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University of California, Berkeley
Lawrence Hall of Science
ASTEROID
WISE
Investigations for high school
...a collaboration of the NASA WISE mission
with the Lawrence Hall of Science
Hands-On Universe project
by Alan Gould, Bryan Mendez, Rich Lohman,
Thomas Morin, Timothy Spuck, Janet Ward,
Glenn Reagan, Roy Morris
revised Feb 2010
Asteroid WISE
Oct 2009
1
Download most up-to-date
version from http://www.handsonuniverse.org/hs/wise
Hands-On Universe (HOU) is a project
of the Lawrence Hall of Science
(LHS), University of California,
Berkeley.
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.
This book is dedicated to
the memory of Roy Morris,
our colleague who cut
to the chase in design of
these materials, but passed
away in the summer of
2009. His kind spirit and
gentleness, and devotion
to teaching will always be
remembered.
Sources of Support
Support from NASA’s Wide Angle Infrared Survey Explorer (WISE) mission has
made this book possible.
The authors have also made significant individual efforts, supported in part by their
respective institutions.
Significant portions of this book are adaptations of portions of A Changing Cosmos
and Solar System Science from the Global Systems Science series.
Financial support does not constitute an endorsement by NASA of the views
expressed in this book.
© 2009 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 94720-5200 or e-mail [email protected].
Cover Image: Asteroid
Eros, captured by the
Near Earth Asteroid
Rendezvous (NEAR)
Shoemaker probe in
2000.
2
Oct 2009
Asteroid WISE
Asteroid WISE
Contents
1. Beware of Large Flying Objects.................................2
2. Astronomers' Tools.....................................................6
Using Star Maps............................................ 8
Browsing the Universe..................................11
3. Asteroid Basics.........................................................16
How Do You Find An Asteroid?.................... 16
Make an Asteroid Movie ............................. 18
What Does an Asteroid Look Like? . ........... 19
4. How Close Will It Come? .........................................25
Doomsday Scenario..................................... 25
5. Spinning Space Rocks..............................................28
Rotation Period Of An “AsterSpud” ............. 28
22 Kaliope Light Curve................................. 30
Exit Ticket..................................................... 35
6. Getting Involved in the Search . ..............................36
Asteroid Search Campaign......................... 36
Appendix A: Space Rock Vocabulary..........................37
Appendix B: Determining Asteroid Characteristics
from WISE Data....................................38
Asteroid WISE
Oct 2009
1
Chapter 1
1. Beware of Large Flying Objects
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 cosmic events 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. Scientists have disagreed
and squabbled for quite a while over the the question,
“What caused the mass extinction at the end of the
dinosaur age?” 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 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.
The Deccan Traps
are extensive lava
flows in India.
Source: © Dr. Keith
G. Cox, University
of Oxford, Oxford,
England.
c. The impact theory — that a really huge object struck the
Earth at about that time, cuasing global devastation. An
underground crater found near Chixulub (pronounced
Chi’-shoo-loob), Mexico, was found to be about 65 million
years old. A 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.
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Asteroid WISE
Chapter 1: Beware of Large Flying Objects
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
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.
Which Theory is Right?
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.
Will Earth be Hit by a Large Asteroid?
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. While in space,
they are called meteoroids. When they enter
the atmosphere, they can heat up so much they
vaporize and leave a streak of light. That’s called a
meteor, also known as a “shooting star” or “falling
star.” But the larger the body, the rarer it is to collide
with Earth.
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.
Asteroids that are made of rock and/or metal
are not the only menace. Comets are bodies of ice
that can go crashing into planets as 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.
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.
Hubble space
Telescope
image of Comet
Shoemaker-Levy 9
fragments before
they collided with
Jupiter.
Asteroid WISE
Chapter 1: Beware of Large Flying Objects
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.
The NASA Wide-Angle Inrared
Survey Explorer (WISE) mission
(launch in December 2009) is especially suited to find a multitude of asteroids
—of immense value in the the overall effort to detect more NEOs.
Understanding, Helplessness, and Empowerment
It is nearly inevitable that Earth will be hit by an asteroid—
only a matter of time, though we do not know if it will be today,
tomorrow, or in many millions of years. But 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. Unfortunately that could create a number of smaller
bodies that would still continue on their trajectories and impact
Earth with devastating effect. Other ideas for averting disaster
are mostly different ways of nudging the asteroid to deflect it
into a path that will not strike Earth.
But the key is “early warning.” The sooner we find that
asteroid “with our name on it,” the more time we would have
to plan action to prevent disaster—another mass extinction.
