gala
______
xy: ___
______
______
______
_____
Galaxy
______
Type:_
______
______
_____
______
Spiral A
_
______
rms B
______
ar ____
Dust La
Ring
ne H
II Regio
ns
Compa
nion G
alaxy
Foregro
und Sta
rs
Galaxy 4: Display: Min: ___ Max: ___ Log Rough Sketch:
Rough Sketch:
Rough Sketch:
Rough Sketch:
Rough
S
Name (see Galaxy Atlas): ____________________
kFeatures
etch:
used to identify galaxy: ______________
_________________________________________
Galaxy Type:______________________________
Spiral Arms Bar Dust Lane
Ring
HII Regions
Companion Galaxy Foreground Stars
Part III: Image Data vs Image Display
Pick any image of the ones you have
opened, and open it twice. For example, if you
open browser6 twice, you will get two windows
titled browser6:1 and browser6:2. Choose an
appropriate zoom size so that you can put the two
windows side by side on your computer screen.
a. In the View menu, there are two “bars”
(Toolbar and Control Bar) and a palette (Tools
Palette). Toggle these on and off to see what
each name refers to.
2.20 With progressively larger and larger
values for Zoom, at what zoom value do
you clearly discern the individual picture
elements—pixels—as little squares? Within
each square, does the color or shading vary?
Chapter 2: Astronomers' Tools
Toggle these off and on
And if you Zoom the image even more, does
that color within each pixel change?
b.About the Image Contrast—Min/Max tool: This
controls the shading (or the coloring). If you
set the palette color as Grey, pixels dimmer
than Min will be black and pixels brighter than
Max white. Everything in between will be a
shade of grey. The software assigns shades of
Hands-On Universe
19
grey or colors across the range of brightness between the Min and
Max. Changing the values to make the range narrower brings out
more detail in the parts of the image whose brightness is within that
narrower range.
c. Cursor Information: The (x,y) coordinates and the brightness in
“Counts” for the cursor’s position are displayed in the Pixel Coordinates
area of the Control Bar [Status Bar in old HOU IP]. Each (x,y) pair of
coordinates identifies a
specific location—picture
element—or pixel for
short.
Control
Bar
Coordinates
of Cursor
Brightness
in “Counts”
2.21 What are the
dimensions of your
“Display Region” (in
pixels of the image
displayed without scrolling)? Find the (x,y) coordinates of the
bottom left corner of the window and then the (x,y) coordinates
of the top right corner of the window. What are the window’s
dimensions?
2.22 How do the dimensions of the Display Region change when
you change the Zoom Factor to other values? Since you have two
windows of the same image open, you can easily compare different
zoom values.
2.23 Does the position image data (x,y coordinates in the status bar)
of a particular star or feature on your image change when you
change zoom value? Change zoom factor; find the star or feature;
click the cursor on it, and read “x,y” in the Pixel Coordinates.
2.24 Does the brightness data (Counts in
the Pixel Coordinates area) change when
you change the image display functions
with the Min/Max tool or the Log scaling
check-box?
• You can return to original Min-Max settings
by selecting “Reset Default Min/Max” in
the View menu.
• Log Scaling (in View menu) brings out
detail in dimmer parts of an image. You
may need to adjust Min/Max to enhance
the features you are interested in. Did you
note the better detail in the lower part of
the image?
d.With Log Scaling in one image and normal linear
scaling in the other, the two images look very
different. The Log On/Off indicator is at the
right end of the Control Bar.
e. From Tool Palette, choose Color Palette Bar.
With the same image in two windows, you
compare changes in settings. The Display
Controls Bar and Color Palette Bar only refer
to the active window, the one with its title bar
highlighted. The Color Palette Bar bar shows
the range of colors in the active window and
shows the relationship between the colors
brightness in Counts.
2.26 When you change Min-Max settings or turn
on Log Scaling, does relationship of colors
and brightness shown in the Color Palette
Bar change? If so, how?
2.25 Does the brightness data (Counts in the
Pixel Coordinates area) change when you
turn on Log Scaling? With two windows open
with the same image, check brightness value
in same place on each image.
20
Global Systems Science
A Changing Cosmos Chapter 2: Astronomers’ Tools
Detectors of Invisible Energies
Even though we generally only have the light from
astronomical objects to learn what we can from them, the
amount of information contained in that light can be quite
rich. Light energies can be described in terms of numbers of
photons which is essentially brightness. But each photon also
has an intrinsic energy that we usually describe in the language
of waves: wavelength (how long the waves are) and frequency
(how fast the waves vibrate). Lower energy photons are longer
wavelength and lower frequency. Higher energy photons are
shorter wavelength and higher frequency.
Chandra X-Ray Observatory
Colors of visible light range rainbow-like from red
colors with long wavelengths (low frequency) to violet colors (short
wavelengths). Higher energies than violet go
from ultraviolet light to x-rays to gamma
rays. Lower energy photons go from infrared
light to microwaves to radio waves.
Spitzer Infrared Observatory
Astronomers have worked with engineers
to create special telescopes and detectors
for sensing these invisible energies. On this
page you see some photos of some such
telescopes.
In the next chapter, we look in a bit more
depth about how we can find out a lot about
stars just by cleverly analyzing the light from
those stars.
The Greenbank
Radio Telescope,
West Virginia
Photon Wavelengths—Electromagnetic Spectrum
Find late breaking news and information about
Astronomers’ Tools at the Staying Up To Date
pages for A Changing Cosmos:
http://lhs.berkeley.edu/gss/uptodate/10acc
Chapter 2: Astronomers' Tools
Hands-On Universe
21
Chapter 3
3. Cosmic Engines
Photo of M42, Great Nebula in Orion,
courtesy Richard Bennion, Ewell
Observatory, Belmont, CA. http://
www.ewellobservatory.com
At the beginning of this book, two of the three ways to “end life
as we know it” were caused by dramatic changes that can happen at
certain stages in the life of a star: at the end of a star’s life, it can
swell up to enormous size in a red giant stage, or it can
blow up in a supernova explosion. The beginning of a
star’s life happens in a gigantic cloud of gas (nebula),
many examples of which are found in Charles Messier’s
catalog that we spoke of in the Investigation Using Star
Maps in the previous chapter.
The way that a nebula becomes a star is by the
gravity force from each individual molecule in the gas
cloud acting on other molecules causing the whole cloud
to contract and shrink in size. In that process, molecules
move faster and faster as the cloud shrinks, and as
you probably know, faster moving molecules means
hotter and hotter gas. This gravitational generation
of heat energy is one of the fundamental “engines”
of cosmic energy. When the gas gets to a certain
“magic” temperature and pressure, and amazing thing
happens—atoms start transforming and a star is born. A good place
to study this is in the nearest star to us: our own Sun!
What Is the Secret of the Sun’s Furnace?
Using instruments called spectrometers
that analyze the color of light from the Sun,
astronomers found that it is composed mostly of
hydrogen (70%) and helium (28%). Just 2% of the
Sun is composed of heavier elements, and almost
none of it is of the variety that will generate
energy by radioactive decay.
In 1920, at a meeting of the British
Association for the Advancement of Science,
Sir Arthur Eddington, who was already a famous
English physicist, speculated about the source
of energy that powered the Sun. His idea turned
out to be an amazingly accurate prediction. In
his presentation, he referred to measurements
that had been made by his colleague, Francis
Aston, which showed that when the nuclei of
four hydrogen atoms were combined, or fused, to
form one nucleus of helium, a bit of matter was
apparently “lost.” This fact—plus his knowledge
of the Law of Conservation of Energy—is what
Eddington needed to speculate about the source
of energy in the Sun.
Aston has further shown conclusively
that the mass of the helium atom is even less
than the masses of the four hydrogen atoms
which enter into it—and in this, at any rate,
the chemists agree with him. There is a loss
of mass in the synthesis amounting to 1 part in
120, the atomic weight of hydrogen being 1.008
and that of helium just 4. Now mass cannot be
annihilated, and the deficit can only represent
the mass of the electrical energy set free in
the transmutation of hydrogen into helium,
other particles and a release of energy. We
can therefore at once calculate the quantity
of energy liberated when helium is made out
of hydrogen....
If, indeed, the sub-atomic [nuclear] energy
in stars is being freely used to maintain their
great furnaces, it seems to bring a little nearer
to fulfillment our dream of controlling this
latent power for the well-being of the human
race—or for its suicide.
22
Global Systems Science
—Sir Arthur Eddington, 1929
A Changing Cosmos Chapter 3: Cosmic Engines
Eddington noted that the amount of energy
liberated when mass is apparently “lost” can be
calculated from Einstein’s famous equation:
E = mc2
This equation means that a certain amount
of energy (E) is equivalent to a certain amount
of mass (m) multiplied by the speed of light
times itself. The speed of light is about 300,000
kilometers per second. If you could go that fast,
you could go around the world seven times in a
single second. This is a very large number, and
when it is squared it is even bigger! So the tiny
bit of mass that is lost when four hydrogen atoms
combine to form one helium nucleus is converted
into a relatively large amount of energy.
In the core of the Sun, about five billion
kilograms of hydrogen is turned into helium every
second. If 1/120 of that mass is converted to
energy—that’s about 50 million kg/sec.—enough
to account for the Sun’s production of energy. The
Sun has been fusing hydrogen at this rate for about
five billion years, and there is enough hydrogen
fuel to keep the Sun “burning” for another five
billion years.
The combination of four hydrogen nuclei into
a single helium nucleus is called nuclear fusion.
The details of this process were worked out in 1938
by Hans Bethe in the United States and Carl von
Weizsacher, working independently in Germany.
It is now widely accepted that this process is at
work in the core of the Sun, producing the energy
that we need to live.
In the late 1930’s, experimenters in the
United States, England, and Germany were
conducting experiments in which they created
fission reactions in the laboratory. This was the
time when Hitler was in power in Nazi Germany,
and World War II was brewing. Scientists around
the world saw the implications of nuclear power
for the making of powerful weapons, and both the
U.S. and Germany started research projects to
create nuclear weapons. The first “atomic bombs”
which used a fission reaction were dropped by
U.S. warplanes on the cities of Hiroshima and
Nagasaki in 1945, killing over a hundred thousand
people.
A much more powerful “hydrogen bomb,”
which used a fusion reaction, was exploded at
test sites on Pacific Islands by the United States
Chapter 3: Cosmic Engines
Image of the Sun from the TRACE spacecraft. Courtesy NASA.
Nuclear Fusion
Four protons
This diagram
(hydrogen nuclei) represents nuclear
P P reactions going on
in the core of the
P
P Sun. In reality,
there is not one
nuclear reaction,
but a series of
several different
nuclear reactions,
two of which are
shown on the next
page.
Energy
Helium
nucleus
in the early 1950’s, and shortly thereafter by the
Soviet Union. The ensuing “arms race,” which
occupied the world for the next few decades, gave
chilling meaning to the last words in Eddington’s
speech.
Hands-On Universe
23
Particles Involved in Nuclear
Reactions:
Proton-proton nuclear
reaction
P
P
p = proton; positively charged; relatively
massive; nucleus of the hydrogen
atom.
n = neutron; no charge; very slightly more
massive than the proton.
e- = electron; negative charge; very light
(1/1840 times the mass of the proton).
Deuteron-proton
nuclear reaction
P
N P
proton
deuteron
e+ = positron; antiparticle to electron—same
mass but positive charge.
N/P = deuteron; composed of a proton and
a neutron bound together; has same
positive charge as the proton; nucleus of
deuterium (heavy hydrogen), an isotope
of hydrogen.
ν
neutrino
N P deuteron
Sunspots
Prominence
y
γ ra
e+ positron
ν = neutrino; massless and chargeless; very
little interaction with matter; can pass
through a whole planet or star without
interacting.
γ = gamma ray; a photon—packet of
electromagnetic energy—much like
ordinary light, but with much higher
energy and very short wavelength.
The prominences seem to float upwards from darker
regions of the Sun, called sunspots. These sunspots
look black from Earth, but from your current vantage
point you can see that they are only slightly cooler
and less luminous than the surrounding areas.
Photosphere
3
P Helium
N P nucleus
Chromosphere
(just above photosphere)
Earth
(to scale by size
but not distance)
Granulation
Convection
Zone
Sunspots
Core
Sun’s Surface
24
Global Systems Science
Radiation Zone
Sun’s Interior
A Changing Cosmos Chapter 3: Cosmic Engines
Investigation
Size and Scale of the Sun
I. How Big is that Prominence?
Materials:
a. Use the HOU Image Processing software to open the image
eclipse1.fts.
This image of the longest total solar eclipse of the 20th
century was taken in Hawaii in 1991 by an HOU team. Look around
the rim of the Sun (often called the limb of the Sun) and see if you
can find prominences—cloud-like or flame-like structures extending
into the corona of the Sun (the Sun’s atmosphere). A prominence
forms in a time period of about a day, but stable ones can last
many days or even months. The bright eruption at the bottom of
the eclipse1 image is an example of a prominence.
• HOU Image Processing
software
• Images:
eclipse1.fts hemma.jpg
m51.fts jupiter.fts
moon.fits
ringnebula.fts
fireballShoemakerLevy.fts
fireballShoemakerLevy2.fts
b. Try some color palettes such as RAIN.PAL and WRMB.PAL.
Adjust the contrast using Min/Max so you can see the Sun’s
rim. See if Log scaling helps.
The big bright blob with the “spike” sticking through it is
probably not a prominence. It’s more likely a feature of a total
solar eclipse called the diamond ring effect, which happens
either right at the beginning or end of totality (totality is when
the Moon completely obscures the disk of the Sun). A tiny piece
of the Sun’s surface is shining through and over-exposing some of
the CCD pixels.
c. Find the prominence that is nearly on the
opposite side of the Sun from the diamond
ring blob and zoom in on it to get as large a
display of the prominence as possible that
still fits on the screen (with no scroll bars
on window).
d. Using the cursor and the Pixel Coordinates,
find the height in pixels of the prominence
above the Sun’s rim. Also find the diameter
of the Sun.
e. Use the fact that the Sun’s diameter is
1,390,000 km to compute height of the
prominence in kilometers.
3.1. How many Earths could fit under
the prominence? (Earth’s diameter =
12,756 km)
f. Another way to measure size is to use the
Slice tool (in Analyze menu). Draw three
slice lines: one across the prominence to
show its width, one out from the Sun to show
it height, and third one all the way across
the Sun. Be sure your slice lines include parts
of the image beyond the prominence.
Chapter 3: Cosmic Engines
g.Make a sketch of your 3 graphs. Drag in one
of the graph windows so the distance and
brightness coordinates are shown and a small
box appears on the slice line in the image.
Drag the cursor to the place on the graph
corresponding to the left or outside edge of
the prominence. In the image window does
the box showing where you are along the
slice also appear to be at the edge of the
prominence? Often it does not.
h.Increase the value for Max until the
prominence almost whites out. Make another
slice on top of one of slices you made in step
g.
3.2. Compare these two Slice graphs. What
is different? What is the same? What is the
distance in pixels between the apparent edge
of the prominence in the image and the edge
shown on the graph?
Hands-On Universe
25
II. Measuring Plate Scale of an Image
Each pixel on a CCD image, e.g. of the Sun, represents
a very small portion of the sky and is colored or shaded to
represent the amount of light received through the telescope
from that part of the sky. The entire sky is like a 360° sphere
surrounding us, and the field of view of the telescope covers a
tiny angle on that sphere with each pixel of the CCD covering
an even tinier angle in the sky. That angle determines a quality
known as the plate scale of telescope-CCD system. The pixel
angles are very small: seconds of arc (see box “What is an
angle of 1 arcsec?). For instance, for a certain CCD camera on
the 30-inch telescope at Leuschner Observatory near Lafayette,
California, where most of the images for our investigations
were taken, the plate scale was 0.99 arcsecs/pixel. Each pixel
on those images is nearly 1 arcsec/pixel in angular size. When
we got a new CCD camera to put on the 30-inch telescope,
the plate scale of the new system became 0.67 arcsecs/pixel.
With that new system, each pixel on the image is 0.67 arc
seconds in the sky.
Using Angles to Measure Size:
The Small Angle Approximation
The angle covered by an object depends on both its actual
size and the distance to the object. Consider the diagram
at right that shows a circle with radius (r) representing the
distance between the observer and an object. The width
(or size) of the object is D, and q is the angle subtended
by the object. The arc length subtended by the object is s.
The arc length of a full circle is the circumference (2πr).
The angle q may be expressed in degrees, which most people
are familiar with. But another unit of angle is the radian. The
angle q is one radian when arc length s = radius r, or s = r.
Since 360° = 2π radians, that means
1° = 2π/360 radians = 0.017 radians
and conversely,
What is an angle of 1 arcsec?
1° is 1/360th of a circle
1° = 60 arc minutes (written 60’)
1’ = 60 arc seconds (written 60”)
therefore
1” = 1/3600°,
which is a VERY small angle.
The angle covered by a star or even a
galaxy is much smaller than a degree.
Size of astronomical objects are usually measured in arc seconds and occasionally in arc minutes for very large
objects. Some of the largest objects
are the Sun and Moon, both of which
are about 1/2 degree (30 arcminutes)
in diameter.
The angle q is
one radian when
the arc length
equals the
radius, or q
s=r
s
D
r
1° = 0.017 radians
1 radian = 57.3°
1 radian = 206,265"
1 radian = 57.3° = 206,265”
The relationship between s and r can be written more
generally in terms of any angle q that is measured in radians:
s = r x q when q is measured in radians.
As q becomes smaller, the arc length s has less
curvature and can therefore be approximated by a straight
line of length D. When q is much less than 1 radian, the
lengths of D and s become almost equal, which gives us the
Small Angle Approximation:
D=rxq
or
Small Angle Approximation:
For very small angles s ≈ D
and the angle in radians is roughly
equal to the ratio of the width of the
object to its distance away
q = D/r
where r is the distance away from the object, D is the
size of the object in the same units as r, and q is the angle in Observer q
radians.
Object D
r
26
Global Systems Science
A Changing Cosmos Chapter 3: Cosmic Engines
You need to be very careful to keep your units of measurement straight
when working with plate scales and the Small Angle Approximation. In order
to measure sizes of the objects on CCD images, there are four steps:
1) Measure the number of pixels covered by the object.
2) Use the plate scale for the image to calculate the actual angle in the
sky covered by the object.
3) Convert this angle to radians.
4) Use the Small Angle Approximation to calculate the size of the object
given its angle in radians and distance away.
Find Plate Scale of eclipse1
In the image eclipse1 of a solar eclipse in 1991, the angle covered in the sky
by both the Sun and the Moon is 1/2°.
a. Use cursor readings in the Pixel Coordinates or use Slice under Analyze
menu to measure the number of pixels across the width of the Moon
in the image.
b. Calculate the ratio of the angle covered by the Moon in the sky when
looking at it with your naked eyes to the number of pixels covered by
the Moon in the image. This is the plate scale of this image in units of
degrees per pixel.
c. Plate scales of CCD images are commonly expressed in arcsecs/pixel.
Use the conversion factor, 1 degree = 3600” (A double quotation mark,
“, is the common symbol for arc seconds) to calculate the plate scale
of the image of the eclipse in arcsecs/pixel.
III. Measuring Size on a CCD Image
Open image hemma.png or hemma.gif.
The image is of Hemma, HOU student/
assistant, sitting at her computer. You can use the
Rotate or Flip option under Manipulation to make
the image right side up. If your computer is slow,
rotating it may take a few minutes.
Astronomers usually look at astronomical images
where you can’t tell which way is sideways. For
this Earthly image, you may want to use the rotate
function of your Image Processing software...or not.
a. Use cursor readings in the Pixel Coordinates
to determine the number of pixels in the
width of the screen on Hemma’s computer.
b. Given the following data:
The height of the active area of Hemma’s
screen = 9.5 inches
The distance of the camera from the screen
= 36 inches
...use the Small Angle Approximation to
calculate the angle covered by Hemma’s
screen as observed by the camera. (See
the Measuring Size with Images Discussion
Sheet for an explanation of the Small Angle
Approximation). This angle is rather large
for the Small Angle Approximation but will
suffice for this activity.
Chapter 3: Cosmic Engines
c. Calculate the plate scale of the hemma image
in arcsecs/pixel. (1 radian = 206,265”)
Hands-On Universe
27
IV. Measuring the Size of Astronomical Objects
In this activity, you may first need to do some image
processing (using the Min/Max adjustment and Log scaling) to
make sure you are measuring the entire width of the object.
Open the following images one at a time and
a. find object width or length in pixels
b. use the plate scale to calculate the angle in arcseconds
c. use the distance to find the actual size, assuming small
angle approximation applies.
A. moon.fts Object: any one of the craters
Plate Scale: 0.45”/pixel
Distance to the Moon: 3.84 x 108 m
3.3. Could a house fit inside this crater? Your city or town?
B. jup1.fts
Object: Jupiter
Plate scale = 0.45”/pixel
Average distance to Jupiter = 7.8 x 1011 m
3.4. How many times bigger is Jupiter than the moon
crater you measured?
C. eclipse1.fts
Object: Sun
Plate scale = 3.0”/pixel
Average distance to the Sun = 1.5 x 1011 m
3.5. How does the size of the Sun compare with the size
of Jupiter?
D. 3ringnebula.fts
Definition
Object: the Crab Nebula
(a planetary nebula; gas from a dying star)
Plate scale = 0.63”/pixel
L ight- ye a r : t h e
distance light
travels in one
year
Distance = 2.300 light years (ly)
You need to convert the distance to the Ring
Nebula from light years to meters:
1 ly = 9.5 x 1015 m.
3.6 How does the width of the Ring Nebula
compare to the Earth-Sun distance?
28
Global Systems Science
A Changing Cosmos Chapter 3: Cosmic Engines
E. m51.fts
Object: M51, a spiral galaxy
Plate scale = 0.99”/pixel
Distance to the galaxy M51 = 30 million ly
3.7a. How wide are the spiral arms in light years?
3.7b. How wide is the entire galaxy?
3.7c. How does this compare to the width of the Crab Nebula?
Extra Challenge:
Determine the field of view for one of the images used in this section
(IV). The field of view is the angle covered by the entire image.
V. Comet Crash
Open image fireballShoemakerLevy.fts and flip it vertically. The
fireball was made by a piece of the comet Shoemaker-Levy 9 in July
1994. The piece was called Fragment G, and it was probably about two
miles (three or four kilometers) across. It hit on the back side of Jupiter,
where no one could see it, but Jupiter’s very fast rotation (period =
10 hrs) brought it into view in only a few minutes. The fireball
was visible for only minutes. This picture was taken with the
largest telescope in the world, the 10-meter Keck telescope
on Mauna Kea in Hawaii.
3.8 How big is that fireball? Are we talking about a bonfire or
something really serious? How big is the fireball compared
to the Earth? [Hint: Jupiter is 11 times the diameter of
Earth.]
Every object has energy by virtue of its
motion—that’s called kinetic energy. Kinetic
energy of an object depends on its mass and how
fast it is moving. Specifically:
E = (1/2)mv2 where
E is energy; m is mass; v is velocity.
Fragment G was moving at over 30,000 m/
sec, so the square of that is a huge number. The
mass of comet Fragment G was also huge: about
100-trillion (1014)kg. So its kinetic energy was
really huge. The energy released when Fragment
G crashed into Jupiter was hundreds of times
more than all the nuclear weapons on Earth -- all
going off at once. Think what an explosion of that
much energy would do to Earth.
Open fireballShoemakerLevy2 and flip it
vertically. The spots in the lower left were made
by three earlier comet fragments. They are
thought to be clouds of dust and sulfur containing
gases left over from the explosion of rocky comet
chunks.
3.11. How big are the spots?
Jupiter’s famous red spot is to the right and above
the three spots. It was there long before the
impacts—first seen hundreds of years ago.
Find late breaking news and information about
Cosmic Engines at the Staying Up To Date pages
for A Changing Cosmos:
http://lhs.berkeley.edu/gss/uptodate/10acc
Chapter 3: Cosmic Engines
Hands-On Universe
29
Chapter 4
4. Fathoming Huge Distances
Star Motion
If our galaxy as viewed by beings outside it looks like
a big spiral, might it not be spinning like a big pinwheel?
Indeed it is. But since the galaxy is made of billions of stars
(plus assorted gases, dust, and heaven knows what), that
means for the galaxy to spin, each star must orbit the center
of the galaxy. They don’t all move in perfectly synchronized
orbits though, so from our vantage point stars seems to
move very slowly with respect to each other. The motion
has two components to it: lateral (sideways) movement and
movement towards or away from us. The sideways motion is
called proper motion, though no one seems to know anymore
what’s proper about it. When we measure a star’s velocity
towards or away from us, it’s called radial velocity (as in
change of length of a radius line of a circle where we’re at
the center and the star is on the circle).
Distance To Things in Our Solar System
For relatively nearby things, like airplanes,
we can use radar waves to measure how far away
they are. Radar waves are like the radio waves
that your radios and TVs at home receive.
Air traffic controllers at airports use radar
systems to measure distances to airplanes. Radio
waves are sent out, and they bounce off airplanes.
The amount of time the wave takes to return tells
the controller how far away the airplane is. The
longer the time the wave takes to return, the
farther away the airplane is. Radar at airports
measure distances to airplanes that may be a few
hundred kilometers away. Astronomical things are
much farther.
The most accurate distances to the Moon,
Sun, planets and other objects in the solar system
are measured by timing waves sent to and from
spacecraft. Speed of those waves is 300,000
kilometers per second (same as the speed of
light). At that speed, it takes about one and a
half seconds for the wave to get to the moon, and
another one and a half seconds to get back, so
30
Global Systems Science
there is a distinct lag time in conversation when
you’re talking by radio to someone on the Moon:
3 seconds.
Rather than express huge distances in
hundreds of thousands, millions, or trillions of
kilometers, it’s handy to describe those distances
in terms of the time it takes radio or light signals
to travel that distance. A light-second is the
distance that light or radio waves travel in one
second. Light-second might sound like a unit of
time, but don’t be confused—it’s really a unit of
distance. In the case of the Moon, we could say
that the Moon’s distance is about one and a half
light-seconds away from Earth.
Mars is usually over 100 million kilometers
away, and as Mars orbits the Sun, there are times
when it is over 15 light-minutes away from us.
There would be about a half hour roundtrip delay time between us and someone on
Mars. Neptune, in the outer reaches of the solar
system, is over 4 billion kilometers away—over 3
light-hours away.
A Changing Cosmos Chapter 4: Fathoming Huge Distances
4.1 If the distance to the Moon is
about 1.5 light seconds, how far
is that in km? Look up the actual
distance to the Moon in km. How
accurate is the statement, “The
Moon is 1.5 light-seconds away
from Earth?”
Distance By Parallax
The position of an object seems to change when you change
your point of view. This is the basis for another distance measuring
method. Imagine that your thumb is a “star” and hold your “star’
out at arm’s length. Look at your star against the background of the
other more distant things. Without moving your arm or head, look
at your star first through one eye and then the other eye. Does the
star seem to shift position against the background stars? The shift in
position is known as parallax.
Now try holding your star closer by bending your elbow, so that
the star is about half an arm’s length away. Do the same thing as
before: without moving the star or your head, look at your star first
through one eye and then the other eye.
Does the star’s position seem to shift less than before? The
parallax shift should be greater, the shorter the distance you make
to your “star.”
The first people who tried this observed stars from different
cities very far from each other, but they saw no shift at all. The stars
were too far away for any parallax shift in position to be noticeable.
They were able to measure the parallax shift for the Moon hundreds
of years before radar was invented. In 150 BC, the Greek astronomer
Hipparchus used parallax to measure a distance to the moon that
was only a percent different from the number we can measure today.
Pretty good for someone 17 centuries before the invention of the
telescope!
Measuring the parallax of the planets required much better
angle-measuring techniques, and it wasn’t until 1672 that French
astronomers just barely succeeded in measuring the parallax of
Mars, and at last we knew how big the solar system is. The Sun
is 150 million kilometers away!
Measuring distance to the
Moon required a baseline
distance hundreds or thousands
of kilometers apart on Earth.
But any baseline on Earth was not long enough for making a
parallax measurement to determine distances to stars.
Chapter 4: Fathoming Huge Distances
Hands-On Universe
31
Investigation
Parallax
To see how parallax works, we’ll observe and measure the parallax angle
of a relatively distant object such as a tree or a flagpole and use that angle to
determine the distance to the object.
Materials: ruler, meter stick,
Parallax Diagram
C
Target
(pole)
Refer to the Parallax Diagram
for these steps:
B
q
b
d A
I. Locate a target object,
like a pole or tree, whose
parallax and distance you
want to measure.
4.2 Make an estimate of the
distance to the target object
in meters, and record your
estimate. This will allow you
to appreciate how well you
q'
D
can visualize distances that are beyond your reach. It will also help in
determining whether your result at the end is reasonable or not.
II. Find an area where you can lay out a baseline about 10 meters long with
these qualities:
(a) you can sight the target at approximately
either end of the baseline, points A and B
a. Hold the ruler in front of your eye and
on the diagram,
measure the distance (x) between C and D.
(b) from near point A you can sight on the
b.At the same time have a partner with a meter
target and line up an easily seen object in
stick measure the distance (y) from your eye
the far distance, preferably a few miles or
to the ruler you are holding. Have more than
more behind the target, point C, and
one pair of people do this measurement for
(c) from the other end of the baseline, near
the most reliable result.
point B, you can line up the target with
c. Compute the parallax angle
another, easily seen object in the far
q' = (x/y) * 57.3 degrees.
distance, point D.
4.4. Calculate the distance, d, to the pole. Assume
III. Mark positions A and B and measure the
the angle is fairly small, so you can use the
baseline distance (b) between A and B in
following approximation:
meters. It should be in the range of 5–10
d = b (57.3°/ q’)
meters. Record that distance on the diagram
4.5. Compare your measured distance to the value
(letter b).
you estimated in question 4.2 above. Do you
4.3. Measure the parallax angle of the target
believe your measured result is reasonable?
by standing somewhere along the baseline
Explain.
where you can view both points C and D in the
distance. The closer you are to the center of
the baseline, the better, but any point along
the baseline will work. With the help of a
partner, measure the angle between points C
and D (angle p’ on the diagram), as follows:
32
Global Systems Science
4.5 Which step of the procedure do you believe
had the most potential for error? Without doing
a major error analysis, approximately what
percent error do you feel there is in your result
of distance to the pole?
A Changing Cosmos Chapter 4: Fathoming Huge Distances
Investigations on Measuring Distances to Asteroids
Two investigations, developed by HOU
teacher Rich Lohman, on using the parallax
technique to find distance to asteroids,
Distance to Asteroid 1998wt and The
Parallax of Asteroid “Austria,” are at the
Staying Up To Date pages for A Changing Cosmos,
Chapter 4:
http://lhs.berkeley.edu/gss/uptodate/10acc
Images for the investigation on Asteroid 1998wt are in
the folder MoreTelescopeImages/AsteroidParallax
Distances to Stars By Parallax
After many failures in attempting to measure distance to stars by the
parallax technique, a breakthrough came when astronomers realized the Earth
itself changes position in space as it travels around the Sun.
As the Earth travels around the Sun each year, we change our point
of view by over 300 million kilometers! That’s the kind of baseline we
need to see the parallax of a star. When astronomers take pictures of
the same region of sky six months apart, some stars—the closest ones to
us—change position! Astronomers tried to use parallax on the stars in the
15th, 16th, 17th, and 18th century: and they all failed. Even with the
enormous baseline of the diameter of the Earth’s orbit, the parallax to the
brightest (and presumably nearest) stars always came out to be 0 degrees.
They were back to having to assume all the stars were infinitely far away.
Finally in 1838 Friedrich Bessel, after a year and a half of observations
of one star, 61 Cygni, succeeded in measuring the parallax to a star. The
parallax was less than one 10-thousandth of one degree! No wonder it was
so hard to measure. Bessel calculated that 61 Cygni, one of the nearest
stars to us, was an incredible 25 TRILLION kilometers away. That’s 25
thousand billion kilometers!
Measuring
distance to a
nearby star
required a
baseline distance
the entire
diameter of
Earth’s orbit.
The Light-Year As a Unit of Distance
A convenient unit for describing such large
distances is not kilometers,or even light seconds,
light minutes, or light hours, but light years.
Astronomers have found that the star which
makes the biggest jump every six months is
Alpha Centauri. It is “only” 10 trillion kilometers
away.
4.6. How many light years is the distance to
Alpha Centauri?
How many light years away is 61 Cygni?
The Parsec Distance Unit
The technique of measuring distances to
stars by parallax led to another convenient unit
for expressing distance. The baseline for such
measurements is the diameter of Earth’s orbit,
or twice the radius of Earth’s orbit. The average
distance from Earth to Sun is often called an
Astronomical Unit or AU. A parsec is a unit of
distance for which one parsec is the distance to
Chapter 4: Fathoming Huge Distances
an object that has a parallax angle of 1 arcsec
with a baseline of 1 AU. The word, “parsec”,
comes from a combination of “parallax” and
“arcsecond.”
1 parsec (pc) ≈ 31 trillion km
≈ 3.26 light years
Star Brightness and Magnitude
For really faraway stars, yet another clever
distance finding method had to be found. The next
trick to determine star distances was to compare their
brightness.
If you observe two stars that put out the same
amount of light and are equal distances away from
you, the two stars appear to have the same brightness.
However, if one of the stars is twice as far away from
you, that star would appear much dimmer.
Hands-On Universe
33
Investigation
A Law of Brightness
A basic physics lab activity using a light sensor to measure
brightness of light source(s) at various distances.
Materials:
Computer light sensor or
Photo cell and ohmmeter
Light bulb(s)
Meter stick
• Hook the photocell to the ohmmeter, and check that the reading on
the ohmmeter changes as light to the cell changes (you can do this
by turning off the lights or by shielding the cell with your hand).
• Place a lit light bulb in an otherwise darkened room. It is important
not to have any background light behind the light bulb or objects
obstructing light from the light bulb.
• Hold the light sensor or photocell one meter away from the light bulb
and take a reading of brightness from the light.
4.7. Record your light brightness reading, and then before taking
additional readings at new distances, make predictions for what you
would expect at two and three meters. Take readings at two and three
meters, record your data, and compare these with your predictions.
• Gather and record data for five additional distances.
4.8. Plot your data (there should be at least
eight points) on a graph with distance on the
horizontal axis and light reading on the vertical
axis. Draw a smooth curve that approximately
connects the points.
4.9. On the basis of your graph, which of the
following relationships between brightness, B,
and distance, D, can you rule out?
(a) B
D (b) B
2
D
(c) B
(d) B
1/D
1/D
A.What is the slope of this line?
2
What function most matches this curve ?
34
Global Systems Science
4.10. Square each of your distance measurements.
Plot light reading vs. distance squared. Draw
a straight line through the points on the
graph.
B.What is the math function for the light
reading in terms of the distance?
A Changing Cosmos Chapter 4: Fathoming Huge Distances
The Magnitude Scale
An ancient Greek astronomer, Hipparchus, devised a system to
classify stars according to their brightness. He divided all of the stars he
could see on a dark, clear night into six groups with magnitude 1 stars
being the brightest group and magnitude 6 stars being the dimmest.
Hipparchus did not have a telescope back in those days, so the stars
he classified were only those visible to the naked eye. Astronomers
still use the magnitude scale to describe the brightness of stars. Since
human eyes see light in a logarithmic fashion, the mathematics of the
magnitude scale is based on logs.
When astronomers considered the stars that Hipparchus must have
seen when creating his magnitude scale, they found the magnitude 1
stars are about 100 times brighter than the magnitude 6 stars. In order
to make this true mathematically, each change of one in magnitude
must correspond to an increase in brightness by a factor of about 2.51
since 2.51 x 2.51 x 2.51 x 2.51 x 2.51 equals approximately 100.
mag 1 = (2.51)1 times brighter than mag 2 -or- Ba = 2.51 x Bb when mb - ma = 1
mag 1 = (2.51)2 times brighter than mag 3 -or- Ba = 6.30 x Bb
when mb - ma = 2
mag 1 = (2.51)3 times brighter than mag 4 -or
Ba = 15.8 x Bb
when mb - ma = 3
mag 1 = (2.51)4 times brighter than mag 5 -or- Ba = 39.7 x Bb
when mb - ma = 4
mag 1 = (2.51)5 times brighter than mag 6 -or- Ba = 99.6 x Bb
when mb - ma = 5
(B is brightness, m is magnitude, and subscripts a and b are for two stars.)
By the same principle each half magnitude corresponds
to a brightness factor of 1.6
(1.6 x 1.6 roughly equals 2.5).
Some of the brightest stars in the sky were not visible
in Hipparchus’ region, so new magnitudes had to be created
to accommodate them. Thus, we now have negative numbers
on the magnitude scale to describe very bright objects.
When measuring a star on a CCD image, you get its
brightness in Counts. To see the magnitude scale in terms
of this brightness value, let’s assume a magnitude 0 star
has brightness = 10000 (note: we are just using an arbitrary
value to demonstrate the scale). Based on this brightness
value, the following magnitudes would have the associated
brightness:
Magnitude
Brightness
-1
25000
0
10000
1
4000
2
1600
3
640
4
256
5
102.4
10
1.0
15
0.01
Chart:
A Magnitude-Brightness
Example
Chapter 4: Fathoming Huge Distances
The chart points out an interesting
problem. The brightest star in the night
sky in the Northern Hemisphere is Sirius, a
magnitude -1 star. On the above scale Sirius
would have a brightness of 25000, which is
near the upper limit of the CCD and the image
processing software. In the same image,
with Sirius at the upper limit of the CCD, a
magnitude 15 star or even a magnitude 10 star
is so dim that the software would not even
identify it as a star. To see dim stars you need
to choose a longer exposure time but bright
stars will be overexposed.
Hands-On Universe
35
Investigation
Star Magnitudes
I. The Magnitude Scale
Using magnitude scale definitions on the previous page, the
following are examples of determining how many times brighter one
star is than another:
• A 10th magnitude object compared to a 20th magnitude object.
A 10th magnitude object is 100 times brighter than a 15th magnitude
object, and a 15th magnitude object is 100 times brighter than a
20th magnitude object. So a 10th magnitude object is 100 x 100 =
10,000 times brighter than a 20th magnitude object.
• A 7th magnitude star compared to a 14th magnitude star.
A 7th magnitude object is 100 times brighter than a 12th magnitude
object; a 12th magnitude object is 2.5 times brighter than a 13th
magnitude object; and a 13th magnitude object is 2.5 times brighter
than a 14th magnitude object. So a 7th magnitude object is 100 x
2.5 x 2.5 = 625 times brighter than a 14th magnitude object.
A 5th magnitude star compared to a 11.5 magnitude star.
A 5th magnitude object is 100 times brighter than a 10th magnitude
object; a 10th magnitude object is 2.5 times brighter than a 11th
magnitude object; and a 11th magnitude object is 1.6 times brighter
than a 11.5 magnitude object. So a 5th magnitude object is 100 x
2.5 x 1.6 = 400 times brighter than a 11.5 magnitude object.
• A negative 5th (-5th) magnitude star compared to a 7th
magnitude star is 100 x 100 x 2.5 x 2.5 = 62,500 times
brighter.
Now, you try a few: How many times brighter is:
4.11. A 5th magnitude star than a 10th magnitude star?
4.12. A 7th magnitude star than a 17th magnitude star?
4.13. A 3rd magnitude star than a 5th magnitude star?
4.14. A 3rd magnitude star than a 6.5 magnitude star?
4.15. A 12th magnitude star than a 22.5 magnitude star?
4.16. Our sun (-26 magnitude) than a 15th magnitude star?
Ask the reverse question. Here are some examples. What is
the magnitude of the star if:
It is 100 times brighter than a 15th magnitude star. A
difference of five magnitudes means a difference of 100
times in brightness. Also, a lower number means a brighter
star, so the star must be a magnitude 10 star.
It is 10,000 times dimmer than a 15th magnitude star. A
difference of 10 magnitudes means a difference of 10,000
times in brightness. Also a higher number means a dimmer
star so the star must be a magnitude 25 star.
36
Global Systems Science
It is 250 times brighter than a 14th
magnitude star. A difference of
6 magnitudes: 8th magnitude.
It is 625 times brighter than a 9th
magnitude star. A difference of
7 magnitudes: 2nd magnitude.
Now you try a few. What is the
magnitude of a star if:
4.17. It is 100 times dimmer than
a 12th magnitude star?
4.18. It is 10,000 times brighter
than a 12th magnitude star?
4.19. It is 625 times brighter than
a 11th magnitude star?
4.20. It is 25,000 times dimmer
than a -5 magnitude star?
4.21. It is 100,000,000 times
brighter than a 5th magnitude
star?
A Changing Cosmos Chapter 4: Fathoming Huge Distances
II. Comparing the Magnitudes of Stars
It is a common practice in astronomy to
compare the brightness of stars on the same
image or on two different images. The ratio of
brightness can be expressed as a difference in
magnitudes.
• Open the image Mgclust. The brightest star on
this image has magnitude, m(v) = 8.0.
• Using Find, get the brightness of stars in a small
part of the image. Try another part to see if
the range of dim stars is similar.
4.22 Knowing the apparent magnitude of the
brightest star, use Equation 2 at the bottom of
the box to the right to calculate the apparent
magnitude of each of the stars in one of your
samples. A spreadsheet is one way to do these
calculations.
4.23 How much brighter is the brighter dim star
than the dimmest? Calculate this two ways:
one based on the difference in magnitudes and
one based on the ratio of Counts. These two
values are probably not the same. Why not?
If we have two stars of brightness B1 and B2
and magnitudes m1 and m2, we know that
if m1 - m2 = 1, then B2 = (2.5)1 x B1
and in general,
if m1 - m2 = n, then B2 = (2.5)n x B1
Using log base 10:
m1 - m2 = 2.5 log(B2/B1)
[Equation 1]
When comparing two stars on the same image,
the ratio of Counts for those stars is equivalent
to the ratio of brightness, so:
m1 - m2 = 2.5 log(C2/C1)
where C1 & C2 = Counts of star1 & star2.