This book is devoted to better understanding the science that
relates directly or indirectly with the challenge of early detection
of "near Earth asteroids."
Chapters 1 and 2 or this book are adaptations of
respective chapters from
A Changing Cosmos,from the
Global Systems Science series
4
Asteroid WISE
Chapter 1: Beware of Large Flying Objects
How Can We Assess the Danger?
If we’ve identified an asteroid in the WISE mission data, there
are key questions that are of great import:
• Will it hit Earth?
• If it were to impact Earth, how bad would it be: a puff of
smoke in the atmosphere or the end of civilization as we
know it?
• What else can we learn from the data?
Position
Time
Intensity/Brightness
Wavelength/Frequency
Distance
Essentially we have 4 key parameters in the data:
Position
Speed/Velocity
Time
Size
Intensity (or brightness)
Temperature
Wavelength
POSITIONS and TIME determine the orbit which can tell us if
the asteroid is likely to hit Earth. This can also give us the
DISTANCE and SPEED of the asteroid at any given time.
From the DISTANCE, INTENSITY, and WAVELENGTH we can
approximate the asteroid’s
SIZE
Rotation rate
Albedo/Reflectance
Density
Composition
Mass
TEMPERATURE
Kinetic Energy
ROTATION RATE
ALBEDO (or reflectance: how light or dark the body is—how
much it reflects light)
From the ROTATION RATE, we can also get an
estimate of the lower limit of the asteroid’s
DENSITY, since an object held together by its
own gravity (a “pile of rubble” as opposed to a
giant rock), will fly apart if spins too fast.
The ALBEDO can also give an indication of the
COMPOSITION of the asteroid. Asteroids
with very low albedos ~ 0.03, that is, very dark
asteroids, are called C-type and are typically
rocky. Brighter asteroids with albedos between
0.1 and 0.2 are either S-type – metallic (nickeliron) mixed with rock (silicate) – or M-type –
purely metallic.
The COMPOSITION also gives another indication
of the DENSITY of the asteroid. The densities
of C, S, and M class asteroids are 1.38, 2.71,
and 5.32 g/cm3, respectively. There is a wide
range of asteroid densities, but if albedo or
composition is unkown, a density of 2 kg/m3
can be assumed.
From SIZE of the asteroid and its DENSITY, the
MASS of the asteroid can be calculated.
Which finally brings us to the KINETIC ENERGY
(Ekinetic) which is
Ekinetic = 1/2 x MASS x (SPEED)2
Chapter 2: Astronomers' Tools
For mathematical computations
needed to arrive at the asteroid
attributes mentioned on this page,
see Appendix B.
It’s this KINETIC ENERGY that tells us how dire
our situation might be if the asteroid hits us— the
answer to that question: “If it were to impact Earth,
how bad would it be: a puff of smoke in the atmosphere or the end of civilization as we know it?”
In SI units, the KINETIC ENERGY is in Joules (the
mass is in kilograms and the velocity is in meters per
second). A typical stick of dynamite contains about
2×106 Joules (a meteoirite might have that sort of
energy. The largest nuclear bomb ever detonated
was about 2×1017 Joules—large asteroids have
many times that amount of kinetic energy.
Asteroid WISE
5
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.
6
Asteroid WISE
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.
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 (").
Asteroid WISE
7
Investigation
Developed by HOU Co-Director, Alan Gould (Uncle Al)
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
8
Asteroid WISE
to 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)?
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).
You can mark the positions of planets on your
Chapter 2: Astronomers' Tools
August 2007: Google announced the
roll-out of its Google Sky software
for exploring celestial objects.
Coordinate Star Wheel, but since they change, it’s
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.
Asteroid WISE
9
Telescopes
Galileo Galilei, in 1609, was
the first person to do serious
observations of sky objects
with a telescope.
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. 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.
Galileo’s telescope was very simple: two lenses, one at each
end of a tube. It was one of the first refractor telescopes.
Today’s largest observatory, 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.
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 the past century
the discipline of astrophotography took advantage of the
fact that 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.
Electronic photography came into being with the invention
of the CCD (charge coupled device) in 1969 by Willard Boyle
and George E. Smith at AT&T Bell Labs. They received the
Nobel prize for this achievement in 2009. Today, it’s common
for people to carry CCD cameras in their purses or pockets all
the time, in the guise of mobile phones with cameras. 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.
10
Asteroid WISE
CCD chip being prepared for the NASA
Kepler mission photometer.
Chapter 2: Astronomers’ Tools
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.
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.