Solving for m1:
m1 = m2 + 2.5 log(C2/C1)
[Equation 2]
III. Absolute Magnitude
So far we have been dealing with apparent
magnitudes, which are how bright stars appear
to us on Earth. Absolute magnitude is how
bright the star is intrinsically, independent of
its distance away. This is related to luminosity
of a star, which is the amount of energy it
emits per second.
The apparent brightness of a star 10 pc away is:
(luminosity)/4π(10pc)2
Using the Equation 1 above:
m1 - m2 = 2.5 log(B2/B1), we get
m - M = 2.5 log [(L/4π(10pc)2) / (L/4πd2)]
where
m = the apparent magnitude of the star
M = the absolute magnitude of the star
L = the luminosity of the star
d = the distance to the star in parsecs
The absolute magnitude of a star can
be obtained from the apparent magnitude if
the distance to the star is known. Absolute
magnitude is defined to be the apparent
magnitude that a star would have if it were
10 parsecs (pc) from Earth.
4.24. Use algebra and the rules for logarithms to
derive the following equation, called the distance
modulus, for the difference between apparent and
apparent brightness = (luminosity)/4πd2
absolute magnitude:
The apparent brightness of a star can be
calculated as follows:
where d = the distance to the star and 4πd2
is the surface area of the sphere over which
the light is spread.
The absolute magnitude, M, is defined
as the apparent brightness of a star 10 pc
away.
Chapter 4: Fathoming Huge Distances
m – M = 5 log (d) – 5
4.25. If a star is 2000 pc away and has an
apparent magnitude of 7.0, what is its absolute
magnitude?
4.26. If the star measured in Part II is 1400 pc away,
what is its absolute magnitude?
Hands-On Universe
37
Cepheid Variable Stars as Distance Indicators
In 1784 a star in the constellation Cepheus was observed night after
night by John Goodricke, and he noted that the star became brighter
and then dimmer. The fluctuation in brightness repeated over and over
again approximately every five days. This was the discovery of the first
Cepheid variable star.
In 1908 at Harvard College Observatory, Henrietta Leavitt was
examining many photographic images of two small galaxies orbiting the
Milky Way, called the Magellanic Clouds. She was studying the Cepheid
variable stars in the Magellanic Clouds and noticed a pattern in their
brightness fluctuations: the brightest Cepheids had the longest fluctuation
cycles and the dimmest stars the shortest fluctuation cycles. Since the
Cepheids were all in the Magellanic clouds, all at the same distance from
us, comparing their apparent brightness was equivalent to comparing
their luminosity. Leavitt arrived at a general relationship between
luminosity and period which she published in 1917. It is now called the
period-luminosity relationship, illustrated in the diagram in the Cepheids
investigation on the next two pages.
The period-luminosity diagram allows an astronomer to infer the
luminosity of a Cepheid simply by measuring the period of its brightness
fluctuation. Since luminosity generally cannot be measured directly,
knowing luminosity from the period of a Cepheid variable is incredibly
valuable for determining distance. Leavitt’s discovery of the periodluminosity relationship is a milestone in astronomy. Before her research,
no one had a reliable tool for measuring the distance to objects farther
away than the closest stars. The technique for determining the distance
of a Cepheid requires three basic steps:
1) Measure the period of fluctuation and infer the
luminosity of the Cepheid.
2) Use a standard star to calibrate the image
and determine the Cepheid’s apparent
brightness.
3) Use the equation for apparent brightness to
calculate the distance to the star, d:
apparent brightness = luminosity/4πd2
To measure the period of fluctuation, the
Cepheid must be observed at least every few
nights for several weeks. The number of Counts
measured for a Cepheid will change from night
to night for two reasons:
1) the changing observing conditions and
2) the changing luminosity of the star.
In order to get a plot of the Cepheid’s
changing luminosity you must remove the effects
of the atmosphere by including a reference star.
Since the Cepheid star and the reference star are
on the same image, the observing conditions are
the same for both stars. If the observing conditions
38
Global Systems Science
did not change from night to night, the reference
star would appear just as bright each night. In
general, observing conditions do change, so the
number of Counts measured for the reference
star will increase or decrease depending on how
much light the atmosphere lets through. If the
atmosphere blocks out a large amount of light on
one night, both stars will appear dimmer; on a
clear night, both stars will appear brighter.
If the Cepheid had constant luminosity, the
ratio of Counts between the Cepheid and the
reference star would remain constant. A Cepheid
is not constant, however. As the luminosity of the
Cepheid increases because of internal changes
in the star, the ratio of Counts measured for the
Cepheid to the Counts measured for the reference
star will increase. By measuring this ratio for each
image, you can plot the true brightness fluctuation
of the Cepheid.
A Changing Cosmos Chapter 4: Fathoming Huge Distances
Investigation
A Cepheid Variable Star
I. Plotting the Light Curve for a Cepheid
A Cepheid was monitored for a 15-day time span, but on only eight of those nights
were the skies clear enough to get good images. You are to measure the brightness
of the star on each image and create a light curve for the star. A light curve is a plot
with brightness on the vertical axis and time (days) on the horizontal axis.
Perform the following procedure on each of the images listed below.
The name of the file gives you the date of observation.
If you want to try working
may06cepheid,
may08cepheid, may10cepheid,
on data from other Cepheid
may11cepheid,
may14cepheid, may15cepheid,
variable stars, look in the folder
may18cepheid,
may21cepheid
MoreTelescopeImages/VariableStars
Each file contains an image of the Cepheid star and a reference star observed on a given
night. The Cepheid is the star on the left and the reference star is on the right.
4.26. Use Auto Aperture to measure the brightness in Counts of each Cepheid and
reference star. Record the data in a table like the one shown on this page.
4.27. Find the Count ratio, Cc / Cr,, where Cc = the Counts of the Cepheid and Cr =
the Counts of the reference star.
4.28. Plot your series of Count ratios and corresponding dates on a graph with axes
like the blank graph shown on this page. Be careful to skip nights when dates are
missing from the observations.
4.29. What is the
period of this
Cepheid?
le
b
a
le T
p
m
a
S
le
p
am
S
Chapter 4: Fathoming Huge Distances
Hands-On Universe
h
p
a
r
G
39
II. Find the Luminosity of a Cepheid
4 . 3 0 . U s e t h e Pe r i o d Luminosity diagram to
estimate Luminosity (V)
of the Cepheid measured
in Activity I. Note: Both
axes are logarithmic
scales and luminosity
is given in solar units;
e.g., 1000 means 1000
times the luminosity of
the Sun.
Period-Luminosity Diagram for
Classical Cepheid Variable Stars
4.31. Use the value for
the luminosity of the
sun through a V filter to
calculate L(V) of your
Cepheid in Watts. L(V)
of the Sun = 5.7 x 1025
Watts.
III. Find the Distance to a Cepheid
The apparent magnitude in V of the reference
star is 8.0. From the Brightness Conversion Table,
this is equivalent to an apparent brightness in V
of 2.28 x 10-12 Watts/m2.
4.32. Calculate the apparent brightness of the
Cepheid.
4.33. Use the luminosity in V for the Cepheid
and the equation for apparent brightness to
determine the distance, d, to the Cepheid
in meters. (For the equation go to the
Cepheid Variable Stars As Distance Indicators
Discussion Sheet.)
4.34. Convert the distance to light years.
1 light year = 9.5 x 1015 m.
We’ll find out more about uses of Cepheid
variable stars in Chapter 9, The Universe
Begins ... and Ends?
40
Global Systems Science
The observations of the Cepheid were made
through a Visible (V) filter. This filter blocks out
almost all light except in the yellow-green part
of the color spectrum. When you calculate the
luminosity and apparent brightness of the Cepheid you must remember that these only refer
to the amount of light coming through the V filter. This is fine for your measurements because
you can compare them to other measurements
taken through the same kind of filter. However,
it is not valid to compare these values to the apparent brightness or luminosity of a star over all
wavelengths. In this unit, all measurements are
through the V filter.
A Changing Cosmos Chapter 4: Fathoming Huge Distances
Techniques of Distance Finding: the Cosmic Distance Ladder
<--- see Chapter 9
Find late breaking news and information about
Fathoming Huge Distances at the Staying Up To
Date pages for A Changing Cosmos:
http://lhs.berkeley.edu/gss/uptodate/10acc
Chapter 4: Fathoming Huge Distances
Hands-On Universe
41
Chapter 5
5. Color, Temperature, and Age
Filters are used on telescopes to determine the brightness of an object
in a specific color. One use of this information is to estimate the color of
stars. Astronomers generally use a set of standard filters, meaning that the
color of light each filter lets through is very
well known. This is so one observer can
compare data with another observer.
To determine the color of a star, a
combination of filters that will show a
sharp distinction between stars must be
used. The diagram on this page shows
plots of brightness versus color for three
stars. Vertical boxes are drawn to show
the approximate position of red, yellow
and blue filters. Astronomers generally
use the yellow and blue filters to measure
the color of stars because the difference
of light through these filters changes
significantly for different stars. The naming convention for filters is
relatively simple: the blue filter is called B, the red filter is called R, but the
yellow filter is called V. This is because yellow is in the center of the visible
color spectrum. To determine the color of a star using filters, the B filter is
used to measure the amount of blue light coming from the star and the V filter
is used to measure the amount of yellow light. These two values are used to
get the B–V index of the star:
B–V index = (magnitude through B) – (magnitude through V)
The B–V index uses magnitudes, which are
units astronomers use to quantify brightness.
For converting magnitude to brightness use the
Brightness Conversion Table In the investigation
Measuring the Color of Stars in the next few
pages.
Quick Tips for Using the Magnitude Scale
Magnitude Tip #1: The magnitude scale is an
inverse scale, meaning that brighter stars have
lower magnitudes than dim stars. One tip to
remembering this is to think about replacing
the word “magnitude” with “class”. One might
expect a first class star to be brighter than a
second class star, just as a first magnitude star
is brighter than a second magnitude star.
Magnitude Tip #2: The magnitude scale is not
linear. This means the change in brightness
from one magnitude level to the next is not
constant. In the magnitude scale, each level
is 2.5 times brighter than the adjacent level.
A magnitude 1 star is 2.5 times brighter than
42
Global Systems Science
a magnitude 2 star and 6.25 (2.5 x 2.5) times
brighter than a magnitude 3 star. This leads to
some trickier mathematics; see Supplementary
Activity 13: Magnitude Calculations in the
Measuring Brightness module.
Magnitude Tip #3: The magnitude associated
with a given brightness depends on which
filter is being used. The conversion table for
magnitudes to brightness in Watts/meter2 has
separate columns for each filter. Be careful
to make sure you are looking in the correct
column for the data you are seeking.
A Changing Cosmos Chapter 5: Color, Temperature, and Age
Investigation
Observing Color and Temperature
A star’s color is a direct effect of the
temperature at its surface. To understand this
look at an incandescent light controlled by a
dimmer or rheostat. As the setting of the dimmer
changes, thus changing the current to the light
bulb and therefore the temperature of the light
bulb filament, note how the color of the bulb is
affected.
5.1. List the different colors you see in the light
as you change the dimmer.
5.2. What color is the light when the dimmer is
on high?
5.3. What color is the light at a middle setting?
5.4. What color is the light at the lowest setting?
5.5. At what setting do you think the light bulb is
coolest?
5.6. At what setting do you think the light bulb is
hottest?
5.7. What color would you expect a very hot star
to appear to be?
5.8. Would a very hot star have a high or low B-V
index? (See the Measuring the Color of Stars
Discussion Sheet for an explanation of the B-V index.)
5.9. What color would you expect a relatively cool star to
appear to be?
5.10. Would a cool star have a high or low B-V index?
5.11. Imagine you could double or even quadruple your distance
away from a star. What would happen to the star’s:
A. Apparent brightness?
B. Luminosity?
C. Color?
Chapter 5: Color, Temperature, and Age
Hands-On Universe
43
Investigation
Measuring the Color of Stars
In this activity you will determine the color of stars that have been observed
with the Leuschner telescope. There are four different stars with two images of
each, one using a blue filter (B) and one using a yellow or visible filter (V). These
stars will be referred to as your target stars. For each target star there is also a
standard star that was observed at nearly the same time so you can assume the
observing conditions are the same. Given the known apparent brightness of the
standard stars, you can calibrate the target stars to determine their apparent
brightness. This procedure is explained in further detail in the Photometry
Techniques Unit in the Measuring Brightness module.
target star
in B
btarg1
btarg2
btarg3
btarg4
target star
in V
vtarg1
vtarg2
vtarg3
vtarg4
standard star standard star
in B
in V
bstan1
vstan1
bstan2
vstan2
bstan3
vstan3
bstan4
vstan4
Perform the following procedure to get the apparent brightness
of each target star through each filter. Record all of your data in
the table provided.
standard
star
bstan1
vstan1
bstan2
vstan2
bstan3
vstan3
bstan4
vstan4
apparent
magnitude
8.0
7.0
9.2
7.2
7.8
7.5
7.0
7.0
5.12. Use Auto-Aperture to get the Counts for each of the stars.
(In most cases the target or standard star is the only star in the
image; if not, it is clearly the brightest star
in the image.)
5.13. Use the Brightness Conversion Table to
get the apparent brightness of each standard
star.
5.14. Calibrate each target star using this fact:
ratio of Counts = ratio of apparent brightness
of the target and standard stars
These ratios are equal because the two stars
were observed at nearly the same time by the
same equipment, so presumably under the
same observing conditions.
Note: There is one exception you must account
for. The exposure time for bstan2 is three times
longer than the exposure time for btarg2. This
means the telescope collected three times
more light from the standard star than it would
if the exposure time had been the same as
the target star’s. You must correct for this in
your ratio. You can find the exposure time for
any image yourself by selecting Image Info
under Data Tools. Scroll down about a page or
more and find “exp. time.” The time is given
in seconds.
44
Global Systems Science
5.15. Use the Brightness Conversion Table at the
end of this Investigation to find the apparent
magnitude of each target star. Find the closest
magnitude that corresponds to your value for
apparent brightness.
5.16. Calculate the B–V index for each target
star.
5.17. Use the Table on the next page to approximate
the color and temperature of each target star.
If your B–V index falls between two values in
the table, estimate the answer.
A Changing Cosmos Chapter 5: Color, Temperature, and Age
le
b
a
le T
p
m
a
S
Table : B–V index, Temperature and Color Data
for Familiar Examples for Main Sequence Stars
Chapter 5: Color, Temperature, and Age
Hands-On Universe
45
Brightness Conversion Table
46
Global Systems Science
A Changing Cosmos Chapter 5: Color, Temperature, and Age
Investigation
How Filters Work
Based on GEMS Color Analyzers activities and work
by Elizabeth E. Roettger [http://www.nthelp.com/eer/
HOAcolorAstron.html], Vivian Hoette, and Kevin
McCarron.
Use colored filters to decode secret messages,
look at rainbows, and learn how astronomers can
decode information from the sky.
Materials:
• Filters - Roscolux: Medium Red #27, Kelly
Green #94 or Dark Yellow Green #90, and
Primary Blue #80
• Astronomy images: posters, slides, e.g. from
ASP Splendors of the Universe slide set, or
Kevin McCarron’s HOU Color Astronomy Page
- http://faculty.oprfhs.org/kmccarron/
HOU/color/
• White and colored paper, colored objects/
fabric/clothing
5.18. Secret codes. Look at Kevin McCarron’s
Visible Spectrum image page [http://faculty.
oprfhs.org/kmccarron/HOU/color/spectrum.
html] and look through red, green and blue
filters to view it. Which filter shows the
“secret message that McCarron hid in
the words?” Then look at the rainbow/
spectrum at the top of the page through
different filters. See if you can figure out
why one color filter works best to reveal
this secret message. Then, once you think
you’ve figured it out, try making your own
secret message will colored pens, crayons,
or computer tools to see if your theory is
correct.
5.19. What is an object’s color? What happens
when you look at a colored object through
different color filters? Objects reflect certain
colors of light, and that’s why they look that
color.
5.20. Color Astronomy. Look at images of
astronomical objects (posters, slides or Kevin
McCarron’s HOU Color Page) through the
different filters. What are we seeing?
Spectra
In the 17th century, Isaac Newton discovered
that white light, when passed through a glass
prism, can be seen to be made of a spectrum
of colors--red, yellow, green, blue, violet. This
ultimately led to use of prisms and then grooved
glass or plastic (diffraction gratings) to build
instruments called spectroscopes, which are used
to analyze colors of light from stars.
Each element absorbs certain discrete
colors of light, so if that element is present, it
results in black lines appearing in a spectrum of
light, known as a line spectrum. The spectra on
this page, hydrogen and helium, the common
elements found in stars, illustrate how line
spectra can show us what stars are made of. To
see spectra of more elements, see
http://jersey.uoregon.edu/vlab/elements/Elements.html
or http://www.colorado.edu/physics/2000/quantumzone/
Helium
Hydrogen
Chapter 5: Color, Temperature, and Age
Hands-On Universe
47
Age of Stars—Stellar evolution
We already spoke of the birth of stars from gravitational
contraction of nebulae, or gas clouds. In the next chapter, we’ll
speak of the most dramatic and violent possible death of stars. But
in between birth and death, stars change slowly, and by examining
millions of stars all at different stages in their lifetimes, we can put
together a picture of what the stages of a single star’s lifetime must
be.
Hertsprung-Russell diagram (Using the HR Diagram)
Between 1911 and 1913, two astronomers were working
independently on the classification of stars and came up with very
similar results. A Danish astronomer, Ejnar Hertzsprung, plotted
stars according to their absolute magnitudes and spectral classes.
An American astronomer, Henry Norris Russell, created a plot of
luminosity vs. temperature for many stars. Their investigations were
seen as roughly equivalent, and the Hertzsprung-Russell (HR) diagram
is a result of their findings. Their goal was to clarify understanding
of the life cycle of stars.
The HR diagram on the next page is called a general HR diagram
because it is based on stars of all different types from many different
regions of the sky. The objective is to show the distribution of various
types of stars and their relative quantities. To create a general HR
diagram, many stars are observed at a given time, their luminosity
and temperature are determined and those values are plotted.
The HR diagram can be thought of as a snapshot plot of these stars
at one time. A star’s position on the HR diagram is determined by
its luminosity and temperature at the time of observation. Since
HR diagrams of many different stars, in many different regions,
observed at many different times all yield similar distributions, it
can be assumed that the general HR diagram describes an average
distribution of stars. More specific HR diagrams of a single star cluster
are used to determine factors about that cluster such as the type of
stars in the cluster and the distance or age of the cluster.
Ejnar Hertzsprung
http://www.phys-astro.sonoma.edu/
BruceMedalists/Hertzsprung/
Henry Norris Russell
http://www.phys-astro.sonoma.edu/
BruceMedalists/Russell/
When examining a general HR diagram, notice that the stars
are clumped into several groups. The broad line of stars extending
from the upper left-hand corner to the lower right is called the
main sequence. Most stars on a general HR diagram are on the main
sequence because this line represents the luminosity and temperature
that exists for most of a star’s life.
After its hydrogen fuel is depleted, a star
When a star begins to fuse hydrogen in its
contracts and begins to fuse helium in its core.
core, it assumes its place on the main sequence
This can occur rapidly or gradually depending on
and stays at that position until its hydrogen fuel
the mass of the star, but in either case it causes
runs out and it evolves into a later stage of its
the star to expand to a greater radius than that of
life. The main sequence lifetime of a star is
the main sequence star. During the expansion the
generally upwards of 90% of its total lifetime.
star cools considerably. A low mass star that was
The temperature, and accordingly the color, of a
a yellow or orange main sequence star evolves
star during its main sequence period are primarily
to a red giant during this expansion period. It is
determined by its mass. High mass stars are very
red because it is cool, and it is a giant because
hot so they are blue, while low mass stars are
it has such a large radius. Similarly, a high mass
cool and red.
blue or white main sequence star evolves into a
yellow or orange supergiant.
48
Global Systems Science
A Changing Cosmos Chapter 5: Color, Temperature, and Age
A red giant will undergo yet another phase of
evolution where it sheds its outer layers leaving a
very dense core of carbon. The outer layers drift
off to become what is called a planetary nebula,
which is a ring of burning hydrogen that looks like
a smoke ring. The dense core is called a white
dwarf. It is white because it is very hot, but a
dwarf because it has a very small radius. In fact, a
white dwarf can have the mass of the sun packed
into an object about the size of the Earth. A white
dwarf does not have enough mass to initiate carbon
burning to produce more energy so it will slowly
grow cooler and fade away.
Facts of life (for stars):
Stars have a life cycle: birth through
death.
Stars consume fuel (initially hydrogen) in
their centers.
The more massive a star, the faster it
consumes its fuel.
After all the hydrogen in a star’s core is
consumed the star becomes brighter,
larger, and redder/cooler.
A Typical HR Diagram
for a Large Population
of Stars.