Chapter 2: Astronomers' Tools
Asteroid WISE
11
Investigation
Developed by Tim Barclay and Jodi Asbell-Clarke, TERC
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/
See diagram of “HOU Image
Processing Screen on next
page.
Part I: Browse
2.19. Using each of the files, browser1 through browser7, use and
familiarize yourself with the following HOU IP functions:
• 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.
Min/Max values can be changed
two ways:
• 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.
HOU Image Processing Screen
Open
Zoom
Sliders for Min-Max
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
should use the grey or igrey palettes.
Min-Max
Log Indicator
Color Palette
Image displayed here.
This one is “browser3.fts”
12
Asteroid WISE
Chapter 2: Astronomers’ Tools
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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?
And if you Zoom the image even more, does
that color within each pixel change?
Chapter 2: Astronomers' Tools
Toggle these off and on
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 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.
Asteroid WISE
13
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.
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.
14
Asteroid WISE
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?
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
Chandra X-Ray Observatory
higher frequency.
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
Chapter 2: Astronomers' Tools
Asteroid WISE
15
Chapter 3
3. Asteroid Basics
Asteroids do not give off their own light, but reflect
sunlight as they orbit the Sun, like planets and
moons. They change position in our starry sky
as they orbit the Sun. Since they are part of our
own Solar System, they are closer to us than the
background stars. Most asteroids are found in the
inner Solar System, inside the orbit of Jupiter. Even
though they are moving very fast in their orbits,
thousands of kilometers per hour, they appear to
move slowly through the sky, since they are many
millions of kilometers away from us. The asteroids
that are closer to the Sun move faster than those
that are farther out near the orbit of Jupiter. Our
Investigation
Earth also orbits the Sun and rotates on its axis,
so it is the combined motions of the asteroids and
Earth that cause the shift in positions of the asteroids in our images. The speed of an asteroid in its
orbit does not vary as much as speed of a comet,
since asteroid orbits are usually not as elongated
as comet orbits.
Asteroids are much smaller than most moons and
planets. They range in size from a few hundred
meters to a few hundred kilometers. Bodies that
are a lot less than a hundred meters or so, would
probably be categorized as meteoroids and not
asteroids.
Developed by HOU Leader, Vivian Hoette
2. Slice tool. Open the files Hildrun1.fts and
Hildrun2.fts. These images were taken 15
minutes apart. Of the three bright objects, two
are stars and one is an asteroid. How can we
find the asteroid? Decide which one you think
is asteroid Hildrun.
University of California, Berkeley
http://lawrencehallofscience.org/gss
1. Visual inspection. Open the images sappho_a508.fts and sappho_a533.
fts from the “asteroids” image folder. Click and drag the image windows to
move them side by side. The image sappho_a533.fts might appear quite
peculiar when first opened. Adjust the Min/Max settings as needed.These
images are of the same region of the sky but were taken about 15 minutes
apart. One of the objects in the image is an asteroid named Sappho. It
appears to be moving relative to the background stars because it is closer
to Earth. Select a color palette and adjust min/max until you see enough
objects in the image to compare and match patterns. Can you tell which
object is Sappho? Prepare a separate paper worksheet and write down
the (x,y) coordinates of Sappho in each image:
In sappho_a508: X= ______ Y= ______
In sappho_a533: X= ______ Y= ______
SOLAR SYSTEM
SCIENCE
Global Systems Science
In this investigation, we use four different methods of finding asteroids
using Image Processing software tools.
Lawrence Hall of Science
How Do You Find An Asteroid?
Solar System Science
By Alan Gould and Vivian Hoette
2009 Edition1
This investigation is
adapted from Solar
System Science, from the
Global Systems Science
series
It might help if you could compare some distances
between the three bright objects, since the distance between the two that are stars would not
change. The distances between a star and an
asteroid will change.
Use the Slice tool in the Data Tools menu to measure the distances
between the three bright objects. Compare measurements in Hildrun1.fts to measurements in Hildrun2.fts to determine which object
is the asteroid.
16
Asteroid WISE Chapter 3: Asteroid Basics
Using the slice tool (or “Plot
Profile”) to measure the
separation of two stars (or
star and asteroid)
Write down the coordinates
of asteroid Hildrun in
the images Hildrun1.
fts and Hildrun2.fts?
Hildrun1: X= ______ Y= ______
Hildrun2: X= ______ Y= ______
3.Subtracting Images. Another nifty tool to
use in finding things that have moved in two
images (such as asteroids) is the Subtract
tool in the Transform menu (HOUIP 2.0).
a. Open Hildrun1.fts and Hildrun2.fts.
b. Click on Hildrun1.fts. In the Transform
menu, select Subtract (or click on Subtract
icon in the Tools Palette).
c. You can choose either, File from disk” or
“Displayed Image,” then choose Hildrun2.
fts as the file to subtract from Hildrun 1.
d. Click on Display in new window. Click
OK.
e. View your results. The image processor
has subtracted the brightness Counts of
every pixel in the first image from each
corresponding pixel in the second image.
Do you see an object with a double
position? It will be a black object at its
initial position in Hildrun1.fts and a white
object at its position in Hildrun2.fts. Is this
the object you thought was the asteroid?
4. Compare Images (Blink Comparator)
Open Ryokan1.fts and Ryokan2.fts. These
images were also taken 15 minutes apart. Most
of the bright objects are stars. One is asteroid
Ryokan! Try using the “Compare Images”
function in the Analyze Menu to identify which
dot is asteroid Ryokan.
Write
down the coordinates of asteroid Ryokan in the
images Ryokan1.fts and Ryokan2.fts:
The images of Hildrun and Ryokan
were taken for HOU with the 3.5 meter
telescope at Apache Point Observatory in
New Mexico from the Adler Planetarium
& Astronomy Museum by University of
Chicago Astronomer, Dave Cole.
Ryokan1: X= ______
Ryokan2: X= ______
Asteroid WISE
Y= ______
Y= ______
5. Which one is Iris?
Write down the coordinates of asteroid Iris in
the images Iris1.fts and Iris2.fts?
Iris1: X= ______ Y= ______
Iris2: X= ______ Y= ______
Which method did you use to find Iris?
Chapter 3: Asteroid Basics
17
Investigation
Developed by HOU Leader, Tim Spuck
Make an Asteroid Movie
The image to the right was taken from Earth by
astronomers using a telescope and CCD camera.
There’s an asteroid in this image. Can you tell which
object is the asteroid? Go ahead and circle it, befrore
proceeding with this investigation. We’ll see if you’re
right later on.
Astronomers use various exposure times for
astronomical images. With shorter exposures it can
sometimes be difficult to recognize the asteroid. But
what if we had whole bunch of short exposures of
the same part of the sky taken at different times?
We could use movie-making software like Windows
MovieMaker or the Mac iMovie to create a time series
video. The distant background stars and galaxies
should remain stationary and the asteroid should
appear to move.
Find the folder labeled A771A_Asteroid_jpg which has a series of 66 images of
asteroid A771A that were taken about six minutes apart (starting with A771A001c.
jpg). Each image was taken using a two-minute exposure so you don’t see the
asteroid as a streak, however the asteroid moves slightly from one image to the
next.
Using either Windows MovieMaker or Mac IMovie to create an asteroid video.
If you’ve never used MovieMaker or
IMovie then there are a number of quick
tutorials out there for you to use. In the
folder along with the rest of the images
for this activity is a document named
MakingMoviesHandout.pdf. Use this
document to familiarize yourself with the
software, or go online to YouTube.com and
search on MovieMaker tutorial or IMovie
tutorial and view one of the many useful
online tutorials.
To begin the process you will need to import a
series of jpg images into either MovieMaker or IMovie.
There are many ways to approach this so feel free to
be creative. For example, you might only import the
first 15 images, or you could import every 5th image
(image 1, 5, 10, 15 …).
Once you have all the images you want to use imported, drag the imported images into your movie in
sequential order, and adjust the time for each image
to 0.5 seconds.
18
Play your movie. Can you see the asteroid?
Look at the image above again. Were you correct about where you thought the asteroid was
located?
Go ahead and finish the movie making process by
adding a title slide including your name, the name
of the asteroid, school, and other information you
teacher may ask for. Also add some audio. You
can either import your personal voice comments or
music, and add it to the movie.
FINAL STEP: The last step is to merge all the
pieces together and create the movie as a single
video file that you can share with others or post on
YouTube. Refer to a YouTube tutorial or the MakingMoviesHandout.pdf document for instructions
on how to do this.
Asteroid WISE Chapter 3: Asteroid Basics
Investigation
Developed by HOU Leader, Tim Spuck
What Does an Asteroid Look Like?
You may have seen pictures of asteroids taken by spacecraft like you see in the figures below.