Diagram by
Richard Powell
http://en.wikipedia.org/wiki/
Image:HRDiagram.png
Chapter 5: Color, Temperature, and Age
Hands-On Universe
49
Investigation
HR Diagrams of Star Clusters
[based on activity “Explore the Life Cycle of Stars using data from the Sloan
Digital Sky Survey” by Jordan Raddick (Johns Hopkins University), Theresa
Moody, and Dr. Wil van der Veen (New Jersey Astronomy Center)]
To create a HR diagram with star brightness vs. color, astronomers
measure a star’s brightness at two wavelengths, usually in the blue
and yellow part of the spectrum. By comparing the amounts of blue
and yellow light astronomers determine the stars color.
To fairly compare star brightness we need to know how far away
they are. However, for stars grouped in clusters, all the stars in the
cluster are at about the same distance, so we can make fair brightness
comparisons without knowing the actual distance. In this investigation,
we’ll make three HR diagrams: one of “Field stars” (stars not in a
cluster), one of a nearby “open cluster”, and one of a “globular cluster”
above the plane of our galaxy.
We will use data from the Sloan Digital Sky Survey, whose main
goal is to obtain spectra for millions of galaxies and quasars (and
some stars), but in the process, it acquires brightness and color data
on everything.
It uses a reflector telescope that is 2.5 meters in diameter and
has a very wide field of view: about 3 degrees (6 full moon diameters)
across. The telescope is actually stationary, and it takes images as Earth
rotates so the sky appears to move by the telescope view.
All Sloan Digital Sky Survey data is available on
the free web site called SkyServer.
Materials
Computer with spreadsheet software (e.g. MS
Excel) and WWW access, specifically to the
SkyServer website
http://skyserver.sdss.org
Part A. Diagramming People
[inspired by the activity “Life Cycle of Stars” from the
NASA Ceres project,
http://btc.montana.edu/ceres/html/EdActivities.html ]
Look at the set of images of people on the next
page.
1. Can you guess the sequence of ages of each
of them? Going by only these pictures, copy
the list of names and put a number “1” by
the youngest, number “12” by the oldest, and
assign 2 though 11 by the others in sequence
from youngest to oldest.
50
Global Systems Science
2. What characteristics did you use in order to
make your guesses? What physical characteristic
data would you like to have in order to make
the best attempt for a correct sequencing?
A Changing Cosmos Chapter 5: Color, Temperature, and Age
Lianna
Bernardo
Donna
Pete
Selena
Margie
Dan
Alan
Georege
Indira
Kingsley
Reiko
Chapter 5: Color, Temperature, and Age
Hands-On Universe
51
3. Now look at the “WHA” (weightheight-age) Diagram of people. How
would you describe the relationships
of weight, height, and age as shown
in the diagram?
WHA Diagram
[Weight-Height-Age]
Part B. Getting Data from the Sloan
SkyServer
1. Go to the SkyServer web site http://cas.sdss.org/
2. Click on “Search” in the first column
“SkyServer Tools”
52
Global Systems Science
A Changing Cosmos Chapter 5: Color, Temperature, and Age
Click on Search
3. Click on “Search
form” (third bullet)
4. Click on “Launch the
Search Form Tool”
Chapter 5: Color, Temperature, and Age
Hands-On Universe
53
5. Fill in the following [ra and dec are for Palomar 5 globular cluster]:
Show me “stars”
in the region “around”
ra: 229.022 dec: -0.111
radius (arcmin): 4
Number of objects: click “All”
Image Data: check “object IDs,” “RA and DEC,” “Magnitudes”
6. Then click “Generate Query” button
7. Select Output Format: “CSV”
54
Global Systems Science
A Changing Cosmos Chapter 5: Color, Temperature, and Age
8. Then “Submit Query
to SkyServer”
9. On “Opening result.csv window,” select
“Save to Disk”
Repeat steps 1-9 for the other target regions
for “Open Cluster” and “Field Stars”
Target regions:
Name
RA
Palomar 5 229.02
DEC
-0.11
Radius
4’
NGC 2420
21.57
14’
21.57
4’
114.59
near NGC 114.875
2420
Chapter 5: Color, Temperature, and Age
Type
Globular
Cluster
O p e n
cluster
Field stars
Hands-On Universe
55
Part C. Make HR Diagrams with Spreadsheet Software
1. Open the CSV file with a Spreadsheet program, e.g. Excel
2. Make two new columns,
one with formula g - r [example: column J: =E2-F2]
and one with simply copy of r [example: column K: =F2]
3. Fill down to last row of data by clicking on upper left cell [J2]
and Shift click on lower right cell [K1425 in this example] and filling
down.
ChartWizard Button
4. Select the two columns
of data...
56
Global Systems Science
A Changing Cosmos Chapter 5: Color, Temperature, and Age
5. Click on Chart Wizard
6. Choose XY (Scatter) then “Next”
7. Fill in Chart Title, e.g.
“HR Diagram for Palomar 5”
Value (X) axis:
“Star Color (g-r) [labels the X-axis]
Value (Y) axis:
“Star brightness (r)” [labels the Y-axis]
and click “Next” then “Finish”
Chapter 5: Color, Temperature, and Age
Hands-On Universe
57
8. Adjust the axes: Reverse the Y-axis,
since magnitude scale is reversed
(brighter stars have lower numbers).
Set appropriate scales.
9. Repeat steps 1-8 for the
other target regions (Open
Cluster and Field Stars)
58
Global Systems Science
A Changing Cosmos Chapter 5: Color, Temperature, and Age
Part D. Analyzing the Diagrams
What can you tell
about the age of
each cluster?
Hint 1: Why would
part of the Main
Sequence be
missing from one
of the clusters?
Hint 2: As stars age,
their position on
the HR diagram
changes. They
are no longer
placed on the Main
Sequence. They
are now placed
in the Giant
and Supergiant
groups.
How would a cluster HR diagram look when the cluster first formed?
How would this differ from a much older cluster?
Hint 3: What happened to all of the large, bright blue stars on the Main
Sequence of Graph 2?
Going Further: Get FITS images of the target regions.
1. Go to Sky Server Tools and find the Navigate
tool on tools menu.
2. Enter the coordinates for each of the target
regions, and use zoom.
3. Click on the quick look tool on the right hand
side of the page, and then click “explore”.
5. Sroll down to Corrected frames, and right click
on the files next to “g” and “r”. For each
file, choose “Save As”, and change the file
extension to .fts.
6. For these target regions, the area is always
about 10x14 arcmin.
4. Under PhotoObj in the left column, click on
FITS.
Find late breaking news and information about Color,
Temperature, and Age of stars at the Staying Up To
Date pages for A Changing Cosmos:
http://lhs.berkeley.edu/gss/uptodate/10acc
Chapter 5: Color, Temperature, and Age
Hands-On Universe
59
Chapter 6
6. Dramatic Change in Stars
We usually think of stars as very stable and constant things.
Suppose you were out looking at the sky on a dark, starry night, and
suddenly you saw a star that wasn’t there a moment earlier! You might
think your eyes were playing tricks on you. You could
check by taking a photograph of the region of the sky
and comparing it to a photograph taken earlier of the
same region. Normally, these photos would be roughly
the same. Certain objects, such as planets, may have
changed position relative to the background stars, and
the brightness or size of the stars may appear different
from night to night, but the arrangement of the stars
relative to each other generally does not change over
a period of nights, years or even centuries.
A supernova could be an explanation for seeing a
new star. The term comes from the Latin word “nova”
meaning new, though ironically a supernova is actually
the event associated with the death of a star—the
unbelievably violent process that a very massive
star undergoes when it dies. Many people think of
M1, the Crab Nebula, remains
supernovae as explosions, and in some cases this is true, but some stars
of a supernova. Image from Ewell
implode rather than explode when they die. Astronomers have studied
Observatory, Belmot, CA.
various types of supernovae and have created possible explanations for
the processes that could cause such events. Certain types of supernovae
can give important clues to the puzzle of the age, size and fate of our
universe, as well as contribute to our evolving
Most elements heavier than hydrogen and
understanding of the structure of stars.
helium are predominantly created inside stars
Although the study of supernovae is a or in the process of the supernova explosion
very active field in astronomy, theories are itself. These elements are ejected into space by
constantly being challenged about the different supernovae and then reused to form new stars
types of supernovae and the stars that produce and planets such as the Earth. The atoms that
them. Currently more than sixty supernovae are make up almost every substance that you deal
discovered each year, but often times they are with everyday, including the chair you are sitting
sighted after the maximum peak of the light curve in, the food you eat, and even your body itself,
so some of the scientific information is lost.
were once inside a star. You are made up of star
Astronomers have classified supernovae matter.
into two kinds, Type I and Type II, based on the
amount of hydrogen observed in the material
surrounding the explosion of the star. Type I have
Both amateur and professional astronomers
no observed hydrogen, leading astronomers to
actively
search for supernovae, and they are
believe the outside layers were already shed.
Hydrogen is observed from Type II supernovae, so being discovered more and more frequently.
they are generally believed to be explosions of Using the same basic strategy, they look for the
higher mass stars. This theory is consistent with appearance of a new star. Supernova SN1994I was
the fact that Type II supernovae are only found discovered based on images taken by Hands-On
in spiral galaxies, and usually in the arms, where Universe (HOU) students at Oil City High School
high-mass star formation is thought to be more in Pennsylvania. Supernova search is an area of
prevalent, whereas Type I supernovae are found active research for HOU students. How does it
work?
in both spiral and elliptical galaxies.
Searching for Supernovae
60
Global Systems Science
A Changing Cosmos Chapter 6: Dramatic Change in Stars
PHOTOMETRY
Photometry is the process of measuring the amount of light received from an object.
When you display an image using HOU Image Processing software, you can use the cursor
to see the amount of light registered by each pixel in the image. This value is given in
Counts. With the Auto Aperture and Aperture tools, routines add up all the Counts within
a specific area of pixels to give the total Counts for a star. The routines are designed to
subtract background light and give only the Counts created by the star itself.
Definitions of Photometry words
Counts - The measure of light that each pixel
of the CCD receives from the star. This
measurement is particular to the equipment
used and to the atmospheric conditions during
the observation. When we display an image,
the grayness or color at each pixel is based on
the Counts for that pixel.
Apparent Brightness - The amount of light reaching
Earth per second from a star under ideal
conditions (as if there were no atmosphere).
This is a standard value that anyone could obtain
from their measurements after correcting for
observing conditions. Units Watts/meter2.
Luminosity - The amount of light emitted per
second by a star. It is an inherent property of
the star, unlike Apparent Brightness, and is
independent of where the observations were
made or what telescope is used. Generally the
To get ready for the Investigation Finding a
Supernova, you’ll need to know something about
photometry—the measurement of light. Sometimes
a supernova is so bright it can be spotted by eye by
just looking at two images taken at different times.
In fact, there is an amateur astronomer in Australia,
a minister named Bob Evans, who can look at a galaxy
and compare it with his memory of this same galaxy
at a previous date. Very impressive. For most of us,
however, this technique is beyond our capabilities.
The best strategy is to compare images of the same
object using image processing tools in order to detect
the presence of a supernova. However, it’s vitally
important that the images must line up and match
perfectly in order for this strategy to work.
There are 3 reasons images may not match:
(A) Alignment. The telescope does not line up on the
object the same each night, so images appear offcenter, or shifted with respect to one another.
(B) Sky background light can vary significantly from
image to image.
(C) Exposure time and other observing conditions,
such as cloudiness or haze, can change from night
to night, so the apparent brightness of all the stars
may seem dimmer or brighter.
Chapter 6: Dramatic Change in Stars
luminosity of a star cannot be measured directly
but must be inferred from other characteristics
of the star. The units for luminosity are Watts.
Reference Star - A star whose apparent brightness
and luminosity does not change from one night
to the next. The apparent brightness value of the
star, however, is typically not known.
Standard Star - A steady star is like a reference star
but with a known, agreed upon value of apparent
brightness.
Apparent Magnitude - A measure of apparent
brightness commonly used by astronomers. The
magnitude scale is inverse, meaning brighter
stars have lower magnitudes.
Absolute Magnitude - This quantity is analogous to
the luminosity but is expressed on the magnitude
scale.
Light we are receiving from stars has traveled vast
distances. Amazingly, the light remains virtually
unaffected by the first 99.999999999999% or so
of its journey. But the last tiny leg of the trip
through the Earth’s atmosphere can reduce the
light drastically and star brightness can differ from
one observation to the next.
Image processing software can correct all three
types of mismatch of images through processes called
(A) shifting (aligning), (B) Sky background subtraction
and (C) Normalization. After the images are properly
shifted, sky adjusted, and normalized, we’re ready
for step D, comparing the images which can be done
one of two ways:
i. Subtraction: you can subtract one image from the
other to examine the difference. If a significant
variation has occurred, such as a supernova, it will
be apparent in the subtracted image.
ii.Blinking: switching the image display alternately
from one image to another can make any object
that has change nearly “jump out at you.”
But before step D, let’s back up and take a
careful look at how to prepare the images with steps
A, B, and C.
Hands-On Universe:
61
A. Aligning Files by Shifting
In order to align two images so they are
ready for subtraction you need to use the Axes
(Centroid) tool in Data Tools and the Shift option in
Manipulation. What happens when you shift a file?
At right is data from a small section of an image
file with brightness values (Counts) given for the
pixel locations to illustrate the result when the
image processor shifts a file “to the right by 2”
In this case as the image was shifted to the
right, the new columns created on the left were
filled in with zeroes. There is an option in the
software to select a “fill value” so that you can
have new columns or rows filled in with a value
that matches the background sky.
Original File:
107
106
106
Differences in brightness may be due to
changes in the background light level, called
“sky”, such as the amount of Moon light.
50
60
52
100
90
52
102
100
55
108
108
108
50
60
52
Shift Right by 2:
0
0
0
0
0
0
B. Subtract Sky Background
108
108
108
107
106
106
Original File:
20
23
21
21
108
50
23
180
90
20
100
60
22
22
20
Subtract Sky value 20 from each pixel
0
3
1
1
88
30
C. Normalize Brightness
To correct for differences due to change
in exposure time, compare the Counts of a
reference star (a star that is known to be of
constant brightness) in each image. Find the
“reference ratio” of Counts for the reference
star in one image divided by the Counts for the
same reference star in the second image. Then
multiply the second image by the reference
ratio. Reference ratio is often referred to as
normalization ratio.
20
23
21
87
160
70
88
80
40
30
2
0
Reference File:
21
108
50
23
180
90
20
100
60
22
22
20
Multiply each pixel by reference ratio
40
46
42
42
216
100
46
360
180
40
200
120
44
44
40
In this case, normalization (reference)
ratio is 2
To summarize the process for finding a supernova:
A. Align (shift) the images to correct for differences due to telescope aim.
Note: Steps A and B can be reversed,
but normalization is best to do
last, just before final subtraction/
comparison of the two images.
B.Remove (subtract) background skylight due to ground lights and
moonlight.
Also, both steps B and D are
C. Normalize the images to correct for differing observing conditions due to subtractions, but in B, the same
count value (sky background) is
haze or high thin clouds.
subtracted from every image pixel
D. Subtract the Reference Image from the new image.
and in D, count value of each pixel
Finally, identify any new light sources.
in a reference image is subtracted
from the corresponding pixel in the
new image.
62
Global Systems Science
A Changing Cosmos Chapter 6: Dramatic Change in Stars
Investigation
Finding Supernovae
Here are a series of exercises on finding supernovae, starting with simple
specially prepared images and progressing to real life image analyses.
Materials
• HOU IP
• Images: m51nor, m51fake1, m51fake2, m51fake3, SNW, SNX, SNY, SNZ,
m51img1, m51img2, and m51img3, snimg1 through snimg12
I. Comparing Images By Subtracting
(Step D)
In this first example m51nor is an image of galaxy M51 as it normally
appears. m51fake1 includes a supernova that has been pasted into the m51nor
image. Since they are nearly the same image, there is no need for Aligning
the images (step A), Subtracting Sky Background (step B), or Normalizing
Brightness (step C). To find the supernova, you can immediately go to step D:
find the difference between these two files by subtracting one from another.
Then you can locate the supernova in the Difference File. Fake supernovae
are used in these first exercises to make it easier to learn to use the image
processor tools.
a. Open m51nor and m51fake1 with the contrast (Min/Max) adjusted to show
the spirals.
b. With m51fake1 highlighted, select Subtract
from the Transform menu [Manipulation in old
HOU IP]. For what you would like to subtract
from it, click on Displayed Image and select
m51nor. Click on Display Result in New Window
and OK.
c. With the new Untitled file window highlighted,
click on the supernova and get its position and
data about its increase in brightness by clicking
on Auto Aperture icon in the Analysis area of
the Tools Palette or selecting Auto Aperture
the Analyze menu.
b. First Subtract m51nor from m51fake2, and
click on Display Result in New Window and
OK. You will need this image at the end of
this activity.
c. Select Centroid (Axes in old HOU IP) from
the Analysis menu, click on OK and box a
reference star in m51nor, (a star that appears
in both images). Repeat for m51fake2.
6.1. What is the increase in brightness for the
supernova, in Counts?
6.2. Record the center (x,y) coordinates of your
reference star in each image.
II. Aligning The Images
Before Subtracting
6.3. Calculate how much to shift m51nor so it
matches m51fake2.
Images of a patch of sky may be slightly
shifted from one night to the next if the telescope
has not been aimed exactly to the same set of
coordinates each night. Before using the image
processing Subtract tool, one of the images must
be shifted so the two “match”. For this you use
a second faked image.
a. Open images m51nor and m51fake2. Adjust
the contrast to show the spirals.
Chapter 6: Dramatic Change in Stars
right shift = x(fake image) – x(normal image)
up shift = y(fake image) – y(normal image).
A negative value means shift left or shift down.
d.Now shift the normal image, with no
supernova, so it is aligned with the fake image
that has a supernova candidate. Use Shift
in the Transform menu, enter your Offset
values, and click on Display Result in New
Window and OK.
Hands-On Universe:
63
e. Verify that the shifted image lines up with m51fake2 by checking
that the coordinates of the reference object are the same in both
images.
f. Subtract the shifted image from the fake image.
6.4. What is different between the two subtracted images, the one before
aligning and the one after aligning?
6.5. Can you find the supernova? Record the position and brightness
data.
III. Adjusting for Brightness Differences
In this section you will learn the two operations you must perform
to correct for whole image brightness differences: Sky subtraction and
Normalization.
a. Open images: m51nor and m51fake3. Adjust the contrast to show
the spirals.
b. To be able to see how important the brightness adjustment steps are,
subtract m51nor from m51fake3, without any brightness adjustments,
and click on Display Result in New Window. Keep this image to
compare with your result after the brightness adjustments.
c. Select Sky to find the brightness of the background sky.
e. Subtract sky value from each image. For each image use the ‘Number
of Counts’ option and enter the respective sky value; choose “Display
Result in New Window,” then OK. Sky is now removed from each
image.
Adjust brightness (normalization) in the two
images.
f. Using Auto Aperture, get the brightness
value for a reference star that appears in
both images.
g. Calculate the Normalization factor, N, which
is the ratio of brightness of the reference
star in the two images: m51nor and m51fake3
(the ones with sky removed).
h. Multiply m51nor (with sky removed) by N,
Display Result in New Window, OK.
i. Subtract this normalized image from the
m51fake3 image (with sky removed).
6.6. What is different between the two subtracted
images, the one before adjusting for brightness
and the one after adjusting for brightness?
6.7. Can you find the supernova? Record the
position and brightness data.
Image of M51 from Ewell
Observatory, Belmot, CA
64
Global Systems Science
A Changing Cosmos Chapter 6: Dramatic Change in Stars
IV. SN1990H
Now look at a series of images of a galaxy to detect the presence of a
supernova. The supernova is SN1990H, which was the 8th one discovered in
1990 (H is the 8th letter of the alphabet). The images were taken at two week
intervals in the Spring of 1990.
IV-1. What can you tell by looking at a single image? Open SNW with the
contrast adjusted using Min/Max to bring out the spiral arms of the galaxy.
Can you tell if there is a supernova? Supernovae are very bright objects,
sometimes brighter than an entire galaxy. In this image, there are five or
six very bright objects - are they all supernovae? Not likely. Objects that
are also typically very bright include the galaxy core and foreground stars
in our own Milky Way galaxy that lie in the same line of sight as the far off
galaxy. For most galaxies, we never see single stars within the galaxy from
ground-based telescopes — supernovae are the one exception.
Galaxy cores and nearby stars tend to keep on being bright. A supernova,
on the other hand, changes brightness over time, flaring up and then slowly
fading over a period of a couple of weeks to a couple of months.
6.8. Write down the coordinates of objects you think are likely candidates
to be SN1990H.
IV-2. What can you tell by looking at four images? Open SNW, SNX, SNY
and SNZ with the contrast adjusted to bring out the spiral arms in each
galaxy. Drag the image windows around until you can see all four images
at once.
6.9. Which bright object is the supernova? Write
down its coordinates—note which image
your coordinates refer to. Is it the one you
A. Align the Images:
guessed?
6.10. The images are out of order, in terms of • Get the coordinates for a Reference Star using
Centroid (Axes) to drag a box around the
when each was taken. What do you think is the
foreground star you have chosen. Do this for
proper order of W, X, Y, Z? (It is ambiguous.)
the same star in each image.
Explain your answer.