Asteroid Gaspra from
Galileo (NASA)
http://photojournal.jpl.nasa.
gov/catalog/PIA00119
Asteroid Eros by NEAR from Surface of Asteroid
Eros by NEAR
124 miles. (NASA)
http://photojournal.jpl.nasa.gov/ from 1150 meters
catalog/PIA03141
(NASA)
AsteroidIdawithmoonDactyl
from Galileo (NASA)
http://photojournal.jpl.nasa.gov/
catalog/PIA00069
Using spacecraft to travel close enough to asteroids to get pictures like these
is very expensive. It can’t be done for the hundreds of thousands of asteroids
in our solar system.
Asteroids are many thousands, millions, or even billions of miles from Earth.
Rather than traveling to these objects for close-up pictures, we use telescopes
and cameras right here on Earth. What does an asteroid look like through
telescopes on Earth? Let’s get started answering that question with this simple
exercise.
How does distance to an object size
affect its apparent size?
10 meters away
http://photojournal.
jpl.nasa.gov/catalog/
PIA03145
1 meter away
1. Suppose you make a drawing in a box (like one
below) of something that is one meter from you.
Then you make a drawing of something about
10 meters (paces) away. Label your boxes
“near me” and “far away.” Example shown at
right: beach ball and elephant.
Near me
Far away
2. Look at your sketches. If you were to have both
objects you selected to draw sitting side by side
(the same distance from your eye), which one
would actually be bigger? Can you estimate about
how many times bigger? [Write the following on a piece
3. Take a closer look at your drawings and use a
ruler to measure the size of each object as you
sketched it on your paper.
Near me: _________ Far away: ________
of paper and fill in the blanks appropriately.]
The ________________is bigger
... about ______ times bigger
Using an apporiate scale ruler on our drawings helps....
Asteroid WISE
Chapter 3: Asteroid Basics
19
4. Which one, the “near me” object or the “far away” object appears to
be bigger in your sketches? By how many times?
___________________
____ times bigger
5. The key word above is “appear”. Have you ever heard the phase,
“Things aren’t always as they appear to be.” In this case please
explain what caused the objects to appear to be a certain size when
in reality they are different in size:
____________________________________________________
____________________________________________________
____________________________________________________
If you said “the distance you were from the object” in question
5 you’re exactly right. Now let’s apply this to asteroids. Look again
at asteroid Eros in figure 3. Eros is a fairly large asteroid, and this is
how big it appears to be from a distance of 124 miles, but remember
we said that asteroids are thousands, millions, or even billions of miles
from Earth. From these great distances, what will an asteroid look like,
even if we were to magnify it 100’s of times using a telescope? The
asteroid would still appear to quite tiny.
If asteroids look like stars how are we ever to tell the difference?
Hmmm … what’s different about stars and asteroids that might help us
out? We know that everything in space is moving. Asteroids, comets,
planets, stars, even galaxies themselves are in motion … right? The
big difference is that asteroids are a whole lot closer
to Earth than stars and galaxies. Asteroids may be
thousands, millions, or billions of miles away, BUT
stars and galaxies are many trillions, quadrillion,
or quintillion miles from Earth.
Do you remember from your sketches that
objects that were farther away appeared to be
smaller? Do you think the same holds true for
movement? Do you think if everything is in
motion, but some objects are a much closer than
others, that the closer objects will appear to move
a greater distance over time? Let’s ‑explore this
concept a bit.
Here is an image from the
Make An Asteroid Movie
investigation. Remember
which one was the asteroid?
20
Asteroid WISE Chapter 3: Asteroid Basics
How does distance to an object affect how fast it
appears to move?
Here’s the experiment set-up …
We placed a camera on a tripod and it
remained in a fixed location. We mounted
two stationary light sources in the distant
trees (And, unlike the trees in Lord of the
Rings, these trees do not walk around.).
We then mounted a fake asteroid on a
small John Deer tractor/lawnmower and
we took five 5-second exposures; one with
the tractor parked at the beginning of the 10
meter path, and one each with the tractor
moving across the 10 meter path, the 15
meter path, the 20 meter path, and the 25
meter path.
To move on with this experiment you
will need to open up two jpg images; one
of the test site during the day, and the
second of the test site at night. You will
also need a ruler to make measurements
in the images.
Aerial View Diagram of Test Site
This is an aerial diagram
(top-down view) of the
test site. We know that
asteroids are in our own
solar system, and stars
are many light years
away outside the solar
system. We also know
that stars don’t appear
to move over time. For
example if you go out
at night and look at the
Big Dipper, and then go
out a week later, or years
later, the Big Dipper
looks the same. It may
change its position in
the sky relative to the
horizon, but the shape is
always the same.
NOTE: If you’re using Window’s you can use Paint,
or if using a Mac, Preview will work fine. If you
really want to be a bit more sophisticated with
your measurements, you can use something
like Image J, or other software that allows you to
make distance measurements on jpg images.
OPEN the following image files and make sure that
you DO NOT resize either of the images. The
images are the same size, and should appear
to be the same size on your screen.
- Test Site Day.jpg
- Test Site Night.jpg
The images should look like the two images
you see below in figures 7 and 8. REMEMBER,
these images should be the same size on your
computer screen.
Images taken with a stationary camera.
Compare these with the aerial diagram above to gain a
Testbetter
Site -understanding
Night
how the test site was set up.
Test Site - Night
Now that you have an understanding of the
test site, and were the fake stars, the fake asteroid,
and the camera are located, it’s time to make some
measurements. If you’re making measurements in
Windows-Paint or Mac-Preview, you’ll simply need
a ruler. If you’re using Image J, or other software,
the measurement tool will be built into the software.
Just keep in mind, the images should be the same
size on your computer screen and make sure you
Asteroid WISE
Chapter 3: Asteroid Basics
21
label the units for all measurements. It will also be helpful if you use
the same units for all measurements.
6. Using a ruler and images Test Site Day.jpg and Test Site Night.jpg
measure the distance between fake star 1 and fake star 2.
Write on paper: “Distance between fake star 1 and fake star 2
in TestSiteDay.jpg __________ “ [and fill in the blank].
and
“Distance between fake star 1 and fake star 2
in TestSiteNight.jpg __________ “
NOTE: You should get the same value for the measured distance
between fake star 1 and 2 in both images. You might be off a little due
to human error, but since the camera lens settings were the same in
both images, the field of view in both images will be the same as well.
If your values were off significantly, double check to make sure you
did not change image size when you opened up the images.
SPECIAL CHALLENGE #1: Can you use the small angle formula to
determine the width of the white distance markers? Here’s the information you
will be given; a) all the distance markers (10 m, 15 m, 20 m, 25m) are the same
width, and the angular distance across (the width) the Test Site Day.jpg image
is 76°. HINT: How many arc seconds are in a degree?
D = ad/206,265
D = width of object
a = angular size in arcseconds
d = distance to object
206,265 = is arcseconds per radian
Take a Virtual Trip - Want to
check out the actual site where
the experiment took place? Use
Google Earth (http://earth.google.
com/­) to visit the test site!
Here are the coordinates:
41° 18’ 33.76 N Latitude,
79° 28’ 55.10 W Longitude
Farmer Tim –
He’s not really
a farmer—he’s
author Tim
Spuck on the
tractor. He
enjoys being
outdoors, but not
sure he could put
in the long days
and short nights most farmers do.
“What I really enjoy is astronomy.
My father took me outside one
night when I was about seven
years old and showed me Venus,
the Big Dipper, and Orion. From
that moment on I was hooked!”
To find out more about Tim see
http://www.ocasd.org/webpages/
tspuck/.
One thing we had to be sure of was
that the speed of the fake asteroid was
the same in each image. The only
thing we wanted to change was the
distance the fake asteroid was from
the camera.
To ensure this was the case, the
gearshift was always placed in 1st
gear and the throttle setting was
always at full (the rabbit).
Let’s move on and put our fake asteroid in
motion; first at a distance of 10 meters from the
camera, then 15 meters, then 20 meters, and finally
25 meters from the stationary camera.
22
Asteroid WISE Chapter 3: Asteroid Basics
The images on this page resulted from four 5-second
exposures with the tractor in motion at different distances
from the camera. The streak of light that you see in the
images is caused by the fake asteroid being in motion
and reflecting light back toward the camera, much like an
asteroid moving in orbit around the sun reflects light back
toward the Earth.
Open up each of the four images...
- tractorasteroid10m.jpg
- tractorasteroid15m.jpg
- tractorasteroid20m.jpg
- tractorasteroid25m.jpg
...using Windows Paint, Mac Preview, or another
preferred software. REMEMBER, do not resize the images
once you open them. All four images are the same size, so
they should appear to be the same size on your computer
screen.
7. Use your ruler or software measurement tool (if using
Image J) to measure the distance (D) between fake
star 1 (f1) and fake star 2 (f2), and the length (L) of
the light streak in each image. Record your results on
worksheet as follows and remember to label units for all
measurements.
Fake Asteroid Moving from 10 m
D f1 and f2 _____ L of streak _____
Fake Asteroid Moving from 15 m
D f1 and f2 _____ L of streak _____
Fake Asteroid Moving from 20 m
D f1 and f2 _____ L of streak _____
Fake Asteroid Moving from 25 m
D f1 and f2 _____ L of streak ____
SPECIAL CHALLENGE #2: How fast does my tractor/
lawnmower travel in first gear at full throttle? The angular
distance across (the width) of each of the four images (figures
10 – 13) is 76°.