IV-3. Subtracting Images To Find a Supernova.
You did not need to use more refined tools to
discover SN1990H because it stands out when
you see all four images. However, that is not
always the case. Now try the A, B, C, D process
on these images. In order to make comparisons
there needs to be both a Reference Image
and Reference Star. A Reference Image is one
without a supernova. Use SNX as the Reference
Image. A Reference Star is a steady star, i.e.
one with constant brightness. Choose one of
the bright objects outside the galaxy that is
presumably a foreground star in our Milky Way
galaxy as the Reference Star.
6.11. Which star did you choose as your reference
star?
Chapter 6: Dramatic Change in Stars
• Use Shift in the Transform menu to match all
images to the Reference Image, SNX. Enter
X and Y Offset values so that your Reference
Star’s pixel location will be the same as its
location in SNX. Refer to the Results window
to get the coordinates of the Reference Star
in each image. Enter offsets to two decimal
places.
B. Remove the background skylight:
• Use Sky to get a median background sky Count
for the whole image.
• Use Subtract in the Transform menu. Enter for
‘Number of Counts’ the ‘Sky’ value listed in the
Results window. This value is the mode - the
most frequent brightness value in the image.
After the subtraction the Sky value should be
0 in each image.
Hands-On Universe:
65
C. Normalize the Images (correct for differing observing conditions, high
haze, variation in exposure time):
• Using the Reference Star, calculate the Normalization Factor for each
non-reference image:
(brightness of reference star in reference image)
(brightness of reference star in new image)
6.12. What normalization factor did you compute for SNY? SNW? SNZ?
• With the new image highlighted, go to Multiply in the
Manipulation menu. For ‘Number of Counts’ enter the
value of your Normalization Factor. This should make the
brightness of the Reference Star the same in each image.
Other objects should also have roughly equal brightness,
except for the supernova, which is new.
D. Subtract Images:
• With the new image window highlighted, subtract the
Reference Image from the new image using Subtract
in the Transform menu. Click on Display Result in New
Window. Adjust the contrast — you should be able to bring
out a “lumpy” detail of black and white spots. Variations
within each image account for why the subtracted image
is not all blank except for the supernova.
Look for a Supernova: Identify any new sources of light
using Find in the Analyze menu.
6.13. Record the brightness of the supernova for each image.
6.14. Graph the brightness of SN1990H over time. This plot is called a light
curve. Plot these dates along the x-axis:
SNW: 5/2/90; SNX: 6/2/90;SNY: 4/19/90; SNZ: 5/17/90
and the brightness values from 6.13 along the y-axis. SNX was taken after
the supernova had died out. Give it a brightness value equal to 0, which
relative to its supernova brightness is a reasonable value. Sketch a curve
to connect the points.
V. Light Curve for SN1994i
In the spring of 1994 several HOU students
were studying M51, the spiral galaxy also known
as the Whirlpool Galaxy. In early April, two girls
at Oil City High School in Pennsylvania received
an important phone call. They had serendipitously
obtained the first images of a supernova in M51.
The brightness of the supernova increases
dramatically and then fades off until it is no
longer visible. The rate at which the brightness
increases and then fades is an indicator of what
type supernova has occurred and what type of
star is involved.
Use images taken by HOU students to create
and study a plot of the brightness of a supernova
as it changes over several weeks.
66
Global Systems Science
You’ll choose a reference star and use the
A, B, C, D steps described earlier.
• Open m51img1, m51img2, and m51img3.
These are images of M51, the whirlpool
galaxy. Scott Miller, an HOU student at Oil City
PA requested the first image of M51, m51img1
on February 12, 1994. The core of the galaxy is
the bright spot near the bottom of the image.
The bright spot near the top is a companion
galaxy. Heather Tartara and Melody Spence,
Scott’s classmates, requested the second image,
m51img2, on March 31, 1994, to further study
the galaxy. Heather and Melody received some
surprising news soon after obtaining their image.
The image m51img3 was requested by Vincent
A Changing Cosmos Chapter 6: Dramatic Change in Stars
Prosapio, an HOU student at Alan B. Shepard High School in Palos Heights, IL,
on April 7, 1994.
• Use Log Scaling and adjust the Min/Max on the images to see more detail
within the region of the core of M51 and try to find what all the excitement
was about. It may be quite tricky.
6.15. Use drawings and words to compare the three images.
6.16. Approximately how many times brighter than the Sun is the
supernova?
The core of M51 (the bright spot in the center) is about as bright as a
million Suns. Use Aperture to compare the brightness of the supernova to the
core of the galaxy. Aperture asks you to specify a Star Radius and Sky Radius
each time you use it. For this unit, you may use Star Radius = 7 and Sky
Radius = 14. For more information on Aperture, Star Radius, and Sky Radius
please refer to Supplementary Activity 16: Tools for Measuring Brightness:
Auto Aperture & Aperture.
6.17. Use a new image of M51 requested by your class or a recent image of
the galaxy from the HOU database. Compare the new image to the images
from Spring of 1994. Describe your findings.
• Open images snimg1 through snimg12. It is probably easiest to use one
image at a time and repeat the procedure below for each one.
These twelve images of the supernova were taken in April and early May
of 1994. The date of observation and other information are listed under Image
Info. To create a light curve you must use only images through the same filter.
All these images were taken through the I filter, which lets through infrared
light.
• Find the night number by looking in Image Info and counting the number
of days between the observation date and March 31, 1994.
• Use the bright star at approximately
45° to the lower left of the galaxy
core as a reference star. You may use
Auto Aperture to measure the Counts
for the reference star, but you should
use Aperture for the supernova since
it is so close to the center of the
galaxy. The aperture tool allows you
to specifically define the region for
measuring brightness.
• Divide the Counts for the supernova by
the Counts of the reference star to get
the Count ratio for each night. (See the
Photometry Techniques Discussion Sheet
for more about the Count ratio, BSN/BR
as a measure of brightness changes.)
6.18. Make a light curve for SN1994i by
plotting the Count ratio versus night
number.
6.19. Compare your light curve with those on this page and infer the type
supernova for SN1994i.
Chapter 6: Dramatic Change in Stars
Hands-On Universe:
67
Science of Supernovae
Type I Supernovae
Most stars in the Universe are found in multiple star systems,
meaning that two or more stars are in a gravitational orbit around a
common center point. When these stars are very close together the
material from one star can spill over onto another star, greatly effecting
the evolutionary process of each star. Current theories suggest that
Type I supernovae occur in binary systems containing a white dwarf
and a massive star.
A white dwarf is the very compact remnant of a low mass star
that has burned up all the hydrogen and helium in its core leaving a
very dense remnant of mostly carbon. The outer layers of unburned
hydrogen were blown off during a burst of helium fusion that created
a planetary nebula around the white dwarf. A white dwarf is always
less than 1.4 times the mass of the Sun. Any additional mass will cause
the white dwarf to collapse and create a different type of remnant
called a neutron star.
When a white dwarf is part of a binary, mass can be exchanged
between the white dwarf and its companion. Each star has an imaginary
shell around it within which all matter is gravitationally bound to that
star. Astronomers refer to these regions as the Roche lobes for the
binary system (see figure 1). As the companion star evolves, its radius
will expand due to thermal pressure. This may cause some of its outer
material to overflow its Roche lobe and fall onto the white dwarf.
The white dwarf gains more and more mass by this method until it
reaches the critical threshold of 1.4 times the mass of the Sun, where
it can no longer support itself. In a violent implosion, called a Type
Figure 1
a) A star and its companion white
dwarf within their Roche lobes.
b) The star bloats into a red giant and
its outer layers overflow the Roche
lobes. The overflowing matter falls
onto the surface of the white dwarf.
c) The white dwarf implodes and ignites
fusion causing a bright flash called a
Type I supernova.
Ia supernova, the white dwarf succumbs to the
increased pressure and, in turn, heats up to the
point where it can burn fuel again. This time the
fuel is carbon. The ignition of the fuel results in a
tremendously bright flash, which then fades over
a period of days or weeks. Discoveries of these
supernova have been made out to the edge of the
visible universe.
The critical threshold of 1.4 times the mass
of the Sun is the same for all white dwarfs.
This means that no matter what the mass or
temperature was for the original star, it will
implode with the same amount of fuel left to
burn. Since the mechanism for ignition is the same
and the amount of fuel is the same, it follows that
the luminosity resulting from the rapid ignition is
the same for all white dwarfs undergoing a Type
Ia supernova. Astronomers call such an object a
“standard candle”, meaning that its luminosity
is known so we can use it as a point of reference
from which to compare other objects. We can
observe the apparent brightness of the supernova
68
Global Systems Science
as seen from earth, and knowing its absolute
brightness as a standard candle, we can then
determine its distance away from us.
Type I supernovae are often categorized
as Type Ia, Type Ib, or Type Ic supernovae. The
different letters refer to differences in the specific
elements detected after the explosion and the
rate at which its brightness fades. Theories that
attempt to explain the differences among the
various categories of Type I supernovae focus on
the specific mass of the original star. It is thought
that a Type Ib or Ic supernova may be caused by
the remnant of a very high mass star, such as a
neutron star that is part of a binary system.
A Changing Cosmos Chapter 6: Dramatic Change in Stars
Type II Supernovae
High mass stars undergo even more violent
explosions called Type II supernovae (see
figure 2). High mass stars achieve much higher
temperatures inside so they are able to burn
heavier elements than low mass stars. A very
dense core of iron builds up within the center
of the star as a result of the burning, with the
lighter elements in the surrounding layers. This
configuration is sometimes referred to as an
onionskin model because of the spherical shells
of various elements.
Through energy-producing nuclear fusion,
only elements as heavy as iron can be produced. Any nuclear
reactions producing heavier elements require an input of
surplus energy. Therefore the star only continues to burn
fuel until iron is produced in the core and then fusion stops.
After the fuel runs out, the core cools to the point where the
gravitational pressure causes the star to come crashing in on
itself. The implosion is so strong that the outer layers of the
star crash into the hard iron core and bounce back out with
tremendous energy. This is called a shock wave. The shock
wave ignites the material in the outer layers of the star and
the result is a sudden explosion that can be one billion times
as bright as the original star. The remnant of the core of a
Type II supernova will either be a neutron star or a black hole,
depending on the original mass of the star.
Figure 2:
a) In a Type II supernova the outer layers of a
high mass star come crashing in and
b) bounce off the dense core sending a shock
wave outward.
The intense brightness of a Type II supernova is caused by the
burning of the lighter elements that are in the outer layers of the star.
This material is thrust outward by the explosion, creating an expanding
bright nebula or halo that can remain visible for thousands of years.
The explosion releases such tremendous amounts of energy that the
surplus energy required for nuclear fusion of elements heavier than
iron is available. In fact, it is believed that supernova explosions may
be responsible for the creation of all material heavier than iron or at
least for providing “seed” iron elements that are the fuel for further
nuclear and chemical evolution. This includes elements such as lead,
zinc, gold, and silver.
Chapter 6: Dramatic Change in Stars
Hands-On Universe:
69
Variable Stars
6.20. The six graphs below are graphs of data (light curves) from four different stars. What
is happening at each of these stars that is causing its brightness to change?
A
B
C
D
E
F
What would happen with two stars orbiting each
other (binary star)? What would cause brightness
to change? What factors would affect the shape
of the curve?
70
Global Systems Science
A Changing Cosmos Chapter 6: Dramatic Change in Stars
Investigation
Eclipsing Binary Stars
Many stars in the Universe are multiple star systems. If a binary
star system (two stars orbiting each other) is oriented in space in a
way so that the orbit plane is in line with us on Earth, then the stars
alternately pass in front of and behind one another. If a star goes behind
another star, it is said to be eclipsed (similar to how the Sun is eclipse
by the Moon during a solar eclipse). Such a binary star system is called
an eclipsing binary star.
The American Association of Variable Star Observers (AAVSO)
maintains a database of observations from many observers over many
years. It is a rich source of information. Their Eclipsing Binary Observing
Program is described at http://www.aavso.org/observing/programs/
eclipser/
6.21. Find the longest and shortest period binary system. The most
obvious thing that is different about such eclipsing binary stars other
than brightness and type of star, is the time it takes for the stars to
orbit one another: the period. Mine the data in the AAVSO database to
see if you can find the shortest period binary system and the longest
period binary system. It’s OK to coordinate your efforts with others
to make things go faster.
a. Go to the AAVSO website and pick subject star from the database. To
use the database, you need to know the star name of the eclipsing
binary star. A list of eclipsing binary names is at http://www.
aavso.org/observing/programs/eclipser/
tom/starlist.html
b. A useful gateway is the Published Times of
Minimum Database at http://www.aavso.
org/observing/programs/eclipser/ebtom.
shtml which lists the times of all the eclipses
that have been observed by AAVSO observers.
When you enter a star name and click the
“Get Data” button, a graph appears, but you
might find it easier to use the text file (.txt)
list that is available there also.
c. The date/time used may seem odd to you—
it’s Julian date, which is the time recorded
in days and decimal fractions of days after
a particular time in history: January 1, 4713
BCE. If you want to know the “normal”
calendar date corresponding to any Julian
date, us the Naval Observatory Julian Date
Converter at http://aa.usno.navy.mil/data/
docs/JulianDate.php
6.22. Use information in the database to
predict when there will be an upcoming eclipse
of an eclipsing binary system and then request
a series of images from a HOU telescope to
record the event. Measure the brightness of
the binary compared with reference stars
nearby and then graph the data. If you do this
for successive eclipses, you might see if one
of the stars in the system is brighter or bigger
than the other star by looking at the difference
in drops in brightness and the shapes of the
light curves that you graph. Light curves on
the previous page will give you a sense of that.
Finally, you may wish to analyze a series of images
of a binary star that you can find in the folder
MoreTelescopeImages/VariableStars/CepheidBDCas_ARO_AndEclipsingBinary.
Find late breaking news and information about
Dramatic Change in Stars, supernovae, neutron
stars and black holes at the Staying Up To Date pages
for A Changing Cosmos:
http://lhs.berkeley.edu/gss/uptodate/10acc
Chapter 6: Dramatic Change in Stars
Hands-On Universe:
71
Chapter 7
7. Planet-Star Systems
We wonder “Where did we come from, in the big scheme of things?”
That leads to questions of how our planet began, which in turn leads to
the question, “Where did our Solar System come from?” and “Where did
the Universe come from?” That last question will be a focus of the last
chapter in this book, but the first question is one that some people have
been struggling with for a long time.
Evolution of Solar System Models
People in ancient civilizations observed the heavens with care and
came to a number of conclusions that were excellent in explaining what they
saw in terms of movement of the Sun, Moon, planets and stars. Babylonian
astronomer-astrologers (Chaldeans) kept thorough clay-tablet records of
eclipse observations covering many centuries, as long ago as 26 February
747 BC. They also knew that the lengths of the seasons are not equal. All
early models of the Universe, based on obvious movements of things in
the sky appearing to move around Earth, placed Earth at the very center
of the Universe.
Hipparchus
Hipparchus, a Greek astronomer, geographer, and
mathematician that lived between 147 BC and 127 BC
used Chaldean records to develop good models for the
motion of the Sun, Moon, and planets that predicted
positions used by sailors for navigation. He was the
first to compile a trigonometric table, which he used
in devising solar and lunar theories that could reliably
predict solar eclipses. He measured the differences in
the length of the seasons through equinox and solstice
observations, finding that spring lasted 94.5 days (spring
equinox to summer solstice), and summer lasted 92.5
days (from summer solstice to autumn equinox). That
was an unexpected result since the prevailing idea was
that the Sun moves around the Earth in a circle at a
constant speed. Hipparchus’ solution was to place the
Earth not at the center of the Sun’s motion, but at some
distance from the center— about 1/24 of the radius of
the orbit. That model described the apparent motion
of the Sun fairly well.
Hipparchus
Hipparchus created a star chart with about 850
stars and is perhaps most famous for the discovery of
precession, the slow change in direction of the axis of
rotation of the earth. He also made estimations of the
distance from the Earth to the moon.
72
Global Systems Science
A Changing Cosmos Chapter 7: Planet-Star Systems
Ptolemy
Claudius Ptolemy, Roman astronomer, mathematician
and geographer living in Alexandria, Egypt from approx.
87–150 AD established a model of the Universe based on the
Greek model that would explain the motions of heavenly
bodies well enough to be the standard for many centuries.
Ptolemy’s model still assumed that the Earth was the center
of not only the solar system, but the entire Universe—a
geocentric theory. In Ptolemy’s system, everything orbits
the Earth in the order Mercury, Venus, Sun, Mars, Jupiter,
Saturn. For accuracy in predicting naked eye positions,
it requires at least 80 epicycles, which are smaller orbit
paths superimposed on the main orbits. The stars move on
a celestial sphere around the planetary spheres.
Claudius Ptolemy
Nicolas Copernicus
Christian Church doctrine based on Greek and Roman
philosophers required a solid belief in an Earth-centered
Universe. The idea of a sun-centered system had been
proposed by Aristarchus of Samos around 200 B.C., but
arguments of Greek philosopher Aristotle prevailed, when
he refuted the Sun-centered system with three questions:
(1) If the Earth spun on an axis, why didn’t objects fly
off?; (2) If the Earth was moving (around the sun), why
didn’t it leave behind the birds flying in the air?; (3) If the
Earth was orbiting the sun, why didn’t the stars
appear to change their position since they were
being viewed from a different perspective (the
7.1 What’s wrong with Aristotle’s questions as reasons
phenomenon of parallax)? This last phenomena,
to believe in an Earth-centered universe?
parallax, does occur, but is much too small to
be seen without a telescope due to the extreme
distance to stars. [See chapter 4.]
Statue of Nicolas Copernicus. From “Copernicus and the
Planet position predictions of Ptolemaic Church” http://filer.case.edu/sjr16/pre20th_europe_church.html
model were getting worse and worse over the
centuries. Polish astronomer Nicholas Copernicus
(1473-1543 A.D.), actually a church official,
favored a Sun-centered view of the Universe, yet
he never publicly announced his views until he
was old so as not to be branded a heretic by the
Church, risking prison or even death. Copernicus’
fears were well founded, as witnessed by later
notable proponents of Sun-centered systems,
such as Giordano Bruno (1548–1600 A.D.) who
was burnt at the stake as a heretic by the Roman
Inquisition.
Copernicus recognized that a Sun-centered—
heliocentric—model could easily explain certain
planet movements that were serious problems
for the geocentric system. He organized the five
planets that were known at that time in the order
that we know they are in today: Mercury, Venus,
Chapter 7: Planet-Star Systems
Hands-On Universe:
73
Earth, Mars, Jupiter, Saturn. The moon orbits around the Earth,
he stated, but the stars are distant and don’t revolve around
the sun. Since the Earth rotates around its own axis, the stars
appear to revolve around the Earth in the opposite direction.
Earth moving around the Sun also explained retrograde
motions of the planets much more easily than the epicycles
of the Ptolemaic model. Alas, Copernicus still thought that
the planets move around the Sun in perfect circles, which
is not actually the case, so his model still needed to have
epicycles—quite a lot of them—to make accurate predictions
for the motions of the planets.
http://www.library.usyd.edu.au/libraries/rare/
modernity/copernicus.html
Copernicus’ work, On the Revolutions of the Celestial Orbs
(published in Latin: De revolutionibus orbium coelestium), was
not published until the year of his death and about 73 years
later (1616) the Church placed it on its Index of Prohibited
Books.
Johannes Kepler’s Laws of Planetary Motion
The problems and messiness associated with epicycles
would not be overcome until Johannes Kepler (1571–1630 A.D.)
came to the rescue. Kepler worked with renowned Danish
astronomer, Tycho Brahe in Prague. Kepler was assigned the
task by Tycho Brahe to analyze the observations that Tycho
had made of Mars. Of all the planets, the predicted position of
Mars had the largest errors and therefore posed the greatest
problem. Tycho’s data were the best available before the
invention of the telescope and the accuracy was good enough
for Kepler to show that Mars’ orbit would precisely fit an ellipse.
Kepler inherited Tycho’s post as Imperial Mathematician when
Tycho died in 1601. In 1605 he announced his first law of
planetary motion.
“In the center of everything the sun
must reside; . . . there is the place
which awaits him where he can give
light to all the planets.”
-Copernicus
Kepler’s First Law:
1. Planets move in ellipses with the Sun at one focus.
For a circle the motion is uniform as shown above, but in
order for an object along an elliptical orbit to sweep out the
area at a uniform rate, the object moves quickly when the
radius vector is short and the object moves slowly when the
radius vector is long.
In work starting in 1602, Kepler calculated the position of
the Earth in its orbit and after several years discovered that
an imaginary line connecting the Sun and Earth sweeps out
greater areas when the Earth is closer to the Sun, indicating
Earth is moving faster in its orbit when it is closer to the Sun.
Kepler stated his finding more precisely in his second law.
http://kepler.nasa.gov/johannes/
Kepler’s Second Law:
2. The planet’s radius line describes [sweeps] equal areas
in equal times.
74
Global Systems Science
A Changing Cosmos Chapter 7: Planet-Star Systems
Kepler published his first two laws in 1609 in his book
Astronomia Nova.