D = ad/206,265
D = distance traveled
a = angular distance (arcseconds)
d = distance to tractor 206,265 = arcseconds per radian
HINT: How many arcseconds are in a degree?
Speed = distance/time
Asteroid WISE
8. Let’s take a close look at your answers in
question 7. Again the camera lens setting
were the same in all four images, so the
distance you measured between fake star 1
and fake star 2 in all four images should be
the same. However, what happened to the
length of the streak? If the speed of the tractor
and the exposure time for each of the four
images was the same, what do you believe
caused the difference? [Write your answer
on worksheet.]
9. Is there any correlation between distance
to the fake asteroid, and how far the fake
asteroid appeared to move? If so, what is
the correlation?
Chapter 3: Asteroid Basics
23
WARNING: Don’t Get the Wrong Idea
In the example above, it was the fake asteroid on
the tractor that was in motion relative to the “stationary”
camera on the ground that caused the streak in the
photographs. In space, the Earth is spinning on its axis
once every 24 hours, the Earth is orbiting around the
Sun at a speed of 100,000 km/hour (about 67,000 miles
per hour), and the asteroid is orbiting the Sun. All these
objects are in motion relative to each other.
In real life, when we see an asteroid moving against the
background stars, as you will see in the next activity, the vast
majority of the apparent motion, or asteroid streak, is caused
by the Earth’s motion around the Sun. So, if we were to have
sufficient space and resources, it would have been more accurate
to put the camera and asteroid in motion around a central point,
and place the asteroid MUCH further away, and the stars many
times that. However, for our purposes the activity demonstrates
sufficiently well what happens when objects are in motion relative
to each other.
The Real Thing
You’ve discovered that more distant objects moving at relatively the same
speed as a closer object can show less motion. As a result, asteroids that are
much closer to Earth than stars and galaxies will appear to move, while stars and
galaxies appear to remain stationary.
You may be asking yourself, “What does that look like?” It looks a lot like our
fake asteroid in the images you just observed.
Date: 03/23/98
Date: 03/23/98
Date: 03/23/98
UT: 07:07:40.4
UT: 08:36:57.3
UT: 09:25:10.2
The images above of an asteroid captured using
the Cerro Tololo Inter-American Observatory (CTIO)
Blanco 4 Meter telescope. Each exposure was 10
minutes in length, and figure 15 was taken about 1.5
hours after figure 14, and figure 16 was taken about
an hour after figure 15. Notice how the asteroid
appears to move while the distant stars and galaxies
stay in the same place. In reality, everything in the
images is in motion, but the asteroid is much closer
so it appears to move while other objects appear to
remain stationary.
Take a minute and go back and look at the
asteroid image in the “Make An Asteroid Movie”
investigation. You’ll notice there is no “asteroid
streak” like you see in the images above, but there
really is an asteroid there. The primary difference
is that with the images in the above images, the
telescope camera shutter was open for ten minutes,
while the image exposure in the Movie investigation
was only two minutes in length making the asteroid
streak much shorter and therefore less noticeable.
24
A
B
D
C
FINAL TEST – This is an image taken by the Hubble
Space telescope (NASA). Virtually all the streaks you see
in the image are asteroids. Order asteroids A, B, C, D in
order from closest to farthest away..
Asteroid WISE Chapter 3: Asteroid Basics
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.
Kepler’s First Law:
1. Planets move in ellipses with the Sun at one focus.
http://kepler.nasa.gov/johannes/
For a circle the motion is uniform as shown above, but
in order for an object along an elliptical orbit to sweep out
Circular and Elliptical Orbits Having the
the area at a uniform rate, the object moves quickly when
Same Period and Focus
the radius vector is short and the object moves slowly when
the radius vector is long.
Kepler’s 2nd Law: The planet’s radius line sweeps equal
areas in equal times.
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.
Kepler’s Second Law:
For elliptical orbit,
speed decreases with
distance from the Sun.
For circular orbit,
speed remains
constant
2. The planet’s radius line describes [sweeps]
equal areas in equal times.
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.
Kepler’s Third Law:
3. The squares of the periodic times are to each
other as the cubes of the mean distances.
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/
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
3
where T1 = period of planet 1
T1
R1
T2 = period of planet 2
=
2
3
R
= orbit radius of planet 1
1
T2
R2
R2 = orbit radius of planet 2
Asteroid WISE
Sample roblems: 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?