It wasn’t until May 15, 1618 that he arrived at his
third law.
Circular and Elliptical Orbits Having the
Same Period and Focus
Kepler’s 2nd Law: The planet’s radius line sweeps equal
areas in equal times.
Kepler’s Third Law:
3. The squares of the periodic times are to each
other as the cubes of the mean distances.
This law he published in 1619 in his Harmonices
Mundi. It can be stated mathematically as follows for
any two planets labelled “1” and “2”:
2
T1
2
T2
=
3
R1
3
R2
where
T1 = period of planet 1
T2 = period of planet 2
R1 = orbit radius of planet 1
R2 = orbit radius of planet 2
7.2 Assuming Earth’s period is 1 year and its orbit
radius is about 150,000,000 km, using Kepler’s
3rd law,
(a) what is Mars’ orbit radius if it takes 687
days to orbit the Sun and
(b) how long is Jupiter’s year if it’s distance
from the Sun is about 780,000,000 km?
For elliptical orbit,
speed decreases with
distance from the Sun.
For circular orbit,
speed remains
constant
Illustration of Kepler’s Second Law of planetary motion. Here
we see two orbits with the same focus point (“center”) semimajor axis (“diameter”), and orbital period: one a circle with an
eccentricity of 0.0; the other an ellipse with an eccentricity of 0.8.
Eccentricity is a measure of how “skinny” an ellipse is, with a
circle having an eccentricity of “0” being the “fattest” kind of
ellipse, and the very “skinniest” of ellipses having eccentricities
approaching “1.” An animated version of this diagram is on this
web page http://kepler.nasa.gov/johannes/
Galileo Galilei
Italian mathematician, physicist, and
astronomer, Galileo Galilei (1564–1642 A.D.)
was a contemporary of Johannes Kepler and a
kindred spirit, to boot. Using the newly invented
telescope, Galileo discovered moons of Jupiter,
mountains and craters on the Moon, phases of
Venus, and sunspots. Some of these observations
supported the Copernican heliocentric theory.
In 1610, Kepler heard of Galileo’s discoveries,
and though they did not have any rapid means
of communication, like Internet, telephones,
or e-mail, Kepler published a letter of support
for Galileo: Dissertatio cum Nuncio Sidereo
(“Conversation with the Sidereal Messenger”).
He also obtained a telescope and published his
observations of Jupiter’s satellites: Narratio de
Observatis Quatuor Jovis Satellitibus (“Narration
about Four Satellites of Jupiter observed”).
These were enormous support to Galileo, whose
discoveries were doubted or denied by many.
Kepler encouraged Galileo to publish his
discoveries and conclusions (see excerpts of
letters on the following page), but when Galileo
published papers that said that the Universe is
Chapter 7: Planet-Star Systems
Galileo Galilei
Original portrait by
Justus Sustermans
painted in 1636.
heliocentric, he was brought before the Inquisition
and accused of being a heretic (1616) for opposing
the Church’s teachings. He was cleared of the
charges but told to keep quiet. When Galileo
published a book in 1632 that indirectly supported
the heliocentric theory, he was again called before
the Inquisition and found guilty of heresy, forced
to recant what he had said, and sentenced to life
imprisonment. Because of his age, he was placed
under house arrest and continued working and
experimenting until his death on January 8, 1642.
Hands-On Universe:
75
[Galileo to Kepler, 1597] ....Like you, I accepted the Copernican position several years
ago and discovered from thence the causes of many natural effects which are doubtless
inexplicable by the current theories. I have written up many of my reasons and refutations
on the subject, but I have not dared until now to bring them into the open, being warned by
the fortunes of Copernicus himself, our master, who procured immortal fame among a few
but stepped down among the great crowd (for the foolish are numerous), only to be derided
and dishonored. I would dare publish my thoughts if there were many like you; but, since
there are not, I shall forebear....
[Kepler to Galileo, 1597] .... You advise us, by your personal example, and in discreetly
veiled fashion, to retreat before the general ignorance and not to expose ourselves or
heedlessly to oppose the violent attacks of the mob of scholars....
But after a tremendous task has been begun in our time, first by Copernicus and then by
many very learned mathematicians, and when the assertion that the Earth moves can no
longer be considered something new, would it not be much better to pull the wagon to its
goal by our joint efforts, now that we have got it under way, and gradually, with powerful
voices, to shout down the common herd, which really does not weigh the arguments very
carefully? Thus perhaps by cleverness we may bring it to a knowledge of the truth. With
your arguments you would at the same time help your comrades who endure so many
unjust judgments, for they would obtain either comfort from your agreement or protection
from your influential position. It is not only your Italians who cannot believe that they
move if they do not feel it, but we in Germany also do not by any means endear ourselves
with this idea....
Be of good cheer, Galileo, and come out publicly. If I judge correctly, there are only a few of
the distinguished mathematicians of Europe who would part company with us, so great is
the power of truth. If Italy seems a less favorable place for your publication, and if you look
for difficulties there, perhaps Germany will allow us this freedom.
Source: Giorgio de Santillana, The Crime of Galileo (1955).
Isaac Newton
If Kepler provided the most accurate descriptions of planet orbits,
it was not until the work of Sir Isaac Newton (1643 -1727 A.D.) that
the orbit motions would be explained in his theory of universal gravity.
Newton made many other discoveries and inventions including:
• white light, when passed through a glass prism, can be seen to be
made of a spectrum of colors--red, yellow, green, blue, violet
• the first reflecting telescope
• three Laws of Motion (see next page for complete description)
In 1666, Newton made the breakthrough of imagining that the
Earth’s gravity extended to the Moon. Using Kepler’s third law of
planetary motion, Newton deduced that there is a force (known as
centripetal force) holding the Moon (or any planet) in orbit, and that
force depends on distance in a certain way. If the distance is doubled,
the force becomes one-fourth as much; if distance is tripled, the force
becomes one-ninth as much. In general, if distance increases by a factor
of “n,” the force decreases by a factor of 1/n2, a relationship known as
the inverse square law. Newton also showed that Kepler’s second law
(that the line joining a planet to the sun sweeps out equal areas in equal
times) can be explained by the fact that a body moving in an elliptical
path and attracted to one focus must indeed be drawn by a force that
varies as the inverse square of the distance.
76
Global Systems Science
A Changing Cosmos Chapter 7: Planet-Star Systems
Newton ultimately concluded that this
applies to all objects, and it became the
Newton’s Laws of Motion
Law of Universal Gravitation: Every object in the
Universe attracts every other object with a
force directed along the line of centers for the
two objects that is proportional to the product
of their masses and inversely proportional to
the square of the separation between the two
objects. The mathematical relation is:
Newton’s First Law of Motion:
I. Every object in a state of rest or in uniform
motion tends to remain in that state unless an
external force is applied to it.
Fg = G (m1m2)/r2
Newton’s exact words were “Every body perseveres
in its state of rest, or of uniform motion in a right
line, unless it is compelled to change that state by
forces impressed thereon.” This is often called the
“Law of Inertia” and is a concept that Galileo first
elucidated.
where: Fg is the magnitude of the gravitational
force between the two objects,
To understand Newton’s second law of motion,
it’s helpful to know that
• G is the gravitational constant,
(a) a force is a push or pull on an object,
• m1 is the mass of the first object,
(b) an object’s speed in a particular direction is known
as the object’s velocity (in other words, velocity is
both speed and direction of motion), and
• m2 is the mass of the second object,
• r is the distance between the objects.
The constant of proportionality G is known as
the universal gravitational constant. It is termed
a “universal constant” because it is thought to
be the same at all places and all times and thus
universally characterizes the intrinsic strength of
the gravitational force.
Given the law of gravitation and the laws
of motion, Newton could explain a wide range of
seemingly unrelated phenomena such as
• apples falling from trees,
• cannon balls falling to the ground at some
distance after being fired,
• the orbit of the Moon, planets, and the
eccentric orbits of comets,
• the causes of the tides and their major
variations,
• the precession of the Earth’s axis,
• the subtle change in motion of the Moon
caused by Sun’s gravity.
Newton’s one system of laws of nature
gave order to most of the known problems of
astronomy and terrestrial physics. The work of
Galileo, Copernicus, and Kepler was united and
transformed into one coherent scientific theory.
The new Copernican world-picture finally had a
firm physical basis.
Chapter 7: Planet-Star Systems
(c) a change in an object’s velocity is known as
acceleration. For example, if you are in a car that
goes from a speed of zero to 50 mph in 5 seconds,
you and the car have experienced an acceleration
of 10 mph/sec.
Newton’s Second Law of Motion:
II. The acceleration of an object is proportional
to the force on it and is in the direction of that
force.
Newton’s exact words were “The alteration
of motion is ever proportional to the motive force
impressed; and is made in the direction of the right
line in which that force is impressed.” Mathematically,
Newton’s Second Law is often stated as follows:
If a force (F) is exerted on an object of mass (m),
then the object undergoes an acceleration (a) in direct
proportion to the force:
F = ma Newton’s Third Law of Motion:
III. For every action there is an equal and opposite
reaction.
This law is exemplified by what happens in the
recoil of a gun that people so often see in TV shows
and movies. When the bullet fires off in one direction,
the gun recoils in the opposite direction: “an equal and
opposite reaction.”
Hands-On Universe:
77
Investigation
Tracking Jupiter’s Moons
Galileo discovered the four largest moons of Jupiter in 1610, and
they are often referred to as the Galilean Moons. He was using a simple
telescope and a keen mind. It is a testimony to his observational prowess
that out of all the stars and bright objects he could see in the sky, he
noticed that Jupiter and these four dimmer lights, which he assumed
were stars, were stretched out along
a straight line. When he looked again
he saw that the positions had changed
from one night to the next, which is
not what stars do. After repeated
observations he determined that they
were moons orbiting around Jupiter.
Materials:
• HOU IP
• Images: jup20020122_0000.fts and
jup20020122a through i
I. Find the Moons
• Open jup20020122a and jup20020122b
with the contrast adjusted using Min/Max
so the moons are visible. To help keep
track of the moons, refer to them as #
1, 2, 3, & 4, starting from the bottom of
the window.
7.3. Record your image settings.
7.4. Which Direction is Each Moon Moving?
Make a sketch of the jup20020122a
image, or use the Print option in the File
menu, then draw an arrow at each moon
showing whether it appears to be moving
closer to or further away from Jupiter.
You can tell by eye which direction the
two moons shown closest to Jupiter are
moving. A way to answer this question
for the other two moons is to compare
position coordinates. Use Find in the
Data Tools menu with the default setting.
Do this for both images.
Adding two images together to make a double
exposure is another way to compare the positions of
the moons in two images taken an hour apart.
• Starting with jup20020122a as the active window,
use Add in the Transform menu (or + in the Tool
Palette). Click on Displayed image and scroll
down to select jup20020122b for what to add.
Click on Display result in new window.
• If you want to save this double image, select Save
As from the File menu and enter a new file name
including your initials, such as “jupab-jd”.
• Use Find to get the brightness Counts for the Sky
and the moons in all three images.
7.5. Adding the two images made the Sky about twice
the value in either image. The moons, however, are
not twice as bright. Why?
7.6. Which image did each moon come from? Compare
moon coordinates in the double image with moon
coordinates in one of the single images. Make a
sketch, or Print out a copy, of the double image
and draw in arrows from the jup5 position to the
jup6 position of each moon.
78
II. Making a Double Exposure
Global Systems Science
A Changing Cosmos Chapter 7: Planet-Star Systems
III. What Happens to the Moons During 6 Hours?
You need to collect data on the
positions of each of the moons in each
of the 10 Jupiter images, jup20020122a
through i taken at 1 hour intervals.
7.7. For each image check the Image
Info (under Data Tools) and record
the date and time that the image
was taken. Date is day/month/year
and time is Universal Time, UT. Make a quick sketch of the image. Universal
Time is the time in Greenwich England.
• In order to see how each moon moves during the time sequence represented by
the six images, combine all six images into one composite image. This may be
done in several ways: by adding all of them together at one time; by adding
them together one at a time and checking after each addition; by subtracting
some and adding some. You may think of some other ways. Try whatever you
like. Once again keep a careful record of all that you do, including the names
of the files you create and how you create them. Remember, your goal here is
to create an image or images that will allow you to see as clearly as possible
how these Moons are moving.
Here are ways to collect moon position data; you may think of more.
4Use the cursor to get the coordinates for the
positions of each moon.
4Use Slice in the Analyze Tools menu to get
the number of pixels between each moon
and the center of Jupiter or between moon
positions. (It helps to make the Slice window
larger.) Drag the cursor on the Slice graph
to display values for distance along the
Slice in pixels and brightness in Counts.
Corresponding pixel (x,y) coordinates and
Counts are shown in the Status Bar - be sure
you understand the differences between the
(x,y) values for the Image window and the
values shown on the Slice graph.
7.9. Identify on your sketch the orbits in which
each moon is traveling by putting the number of
the moon at its initial position in jup20020122a
and in its last position in jup20020122i.
4Use Find to get cursor coordinates for all
six positions of each moon, and use the
Pythagorean Theorem to compute distances
and speed. A hand calculator helps here.
7.11. Record the direction and speed of each
moon. Your units of speed will be either pixels/
hr or mm/hr, depending on your method of
collecting the data.
7.8. Make a sketch (or printout, if possible) of your
composite image. If you sketch it, please take
enough time so that it’s clear to someone else
who looks at it. Share your results with other
groups around you and see what approach they
used that might be different from yours. This
is particularly valuable as you begin to answer
the questions below.
Chapter 7: Planet-Star Systems
7.10. Which moon(s) appear to be traveling the
fastest? Slowest? Does this depend on the
portion of the orbit you are examining? Explain
your reasoning.
7.12. How do you explain the apparent paradox
that, despite the fact that the moons all move
at roughly constant speeds around Jupiter in
almost circular orbits, your data shows that
the speed seemed to change?
7.13. Draw a top view of Jupiter and each moon
in its 10 successive positions.
Hands-On Universe:
79
IV. Interpreting Your Data
The four moons Galileo discovered in 1610 are named Io, Europa,
Ganymede, and Callisto. This table shows the period and orbit radius
for each moon. The period is the time for one complete
revolution.
Moon
One more piece of information: the further the orbit
from Jupiter, the slower the speed of the moon. This is
Io
because Jupiter’s gravity weakens with distance.
Europa
7.14. Who Is Io? For each moon, see if you can match the
Ganymede
name with its number. Use a process of elimination,
Callisto
crossing out numbers that are not candidates.
Period
(days)
1.8
3.5
7.2
16.7
Orbit Radius
(km)
421,600
670,900
1,070,000
1,883,000
7.15. Explain how you decided on the name for each
moon.
The moon Io.
The moon
Europa.
The moon Ganymede
The moon
Callisto
80
Global Systems Science
A Changing Cosmos Chapter 7: Planet-Star Systems
V. The Mass of Jupiter
By analyzing images of Jupiter and its moons, you can
determine values for the variables D and T in the equation
below and solve for the mass of Jupiter, MJ.
MJ =
2
4π D
G T2
Information Box
3
1 degree = 60 arc minutes:
1° = 60’
1 arc minute = 60 arc sec:
In this equation, D is the radius of orbit of one of
1’ = 60”
Jupiter’s moons and T is the time it takes the moon to
complete one orbit (the orbital period). G, the constant
1 pixel = 0.63 arcsecs (Plate scale for
of universal gravitation, has a currently accepted value of
telescope that took this image)
G = 6.67 x 10-11 m3/kg-sec2. Note that this equation looks
1 radian = 57.3 degrees
exactly like Kepler’s Third Law, as modified to incorporate
= 206,265 arcsec
Newton’s universal gravitation constant—it applies to any
Distance from Jupiter to Earth in
central body that is being orbited by a much less massive
object; e.g., The Hubble Space Telescope orbiting the Earth,
jup5-jup10 images: 6.63(108)km
a moon around a planet, one of the planets around the sun,
1 km = 1000 m
or the sun around the center of our Milky Way galaxy. In all
these cases the mass of the orbiting body is insignificant
compared to the mass of the central body, and as you can see, its
mass is not even included in the equation. If the mass of the orbiting
body were significant, it would be orbiting around a common center,
and a different equation would be needed.
7.16. As a practice problem, use the equation
above to find the mass of the Earth in kilograms
given the following observational data. The
period of the Moon around the Earth is 27.3
days and the mean radius of its orbit is 384,000
km. Use meters for the units of D and seconds
for T.
Determining the mass of Jupiter
a) You need the distance data you determined
in the Tracking Jupiter’s Moons Unit for the
images jup5 through jup10. Distances need to
be in pixels; go back to the Tracking Jupiter’s
Moons Unit and redo this if your original
measurements were in millimeters.
b) For each image you also need to know the
time of day of the exposure. Use Image
Info in the Data Tools menu. Time is given
as Universal Time, UT, which is the time at
Greenwich, England. Universal Time is based
on a 24-hour clock rather than our familiar
12 hour ones.
7.18. For all four moons in all the images, plot
the pixel distance from the center of Jupiter
versus the time the image was taken.
7.19. What does the plot you made above
represent?
7.20. Use your plot to estimate the maximum
distance for the moon that reaches its turnaround point; i.e., the moon that seems to
stop getting further away from Jupiter.
Your pixel distance from question 7.7 can
actually be thought of as the angle subtended
by imaginary lines connecting Jupiter and
its moon. Line D is the radius of the moon’s
orbit.
We can use this “pixel angle” to find the
radius, D, in km once we convert the pixel
value of Angle A to units of radians.
7.17. Organize your distance and time
data in a neat table before you
proceed. Call the distances for the
moons to the left and below Jupiter
in the image negative (-) and the
distances to the right and above
Jupiter positive (+).
Chapter 7: Planet-Star Systems
Hands-On Universe:
81
7.21. Convert the pixel value you found above to radians using the
Information Box on the previous page.
7.22. Use the Small Angle Approximation (pp. 26–29) to determine
the radius of the moon’s orbit in kilometers.
D= dxA
where D is the radius of the moon’s orbit, d is the
distance from Earth to Jupiter at the time the
images were taken, and A is the angular distance
of the moon from Jupiter in radians.
This is the value for one of the two variables you need in order to
solve for the mass of Jupiter. To determine the period of the moon,
which is the other variable, T, you need to extrapolate from your
data by sketching what you think the graph would look like with
data for more hours. Use your extrapolation to estimate the time
for one quarter of an orbit and for one half an orbit.
7.23. Use your estimates of time for 1/4 and 1/2 an orbit to determine
the period of the moon.
7.24. Estimate how much possible error there is in your value for the
period and explain how you made your error estimate.
7.25. You now have the period and radius for one of the moons. Use
this information to determine the mass of Jupiter from the equation
for MJ. Use meters for the units of D and seconds for T.
7.26. Find a data table and look up the currently accepted value for
the mass of Jupiter. Determine the percent difference between the
accepted value and your calculated (experimental) value using the
following equation:
% Difference =
accepted value - experimental value
accepted value
x 100%
Wrap Up:
7.27. Design an experiment that would allow you to obtain a more
accurate value for the mass of Jupiter. Be specific.
82
Global Systems Science
A Changing Cosmos Chapter 7: Planet-Star Systems
How Do Star-Planet
Systems Form?
M42, the Great Nebula, star forming region in Orion
To finish the story that was begun at the
beginning of Chapter 3, a nebula — a huge cloud
of gas and dust in space — starts to collapse, with
gravity pulling the gas and dust together. The
explosion of a nearby star (a supernova), may
generate shock waves in space which squeeze the
cloud and trigger the collapse. Just like a dancer
that spins faster as she pulls in her arms, the cloud
spins faster and faster as it collapses.
Space Telescope Science Institute
http://hubblesite.org/gallery/album/
At the same time, the
cloud gets hotter and denser
in the center and forms into
a disk that gets thinner and
thinner.
When the center of the cloud gets
hot enough, nuclear reactions start
occurring and a star, like the Sun, is born.
The star not only radiates heat and light
but blows its own particles outwards,
pushing out remaining gas and dust of
the new star system with sort of wind
called a stellar wind.
Chapter 7: Planet-Star Systems
Image of NGC 281 taken with NASA’s Hubble Space Telescope
in October 2005 shows an example of dense knots of dust and
gas in our Milky Way Galaxy. This is part of an emission nebula
and star-forming region located nearly 9,500 light-years away in
the direction of Cassiopeia. Image is a region about 6 LY across.
The dark, opaque knot of gas and dust is an example of a “Bok
globule,” cosmic dust and a concentration of elements responsible
for the formation of stars.
Hands-On Universe:
83
Giant planets, rocky planets, asteroids,
comets, meteoroids.
Meanwhile, particles have been colliding and
sometimes sticking together in clumps, eventually
forming planets and moons. Two main types of planets
form: smaller planets of mostly rocky material (e.g.
Earth, Venus, Mercury and Mars), and large planets
made of icy material and gas (e.g. Jupiter, Saturn,
Uranus, and Neptune). Other icy material settles in
the outer regions of the disk along with rocky material,
where they form a myriad of smaller bodies.
We often refer to two types of planets, rocky
planets and giant planets, but there is really a whole
range of size of objects, all the way from dust grains to
the giant planets. The smaller bodies are mixtures of
different kinds of rock and ice—not just water ice, but
other types as well, such as ammonia ice. Historically,
small rocky bodies have been referred to as asteroids,
while the icy bodies, that partly vaporize and form long
beautiful tails when they travel to the inner parts of
the solar system, are referred to as comets.
[Not to scale]
Giant planet
Rocky planet
Giant planets in our solar system are
Jupiter, Saturn, Uranus, and Neptune.
The rocky planets are
Mercury, Venus, Earth and Mars.
Very small bodies, either icy or rocky are
called meteoroids. When a meteoroid falls
into Earth’s atmosphere, it interacts with the
atmosphere, heats up and leaves a streak of light
in the sky that is called a meteor. If it makes it
all the way to the ground, the rocky visitor from
space is called a meteorite.
Studying meteorites, which are thought to be
left over from this early phase of the solar system,
scientists have found that the solar system is
about 4.6 billion years old.
A Galileo spaceraft image of Jupiter’s moon Callisto, showing
evidence of a chain of craters that may have resulted from a
fragmented comet similar to Comet Shoemaker Levy 9.
84
Global Systems Science
Hubble space Telescope image of
Comet Shoemaker-Levy 9 fragments
before they collided with Jupiter.
A Changing Cosmos Chapter 7: Planet-Star Systems
Image of asteroid Eros. Courtesy NASA,
Near Earth Asteroid Rendezvous (NEARShoemaker) mission. Asteroids are solar
system bodies that are smaller than planets—
anywhere from the size of a boulder to a few
hundred miles in diameter.
Investigation
Asteroid Searches
In Chapter 1, we saw how asteroids can be
major threats to the well being of life on Earth.
You can find out more about the NASA efforts
concerning near Earth asteroids at the NASA Ames
Research Center’s Asteroid and Comet Impact
Hazards page
http://impact.arc.nasa.gov/
You can join the Hands-On Universe Asteroid
Search, which began as a research project started
by high school teachers Hughes Pack and Tim Spuck
in 1996. In October of 1998 students at Northfield
Mount Hermon School in western Massachusetts,
USA, discovered a faint and distant Kuiper Belt
object, now known as 1998 FS144. The project has
used images from large telescopes, observatory
archives, and small telescopes for asteroid
tracking, searching, and discovery. The web site
currently has four main options.
Current status of the Hands-On Universe
research projects can be found through the
“Staying Up to Date” pages for A Changing Cosmos
chapter 7
http://lhs.berkeley.edu/gss/uptodate/10acc
The worlds come into being as follows: many bodies
of all sorts and shapes move from the infinite into a
great void; they come together there and produce a
single whirl, in which, colliding with one another
and revolving in all manner of ways, they begin to
separate like to like.
—Greek philosopher (atomist),
Leucippus (~480-420 B.C.)
Chapter 7: Planet-Star Systems
For example, the International Astronomical
Search Collaboration (http://iasc.hsutx.edu/) is an
educational outreach program for high schools and
colleges, provided at no cost to the participating
schools. IASC (“Isaac”) a collaboration of
• Hardin-Simmons University (Abilene, TX),
• Hands-On Universe, (HOU - Lawrence Hall of
Science, University of California, Berkeley),
• Astronomical Research Institute (http://ari.home.
mchsi.com in Charleston, IL), and
• Astrometrica (H. Raab, Austria).
Most recently, HOU collaborates the
NASA WISE mission (Wide-field Infrared Survey
Explorer)
http://wise.ssl.berkeley.edu/mission.html
WISE will survey the whole sky in infrared
light, producing an all-sky image atlas and
catalogue of over 300 million infrared sources.
In addition to asteroid research, WISE scientists
will study the coldest and nearest stars, regions
of new star and planet formation, the structure
of the Milky Way Galaxy, Ultra-luminous infrared
galaxies, and the large scale structure of the
Universe.
Find late breaking news and information about PlanetStar Systems at the Staying Up To Date pages for A
Changing Cosmos:
http://lhs.berkeley.edu/gss/uptodate/10acc
Hands-On Universe:
85
8. Search for Habitable Planets
We know of one habitable planet in the Universe, habitable
meaning suitable for supporting life such as that we are familiar with.
That one habitable planet is our own: Earth. For centuries, some
people have speculated that there may be many many such planets
in other planet-star systems. Until the latter part of the 20th century,
there was no evidence that planets of any sort around other stars even
existed, much less habitable planets like Earth. That’s not surprising.
It’s nearly impossible to see exoplanets because they are very
distant, very faint and lost in the overwhelming glare of the
stars they orbit. As of July 2007, only four exoplanets were
observed with direct imaging methods—planets that were very
large and orbiting very faint stars with very large orbit radii.
But although we cannot easily observe exoplanets directly,
we have detected lots of them by certain effects they have
on the stars they orbit. Here are the main methods that have
been thought of:
Chapter 8
Planets orbiting other stars are called
exoplanets, or extrasolar planets.
Planets in any way similar to Earth are
called terrestrial planets.
8.1 What factors make a planet
habitable?
The first detection of extrasolar planets was made by
Alexander Wolszczan in 1994 by measuring the periodic change
in arrival time of radio pulses from a pulsar—an incredibly
dense neutron star, which is the remains of a supernova, that
normally emits very regular pulses of radio waves.
Geoffrey Marcy (right) and Paul Butler
Most exoplanet discoveries have been the result of looking for
at Lick Observatory, where they made
movement of the “parent” star. In Kepler’s Laws, the Sun is fixed at a
their first exoplanet discovery in 1987:
point in space and the planet revolves around it. But why should the
70 Virginis b in the constellation Virgo
Sun be thus privileged? Kepler had rather mystical
and 47 Ursae Majoris b in the Big
ideas about the Sun that justified its special place.
Dipper. (photo: Mickey Pfleger)
However Newton, in connection with his 3rd Law,
showed that the Sun does not occupy a privileged
For up-to-date accounting of all exoplanet
position. As a planet orbits its star, its gravity
discoveries, see The Extrasolar Planets Encyaffects the star so that the two bodies actually orbit
clopaedia at http://exoplanet.eu/
each other. Of course the larger body dominates
and the smaller body moves a lot more. But the
small movement of the star as the orbiting planet
tugs on it can in theory be detected in two ways:
(1) If the star alternately moves towards us and
The other practical way to discover
away from us, its spectrum should shift slightly
back and forth, alternately towards the blue end exoplanets is to watch the periodic dimming of
then towards the red end—a spectroscopic shift. the star caused by a planet passing in front of
(2) We should be able to see the position of the the star—an event known as a transit. Measuring
star shift as well. Accurate measurement of position brightness is known as photometry. This method
is known as astrometry. Spectroscopes have in theory, with four years of observing, could
been used to detect star spectrum shifts caused detect planets about half the mass of Earth in a
by orbiting giant planets. From ground-based 1 AU radius orbit about a sun-like star or a Mars
observatories, spectroscopists can measure shifts mass planet in a Mercury-like orbits. Planets
due to velocity changes as small as 3 m/sec. This with orbital periods greater than two years are
corresponds to a planet at least 33 times the mass of not readily detectable, since their chance of
Earth orbiting a Sun-like star. No exoplanet being properly aligned along the line of sight
detections have been confirmed using astrometry, to the star is very small. Photometry is the only
but there have been many exoplanet discoveries practical method for finding Earth-size planets in
the habitable zone.
with the spectroscopic method.
86
Global Systems Science
A Changing Cosmos Chapter 8: Search for Habitable Planets
Investigation
Exoplanet Transits
Plot and analyze a light curve for a planet
transit. Then, from transit data, find out critical
properties of a planet that could make the
planet habitable or not.
This is a rather idealized light curve—most
are quite a bit more rough or difficult to
discern the brightness drop.
Materials
• HOU IP software and computer
• 19 Images of star SAO_107623 *
These are 19 observations of a star named
HD209458 during a transit. This was the very first
star for which planet transits were observed.
The planet had already been discovered by the
spectroscopic method. The planet is known as HD209458b. Planets around a
star are designated by a letter of the alphabet, with the star taking the letter
“a” and each orbiting body taking a letter in the order of their discovery.
Thus, HD209458b is the first planet discovered around star HD209458. Each
image is really 20 or so images “stacked” on one another so that “noise” in
the resulting image is kept to a minimum.
First let’s have another look at graph E of the light curves near the end
of chapter 6.
8.2. What would determine how much dimming occurs during a transit of a
planet in front of a star?
Check the “Staying
Up To Date”
web pages for A
Changing Cosmos
chapter 8
http://lhs.berkeley.edu/gss/
uptodate/10acc
for possible new
sets of images for
Exoplanet Transits.
8.3. What would affect how long the transit lasts?
8.4. What would determine how often a transit occurs?
8.5. What properties of a planet could we tell from observations of transits?
I. Plot a Transit Light Curve
In order for a planet transit to be observed:
• The planet’s orbital plane must be in line with
our view of the star (as with eclipsing binary
stars).
• The planet must be large enough for us to detect
a drop in brightness. Earth based observations C. Find reference star(s). The bright star about 45°
to the upper right of HD209458 (x = 564, y = 266)
can detect a drop of 1% from a transit of a
can be a reference star. Even better reference
Jupiter sized planet.
stars are at (x = 185, y = 181) or (x = 311, y =
With each of the nineteen images of HD209458,
276).
use the following procedure (like the Finding
8.6. Using Aperture, measure and record the Counts
Supernova investigation—Chapter 6)
of HD209458 and the reference star. Then divide
A. Find the time of each image from the Image
the Counts for HD209458 by the Counts of the
Header Info. Find the difference, in minutes,
reference star to get the Count Ratio for each
between the observation time and the time of
image. Make a light curve for HD209458 by
the first image (i.e. 10/20/2001, 3:06 UT).
plotting the Count Ratio versus time (in min).
B. Identify the correct star on the image. Use your
Before graphing, look at the range of Count
judgment (or a finder map if available). For the
Ratios and optimize the range of y-axis values
image set of star SAO_107623, the star that is
(maximum value just above the highest Count
the brightest is HD209458, so take some Counts
Ratio and the minimum value just below the
measurements using the Aperture tool.
lowest Count Ratio on the axis).
Chapter 8: Search for Habitable Planets
Hands-On Universe
87
II. Examine the Light Curve
DURATION
8.7 If you do not have data for a full transit, is there any way you could
still determine the transit duration?
8.8 What was the duration of the transit you plotted in Part I?
8.9 Would the duration be the same for all transits of a given star-planet
combination?
TRANSIT DEPTH
Transit Depth is the dip in the light curve. This is the drop in
brightness of the star as a planet passes in front of it.
8.10 What is the Transit Depth (TD)—the maximum dip in brightness— of
the transit you plotted in Part I, expressed as the ratio between the
brightness before the transit and the brightness at the deepest point
in the curve?
TD = fraction decrease in brightness of the star due to the transit
= (B1- B2)/B1 or (C1- C2)/C1 [B = brightness; C = Counts]
8.11 What makes it difficult to find the Transit Depth for this planet?
III. Find the Planet’s Size
The transit depth (TD) is related to the size
of the planet in a very simple way: the area of
light blocked when the planet transits is exactly
the area of the apparent disk of the planet. So,
the ratio of area of planet disk to star disk should
directly determine the drop in brightness.
TD = (area planet)/(area star)
Since area = πr
TD = (πrplanet 2)/(πrstar 2 )
TD = (rplanet /rstar )2
2
,
8.12. What is the radius of planet HD209458b?
First find the radius of star HD209458a (from
Internet or clues from teacher or colleagues),
and then use the transit depth equations in both
II and III to find the radius of the planet]
Size Matters
The size of the planet gives us crucial
information about its possible habitability. It’s
a little like the Goldilocks story.
If the planet is too small (like Mercury
or Mars), it will not have enough gravity to
hold on to an atmosphere—gas molecules will
escape the planet over a time-span of not
many years in the lifetime of the planet-star
system.
If the planet is too large, it will retain a
huge amount of atmosphere and have crushing
atmospheric pressure, like the giant planets
Jupiter and Saturn.
PERIOD
8.13. What does Kepler’s Third Law tell us about
how the period of a planet is related to its
distance from a star?
One light curve cannot show the period of the
planet. The star must be observed for many
days, weeks or months in order to establish
that the transits occur in a regular period.
IV. Find the Distance of
the Planet from its Star
8.15 Using Kepler’s Third Law, what is the orbit
radius of planet HD209458b in Astronomical
Units?
8.14. What is the period of planet HD209458b?
(Use library or Internet search.)
88
Global Systems Science
A Changing Cosmos Chapter 8: Search for Habitable Planets
Distance Matters
The distance of the planet from its star
gives us crucial information about its possible
habitability. Again, it’s like the Goldilocks
story, but an even closer analogy, since the
“soup” will be either too hot or too cold for
life. More precisely, the temperature must be
in the range to allow for liquid water, which is
an essential ingredient for nearly all life forms
that we know of. If the planet is too close to
its star, all water vaporizes, and if the planet
is too far from its star, water is all frozen.
To find out about the NASA mission to find
Earth-size exoplanets, see the Kepler mission
website - http://kepler.nasa.gov
b-v
Surface
magnitude Temperature
(Kelvin
-0.31
34,000
-0.24
23,000
-0.20
18,500
-0.12
13,000
0.00
9,500
0.15
8,500
0.29
7,300
0.42
6,600
0.58
5,900
0.69
5,600
0.85
5,100
1.16
4,200
1.42
3,700
1.61
3,000
V. Conclusion—Is the
Planet Habitable?
8.16. What factors besides distance from star
might impact the temperature of a planet?
8.17 Is planet HD209458b habitable? Justify your
answer with results from parts I through IV of
this investigation.
More advanced exoplanet investigation
Visit the TransitSearch website - http://www.
transitsearch.org - to find and download data on
exoplanets with observed transits. Find the time
between consecutive transit observations to find
period. Find the transit depth. If possible, get
information about the parent star to determine
the size of the planet and its orbit radius.
Visit the Sloan Digital Sky Survey (SDSS) web page on Calculating the radius
of a star - http://cas.sdss.org/dr6/en/proj/advanced/hr/radius1.asp. See the
meaning and derivation of a formula that can be used to compute a
star’s radius in relation to our Sun’s radius:
R/Rs = (Ts/T)2(2.51)
(ms-M)/2
Where R = star radius
T = Temperature of the star
Rs = Sun’s radius
Ts = Temperature of the Sun
M = absolute magnitude of the star
ms = absolute magnitude of the Sun = 4.83
Relationship of b-v magnitude and temperature is in chart at left.
Absolute magnitude is
M = m - 5 log d + 5
Where d = distance to the star in parsecs.
Use the Hipparchos skyplot to find parallax, distance to star,
and compute absolute magnitude - http://www.rssd.esa.
int/?project=HIPPARCOS&page=Sky_plot
Finally, visit the AAVSO website (http://www.aavso.
org) and look for any exoplanet “campaigns”
that are there (e.g on http://www.aavso.org/
news/campaigns.shtml)
Also, try getting names of stars known to have
transiting exoplanets from http://exoplanet.eu/
catalog-transit.php (52 as of July 2008) and then
do a search on the AAVSO website for any light
curves they have for any of those stars.
Find late breaking news and information about the
Search for Habitable Planets at the Staying Up To
Date pages for A Changing Cosmos:
http://lhs.berkeley.edu/gss/uptodate/10acc
Chapter 8: Search for Habitable Planets
Hands-On Universe
89
9. Cosmos Begins...and Ends?
Viewing the largest realms of the Universe
requires really good telescopes, since the farther
away objects are, the dimmer they appear. In
chapter four, we found out about distance finding
by observation of brightness of Cepheid variable
stars. Distances to nearby galaxies can be found by
observing Cepheid variable stars and other types of
variable stars in those galaxies. The Cepheid variables
that Henrietta Leavitt studied were all about the
same distance away, in a nearby galaxy—the Small
Magellanic Cloud—about 160,000 light-years away
from us. Though the Magellanic Clouds are nearby
in relation to other galaxies, they are extremely
far away compared to the stars in our immediate
neighborhood. To say that all the stars in one of the
Magellanic Clouds are roughly the same distance away
from us is somewhat like saying that all the people
in New York are about the same distance away from
Los Angeles.
To find distances to the most distant galaxies,
Cepheid variable stars are of no use, since we cannot
see individual stars in galaxies that far away. For great
distances we use “standard
galaxies.” Studies of Cepheid
variables in nearby galaxies
have shown that certain types of
galaxies have fairly predictable
absolute brightnesses. We
assume that those same types
of galaxies have the same
absolute brightness no matter
how far away we find them.
Then, just as we did with the
Cepheid variable technique,
we can figure out how far away
the galaxy is by measuring its
apparent brightness.
90
Global Systems Science
Zoomable version of this “Goth Strip” is at
Where did the Universe come from? How did
it start? What were things like way back when? Will
the Universe end and if so, how? Contemplating such
questions is a realm of study called cosmology.
Getting at answers can take us to the very largest
realms of the Universe—galaxies and arrangements
of galaxies—and to the very smallest realms of the
Universe—subatomic particles.
http://hubblesite.org/newscenter/archive/releases/cosmology/2007/06/image/
Chapter 9
Mosaic of more than 500 images
near the handle of the Big Dipper
taken with NASA’s Hubble Space
Telescope reveal at least 50,000
galaxies yielding clues about the
Universe’s youth, from its “preteen” years to young adulthood.
This is part of a larger project to study
galaxies: the All-wavelength Extended
Groth Strip International Survey
(AEGIS), observing the same small
region of sky in the radio, infrared,
visible, ultraviolet, and X-ray regions
of the electromagnetic spectrum. Team
co-leader Marc Davis, professor of
astronomy at the University of California
at Berkeley said, “The goal was to study
the Universe as it was when it was
about half as old as it is at present, or
about 8 billion years ago, a time when
youthful galaxies undergoing active
formation were becoming quieter mature
adults.” From News Release Number:
STScI-2007-06. NASA, ESA, and M.
Davis (UC Berkeley)
A Changing Cosmos Chapter 9: The Universe Begins ... and Ends?
Doppler effect and Red shift
Yet another way to tell what’s happening at great
distances from us is to look carefully at the spectra of
distant objects. It’s helpful first to recall what happens
when you hear a train or fast moving car first come
towards you and then go away after it passes by. You
hear a distinct change of pitch—higher pitch as the train
or car approaches you, and lower pitch as the train or
car is going away. The sound waves are vibrations of air
molecules. The pitch of the sound is related to basic
properties of the sound waves: wavelength (length of
each sound wave) and frequency (how “frequently” the
sound is vibrating). The higher pitch waves are higher
frequency and shorter wavelength than the lower pitch
waves.
Hearing the Doppler Effect with
Sound Waves
Aside from seeking out a train, fast
moving car or motorcycle, it’s possible to
create a Doppler shift sound effect using a
loud sound generator, like a beeper, alarm
clock, watch alarm, or buzzer. You’ll need to
figure out how to very securely attached the
buzzer, beeper, or alarm to a rope, heavy-duty
fishing line, or very heavy duty string about
one meter long. Once secured, start the sound
generator whirling around so that it alternately
goes towards and away from friends nearby.
For safety, it is best to whirl the sound
generator in a vertical circle, so if the device
accidentally slips away, it’s less likely anyone
will be struck. However, using a longer string
can get a more noticeable Doppler shift, but
you will probably have to whirl it horizontally
rather than a vertically. How does the sound
frequency change when the sound source is
coming towards you?” [Should get higher.] How
does it change when the sound source is going
away from you? [Should get lower.]
Light waves can exhibit Doppler effect as well,
only higher frequency (shorter) waves are not higher
pitch sound but instead colors towards the bluer end
of the spectrum, and lower frequency (longer) waves
are towards the red end of the spectrum. Light also
can be described as particles called photons, each with
a set amount of energy. Photons of red light are lower
energy, corresponding to lower frequency waves, while
photons of blue light are higher energy.
Chapter 9: The Universe Begins ... and Ends?
Model Waves
With a partner, you can model sound
waves with a slinky, long skinny spring, or even
a long rope. Each of you holds one end of the
spring and stretch it out. As a model, the spring
represents air molecules (or air pressure, be
more exact). Real sound waves travel through
air much faster than spring waves—about 1/3
km/sec. One partner holds their end still as the
other shakes their end of the spring. See if you
can produce single wavelength (with two crests
going up and down alternately), a half wave
(a single crest going up and down, like a jump
rope, two, three, and four waves. What is the
relationship between a wave’s frequency and
its wavelength? You’ll probably find that higher
frequencies correspond to shorter wavelengths.
You’ll also find that it takes more energy—more
“oomph”—to make the higher frequency waves.
A common unit of frequency is “cycles/sec” also
known as “hertz.”
One full wave
Two waves
Three waves
Hands-On Universe:
91
Investigation
Hubble’s Law
What’s the evidence that our Universe is expanding, contracting, or
staying the same?
Materials
• Worksheet “Spectra of Fast-Moving Galaxies”
• Worksheet “Hubble’s Law”
The line spectrum of hydrogen, the most
common element in the Universe, has characteristic
lines (wavelengths or frequencies) in the regions
red, turquoise, blue, and violet. The boldest line in the hydrogen
spectrum is in the red region. That is if the star or galaxy is not
moving towards you or away from you. If it is moving towards you
or away from you, each spectrum line will be shifted either toward
the red or toward the violet end of the spectrum because of the
Doppler effect.
9.1. If a star is coming towards us, which end of the spectrum will
its spectrum lines be shifted towards? If a star is going away from
us, which end of the spectrum will its spectrum lines be shifted
towards?
On the “Spectra of Fast-Moving Galaxies” data sheet there are
spectra of a number of galaxies. The darkest line indicated in
each the spectrum is the one that is normally in the red region
of the spectrum. With extreme Doppler shifts, that bold line
can appear in radically different parts of the
spectrum. The scales at the top and bottom of
the sheet relate Doppler shifts of the galaxies’
spectra with velocities of the galaxies. Positive
velocity means the galaxy is moving away from
us and negative velocity indicates the galaxy
is moving towards us.
9.2. If a galaxy’s spectrum is shifted towards the
red end of the spectrum, is the galaxy moving
towards us or away from us?
Find out how fast each galaxy is moving. Plot the
speed on the “Hubble’s Law” worksheet to
create a graph of distance vs velocity.
9.3. What does the graph tell you?
The relationship between galaxy distance and
velocity that you determined is called the
Hubble Law because it was first discovered by
astronomer Edwin Hubble.
9.4. What does Hubble’s Law imply about how
our Universe is behaving?
92
Global Systems Science
Measuring red shift turns out to be yet
another powerful way to find the distances to
the most far away galaxies. Assuming Hubble’s
Law applies for most galaxies, astronomers
estimate distances to the most remote galaxies
by measuring red shifts, finding velocities, and
calculating distances from Hubble’s Law.
9.5. How distant is a galaxy that is found to be
receding from us at 120,000 km/sec?
A Changing Cosmos Chapter 9: The Universe Begins ... and Ends?
Spectra of Fast-Moving Galaxies
Chapter 9: The Universe Begins ... and Ends?
Hands-On Universe:
93
Hubble’s Law
94
Global Systems Science
A Changing Cosmos Chapter 9: The Universe Begins ... and Ends?
Age of the Universe
When we talk about how big the Universe is, we start speaking
in light-years, which, though not a measurement of time, certainly
reminds us of time. When we look at a galaxy a hundred million lightyears away from us, we must realize that the light that reaches us
from that galaxy has been traveling for a hundred million years. We
are looking out into space and back in time as well. It makes you
wonder about the age of our Universe. One of the main objectives of
the Hubble Space Telescope is to see farther into the Universe than
ever before. The farthest galaxies detected are several billion lightyears away. That’s extremely old light.
The overall movement of distant galaxies leads us to the idea
that if we imagine backtracking in time, the Universe may have
started as a sort of fireball of unimaginably dense energy. Such an
event is often called the Big Bang. The age of the Universe can be
estimated by backtracking in a cosmological model based on the
Hubble constant. As of 2007, the best estimate of age is 13.7 billion
years (+/- 0.2 Gyr).
There are other independent ways of estimating the age of the
Universe, for example the age of the chemical elements, the age
of the oldest star clusters, and the age of the oldest white dwarf
stars.
Mysteries of the Universe
There are many mysteries in modern cosmology.
Dark Energy
A discovery that the rate of expansion of
the Universe is increasing led to problems with
previous cosmology models and is leading to the
idea that there is some sort of unknown form of
energy causing the “anti-gravity” force that is
pushing everything in the Universe away from
every other part of the Universe. That unknown
form of energy is referred to as dark energy.
Dark Matter
Way before the discovery of increasing rate
of expansion of the Universe, odd behavior in the
spinning of galaxies led observers to conclude that
there must be some additional matter in those
galaxies that would explain the odd behavior. In
fact, we were shocked to realize that there must
be way more unseen matter in the Universe than
matter that we can see.
Considering matter and energy together, and
referring to both as energy, only about 4% of the
total energy in the Universe can be seen directly.
About 22% is very likely of dark matter. and the
remaining 74% is likely dark energy.
Global Systems Science
We do not know much about either dark
matter or dark energy. But we see their effects.
The myriad of galaxies in the Hubble panorama
images at the beginning of this chapter does not
appear evenly spread out. Some galaxies seem
to be grouped together. Others are scattered
through space. This uneven distribution of
galaxies traces the concentration of dark matter,
in an apparently invisible web-like structure
stretching throughout space. Galaxies form in
areas rich in dark matter.
And students of astronomy form in areas rich
in cosmic mysteries.
You can get the whole book, A Changing Cosmos, for
HOU high school courses at:
http://www.handsonuniverse.org/hs/
Contact Alan Gould <[email protected]> if you
want a print-enabled version, or would like to get
the Image Processing software. Also, feel free to
send him any comments or suggestions.
A Changing Cosmos
95
List of Investigations
Using Star Maps.............................................................................. 10
CCD Image Color Coding................................................................ 14
Browsing the Universe.................................................................... 15
Size and Scale of the Sun............................................................... 25
Parallax........................................................................................... 32
A Law of Brightness......................................................................... 34
Star Magnitudes.............................................................................. 36
A Cepheid Variable Star.................................................................. 39
Observing Color and Temperature.................................................. 43
Measuring the Color of Stars........................................................... 44
How Filters Work............................................................................. 47
HR Diagrams of Star Clusters......................................................... 50
Finding Supernovae....................................................................... 63
Eclipsing Binary Stars..................................................................... 71
Tracking Jupiter’s Moons................................................................. 78
Asteroid Searches........................................................................... 85
Exoplanet Transits........................................................................... 87
Hubble’s Law................................................................................... 92
96
Global Systems Science
A Changing Cosmos Chapter 8: Search for Habitable Planets
References
Alvarez, Walter, Alvarez, Luis Michel, Helen, and
Asaro, Frank, Science, June 6, 1980.
Alvarez, Walter and Asaro, Frank, and Courtillot,
Vincent E., “What Caused the Mass Extinction?”
Scientific American, Vol. 263, No. 4, page 7692, October, 1990.
Dobb, Edwin, “Hot Times in the Cretaceous,”
Discover, February, pages 11-13, 1992.
Gribbin, John, Blinded by the Light: The Secret
Life of the Sun, New York: Harmony Books,
191991.
Milne, Lorus J., and Milne, Margery, Understanding
Radioactivity, New York: Atheneum, 1989.
Monastersky, Richard, “Closing in on the Killer,”
Science News, Vol. 141, No. 4, pages 56-58,
January 25, 1992.
Morrison, David, Wolff, Sidney, and Fraknoi,
Andrew, Abell's Exploration of the Universe,
Seventh Edition, Philadelphia: Harcourt Brace
Jovanovich College Publishers, 1995.
Smithsonian Exposition Books, The Fire of Life,
New York: W.W. Norton & Company, 1981.
Wentzel, Donat G., “The Solar Chimes: Searching
for Oscillations Inside the Sun,” Mercury, May/
June, 1991, pages 77-84.
Global Systems Science
A Changing Cosmos
97
Acknowledgments
Staff of the Global Systems Science Project
Director: Alan Gould
Series Authors: Richard Golden
Eloise Farmer
John Pickle
John Michael Seltzer
Alan Gould
Karen Hoffman
Ted Robertson
Joe Snider
Cary Sneider
John Erickson
Brian Rogan
Sylvia Velasquez
TERC Authors: Jodi Asbel-Clarke, Tim Barclay (Hands-On Universe Project)
Editors: Kay Fairwell
Librarian: Marian Drabkin
Assistants: Harriette Searle
Precious Perry
Andrys Basten
Design: Jim Hurd Design
Illustrations: Audre Newman
Cary Sneider
Carl Babcock
Miho Rahm
Jennifer Yim
Hemma Mistry
Alan Gould
Liz Unger
Peggy Storrs
Neeraja Venkateswaran
Reviewers:
The following individuals reviewed all or
part A Changing Cosmos and provided feedback
and suggestions:
Carleton Pennypacker, Lawrence Berkeley
National Laboratory
Tom Morin, Belmont High School, New
Hampshire.
Michael Kran, Amateur Astronomer
Kristin Nagy-Katz, Evaluator, Lawrence Hall of
Science, University of California, Berkeley
GSS Advisers
Hans Anderson, president, National Science
Teachers Association, Washington, D.C.
Roger Bybee, executive director, Center for
Science, Mathematics, and Engineering
Education, National Research Council,
Washington, D.C.
Victor J. Mayer, Earth Systems Education Program,
The Ohio State University, Columbus, Ohio.
Senta Raizen, director, National Center for
Improving Science, Education, Washington,
D.C.
98
F. James Rutherford, director, Project 2061,
American Association for the Advancement of
Science, Washington, D.C.
Steven Schneider, professor, Department
of Biological Sciences and Institute for
International Studies, Stanford University,
Stanford, California
Herbert Thier, director, Science Education for
Public Understanding of Science (SEPUP)
Project, Lawrence Hall of Science, University
of California at Berkeley, Berkeley, California
Global Systems Science
A Changing Cosmos
Thanks!
Development of the Global Systems Science course would not have been possible
without the creative input of the more than 150 teachers, listed below, who suggested
improvements in the printed materials, and developed new laboratory activities. We
are indebted to them and to their students, who helped to test the course materials.
Tracey Ackerman
Mother of Mercy H.S.
Cincinnati, Ohio
Terry Anderson
NRHEG High School
New Richland, Minn.
Martha Andreski
North Springs H.S.
Atlanta, Georgia
Jay Atkins
Director of Education
Winston-Salem, North
Carolina
Valerie Ayala
Valley High School
Sacramento, California
Janet Baker
Tucson High Magnet
Tucson, Arizona
Linda Baker
Davis High School
Davis, California
Bob Banõs
Lowell High School
San Francisco, California
Gary Barrigar
Elizabethton H.S.
Elizabethton, Tennessee
James Beaber
Fort Lupton H.S.
Fort Lupton, Colorado
Richard Beadle
Spokane School Dist.
Spokane, Washington
Arnold Beckerman
Jamaica High School
Jamaica, New York
Larry Beeson
North High School
Sioux, Iowa
Doug Bell
Centennial H.S.
Gresham, Oregon.
Deborah Bennett
Hamilton County H.S.
Jasper, Florida
Joan Bennett
Baton Rouge Magnet H.S.
Baton Rouge, Louisana
Dianne Bernaciak
Hudson High School
Hudson, Ohio
Charles Berry
Eastwood H.S.
El Paso, Texas
Daphne Blyden
Boschulte J.H.S.
St. Thomas, U.S. Virgin
Islands
Global Systems Science
Burt Blumkin
New Rochelle H.S.
New Rochelle, New York
Susan Boone
Elk Grove H.S.
Elk Grove, California
Daniel Borick
Norcum High School
Portsmouth, Virginia
Evelyn Bradshaw
Cleveland Hts. H.S.
Cleveland Hts., Ohio
Gayle Brickert-Albrecht
Tucson Magnet H.S.
Tucson, Arizona
Patricia Brown
Brownell-Talbot H.S.
Omaha, Nebraska
Sarah E. R. Brown
Phelps Career H.S.
Washington, D.C.
Lori Bryner-Goldstein
Northglenn H.S.
Northglenn, Colorado
Gro Buer
BEST Alternative H.S.
Kirkland, Washington
Keith Camburn
West Mecklenburg H.S.
Charlotte, North Carolina
Joycelin Cayetano
Polytechnic H.S.
Sun Valley, California
Alan Chan
Glencoe High School
Hillsboro, Oregon.
Jayson Chang
Concord High School
Concord, California
John G. Clarke
Tewksbury H.S.
Tewksbury, Massachusetts
Dora J. Coleman
Provine H.S.
Jackson, Mississippi
Gerard Collins
Wakefield H.S.
Arlington, Virginia
Paul Conway
Glendale Jr/Sr H.S.
Flinton, Pennsylvania
Gary Courts
Miamisburg H.S.
Miamisburg, Ohio
Deborah Crough
Saddleback H.S.
Santa Ana, California
Linda Culp
Thorndale H.S.
Thorndale, Texas
Bonita Deiter
Jefferson W. H.S.
Meriden, Kansas
Don Deresz
Ctr. Environmental Ed.
Miami, Florida
Christine Donovan
Sunnyside H.S.
Tucson, Arizona
Jimmy Early
Van Horn Eng./Tech
Independence, Missouri
Tom Estill
Lyme School
Lyme, New Hampshire
Christine Falta
Englewood H.S.
Englewood, Colorado
Eloise Farmer
Torrington High
Torrington, Conneticut
William Feddeler
Macomb MSTC
Warren, Michigan
Aaron Feik
Northshore Schools
Bothell, Washington
Neil Fetter
Drew College Prep
San Francisco. California
Kathleen Field
Haverhill H.S.
Haverhill, Massachusetts
Sharon Fisher
North High School
Des Moines, Iowa
H.L. Flisser
Scarsdale M.S
Scarsdale, New York
Adele Gomez
St. John’s School
San Juan, Puerto Rico
Kathleen Green
Hillsboro High School
Beloit, Wisconsin
Susan R. Green
Miami Beach Sr H.S.
Miami Beach, Florida
Joni Grisham
Pittsburg High School
Pittsburg, California
William Hanneken
Turpin High School
Cincinnati, Ohio
Manisha Hariani
Roanoke Valley School
Roanoke, Virginia
A Changing Cosmos
Thomas Havel
Stadium High School
Tacoma, Washington
Elizabeth Hedgepeth
Mt. Ararat School
Topsham, Maine
Sharon Heineman
Sabinal High School
Sabinal, Texas
Charlsa Henderson
Wellington High
Wellington, Florida
Dean Heyenga
Oceanside High
Leucadia, California
Lynn Higgins
Proviso Twnship H.S.
Maywood, Illinois
Linda Hill
Bothel High School
Bothell, Washington
Steve Hilton
L.H. Watkins H.S.
St. Louis, Missouri
Phyllis Hoar
G H Braddock Sr. H.S.
Miami, Florida
Glenda Holmes
Wilson Senior H.S.
Washington, D.C.
Jennifer Huntsperger
Gadsden H.S.
Anthony, New Mexico
Chad Husting
Bishop Fenwick H.S.
Middletown, Ohio
Matt Huston
Flint Hill School
Oakton, Virginia
Craig Huff
University High
Irvine, California
James Ingram
San Andreas H.S.
Holister, California
Teresa Jimarez
Coronado H.S.
El Paso, Texas
Elizabeth Jones
Springbrook H.S.
Silver Springs, Maryland
Connie Jones
Enka High School
Enka, North Carolina
Dean Karagianes
Mira Loma H.S.
Sacramento, California
Carl Katsu
Fairfields Area School
District
Fairfield, Pennsylvania
Arnold Kaufman
Jefferson High School
Brooklyn, New York
99
LaToy Kennedy
GAMSEC-MC A&T State
Greendboro, North Carolina
Hellon Key
Oakland Technical High
Oakland, California
Rick Kincaid
Glenelg High School
Glenelg, Maryland
Wesley Knapp
Scotia-Glenville Schools
Scotia, New York
Marjory Knights
MacArthur Sr. N. H.S.
Hialeah, Florida
Frank Kowalczyk
State College High
State College, Pennsylvania
Al Krulock
Mission High School
Mission, Texas
Joseph Krupens
Bell J. High School
San Diego, California
R. James Kurtz
Univ. Detroit Jesuit H.S.
Detroit, Michigan
Victoria Lamkey
Wichita N. High School
Wichita, Kansas
Peter Leddy
Norton High School
Norton, Massachusetts
Steve Lege
Davis Senior H.S.
Davis, California
Angela Lewis
Stoneman High School
Parkland, Florida
Jim Lockard
Shawnee Mission E. H.S.
Prarie Village, Kansas
Janice Lord-Walker
Skyline High School
Oakland, California
Kerry Lohr
Highline High School
Seattle, Washington
James Lucey
Wilton High School
Wilton, Conneticut
Melissa Marchino
Heritage High School
Littleton, Colorado
Michael Martin
Iowa City Schools
Iowa City, Iowa
Carl Max
Los Alamos H.S.
Los Alamos, New Mexico
Megan McCarthy
Kingston Junior High
Kingston, Washington
100
Elizabeth McCullough
Thomas Johnson H.S.
Frederocl, Maryland
Jake McDermott
Brattleboro Union H.S.
Brattleboro, Vermont
Robin McGlohn
Burton Academy
San Francisco, California
Nancy McIntyre
Chaminade College Prep
West Hills, California
Donna Millett
Attleboro High School
Attleboro, Massachusetts
Hector Montano
Canutillo High School
Canutillo, Texas
Catalina Moreno
Boston Public Schools
Boston, Massachusetts
Donna Morey
Fair High School
Little Rock, Arkansas
Isabella Morrison
Shorewood H.S.
Seattle, Washington
Sandra Morrow
Hot Springs H.S.
Truth or Consquences, New
Mexico
Cindy Y. H. Moss
Cicero-N. Syracuse H.S.
Cicero, New York
Irene Munoz
North CarolinaaliforniaR
Boulder, Colorado
Stephen Nakano
Waipahu High School
Waipahu, Hawaii
Patricia Owens
Homewood H.S.
Birmingham, Alabama
Shelly Pelham
Garrison Forest School
Owings Mills, Maryland
Glenda Pepin
Dorsey H.S.
Los Angeles, California
Kenneth Pitman
Heritage High School
Littleton, Colorado
David Podd
Rio Tierra J.H.S.
Sacramento, California
Gilbert Richardson
Shabazz High School
Madison, Wisconsin
Amy Ryken
Berkeley High School
Berkeley, California
Faimon Roberts
LSU Lab School
Baton Rouge, Louisiana
Robena Robinett
North Caroline H.S.
Ridgely, Maryland
Brian Rogan
Dublin School
Dublin, New Hampshire
Lina Russ
Alice Deal H.S.
Washington, D.C.
Thomas Russell
San Pedro High School
San Pedro, California
Fernando Salvador
City as School H.S.
New York, New York
Sallie Sanders
North Atlanta H.S.
Atlanta, Georgia
Erin Servillo-Gross
AIM Center
Trenton, New Jersey
Alan Sills
West Essex Reg. H.S.
North Caldwell, New Jersey
L. Trevor Smith
Troy High School
Troy, Michigan
Doug Squire
Union H.S.
Union, Oregon
Joseph Stanislaus
Samoa High School
Pago Pago, American Samoa
John Stegmaier
Gunnison High School
Gunnison, Colorado
Thelma Stepan
Holy Cross H.S.
Waterbury, Conneticut
Michelle Stern
Terra Linda H.S.
San Rafael, California
Elizabeth Stewart
Westside High School
Memphis, Tennessee
Ellen Strother-Pitts
Western Sr. H.S.
Baltimore, Maryland
Richard Sturgeon
Glastonbury High
Glastonbury, Conneticut
Cindy Suchanek
Mira Loma H.S.
Sacramento, California
Christopher Sullivan
E. Longmeadow H.S.
E. Longmeadow, Massachusetts
Irene Swanson
Northridge High
Northridge, California
Teresa Thompson
Grapevine H.S.
Grapevine, Texas
Jane Ann Toth
East High School
Kansas City, Missouri
Global Systems Science
Louis Tremblay
Avon High School
Avon, Conneticut
Jon Valasek
School for Math/Sci.
Columbus, Mississippi
Larry Walker
Academy of Sci/Tech
Conroe, Texas
Charles Walsh
Vianney High School
St. Louis, Missouri
Margery Weitkamp
Chaminade College Prep.
West Hills, California
Tom Wellington
Wilton High School
Wilton, Conneticut
Tom Wellnitz
Shore Country School
Beverly, Massachusetts
Fred Wetzel
Science Hill H.S.
Johnson City, Tennessee
Jane Whitaker
Lenoir City H.S.
Lenoir, Tennessee
Rich White
Cholla High School
Tucson, Arizona
Patrick Wildermuth
Lowell High School
San Francisco, California
Belinda Wight
John T. Hoggard H.S.
Wilmington, North Carolina
Peter Wilding
San Rafael H.S.
San Rafael, California
Bill Williams
Williamsburg Scools
Williamsburg, Virginia
Rocky Wolf
Sonora High School
Sonora, California
Agnes Wu
Greyhills High School
Tuba City, Arizona
Ron Yob
Native American Learning
Center
Grand Rapids, Michigan
Jonathan Yoder
North Salem High School
Salem, Oregon.
Paul Zastrow
Hood River Valley High
Hood River, Oregon.
Anne Zellinger
Kahuku High School
Kahuku, Hawaii
Glenn Zwanzig
DuPont Manual H.S.
Louisville, Kentucky
A Changing Cosmos
M51, courtesy Ewell Observatory, Belmont, CA
Global Systems Science
A Changing Cosmos
101
Solar System Science
2009 Edition1
By Alan Gould and Vivian Hoette
SOLAR SYSTEM
SCIENCE
Global Systems Science
http://lawrencehallofscience.org/gss
Lawrence Hall of Science
University of California, Berkeley
Global Systems Science
http://lawrencehallofscience.org/gss
102
Global Systems Science
A Changing Cosmos