Chapter 3: Asteroid Basics
25
4. How Close Will It Come?
Investigation
Chapter 4
Developed by HOU Leader, Janet Ward
Doomsday Scenario
99942 Apophis Asteroid, discovered in 2004, was
designated as a Level 4 on the Torino impact hazard
scale (a scale of 0–10, 0 being no hazard). Level 4 means
”a close encounter, meriting attention by astronomers.
Calculations give a 1% or greater chance of collision
capable of regional devastation. ...Attention by public
and by public officials is merited if the encounter is less
than a decade away.” It was later demoted to Level 0 on
Torino scale. NASA Near Earth Object Apophis Position
Uncertainty:
http://neo.jpl.nasa.gov/apophis/apophis_image3.html
To target Earth it will have to pass through a 600m
gravitational “keyhole” in 2029 and then impending
collision would happen on April 13, 2036. But … it warrants
closer scrutiny.
1. Orbital Elements: Asteroids travel about the sun in a three dimensional
path that is described by mathematical terms called orbital elements. The while
the paths are somewhat predictable, they change over time due to localized
gravitational events and relativistic effects.
Orbital Inclination
Right Ascension of Ascending Node
Argument of
Perigee
Mean Motion
Eccentricity
26
Asteroid WISE Chapter 4: How Close Will It Come?
2. Snatching the Elements
Log on to the JPL Small-Body Database Browser: http://ssd.jpl.nasa.gov/sbdb.cgi
On paper, make a table to record orbital elements for 99942 Apophis and answer the
questions below it (include diagrams):
Object: 99942 Apophis
Element
eccentricity
semi-major axis (AU)
parhelion distance
inclination (degrees)
longitude of the ascending
node (degrees)
orbital period (days)
aphelion distance (AU)
absolute magnitude
Diameter (km)
Symbol
e
a
q
i
node
Value
period
Q
H
a. Consider the diagram of orbital eccentricities (right) and make
the following predictions:
Which “e” value(s) represent the shape of an orbit of most moons about planets
and some planets about a star?
Which “e” value(s) represent the shape of the orbit of near earth asteroids and
planets far away from their stars?
Which “e” value(s) represent shape of orbits of comets?
b. Consider the value for the eccentricity of the Apophis asteroid and examine the
table of eccentricities below. How would you describe the shape of its orbit?
3. Where is it and will it hit the planet?
99942 Apophis will make its first
closest approach to Earth on April
14, 2029. Verify this on the simulator and report how closely it will
graze Earth.
Scroll until
this date
reflects closest
approach
near April
14, 2029 and
2039.
Keep an eye
on the Earth
Distance
until it is the
smallest value.
Scroll using “1
Year” first…
Asteroid WISE
a. Click on the “Orbit Diagram” tab
and select “1 Year.” Then use the
advance arrows to scroll to the
Year 2029. Continue to narrow the
date using “1 Month” then “”1Day”
“1hour” until the date in the bottom
of the right screen reads “April 14,
2009” and the “Earth Distance” is
the smallest number.
b. Write “The closest approach of
Apophis to earth is
______________ AU.”
Chapter 4: How Close Will It Come?
27
c. Using the conversion factor of 1 AU = 92 955 887.6 miles, convert this
value to miles. Write “Apophis will be
_______________ miles from Earth on April 14, 2029.”
d. The closest approach of Earth’s moon at perigee is 363, 104 km.
Using the conversion factor 1 km = 0.62 miles, convert the Apophis
approach from miles to kilometers: _________________ km
e. Will Apophis be outside the Moon’s orbit or closer to Earth than the
moon at this point? f. PLAY TIME: Use the “ZOOM” scroll bars and the 3-D Orientation scroll
bars that surround the orbital diagram to resolve the physical proximity
of Apophia relative to Earth. Using the “SAVE IMAGE” tab, this can be
captured and pasted in another file if you would like to save it.
g. Now repeat this simulation for the next approach date on April 13,
2039. What is the date and distance to Earth of the closest approach
near this date? Write:
Date: Earth Distance: h. Based on this simulation, what is the likelihood that Apophis will collide
with Earth in 2029 or 2039? Support your prediction with simulated
data.
.
APPENDIX
Eight Orbital Elements:
shape and location of an orbit at a snapshot in time
Element
epoch
Symbol
To
orbital
inclination
right
ascension
argument of
perigee
eccentricity
mean
motion
mean
anomaly
drag
Io
Oo
Wo
Eo
No
Mo
N1
Which means . . .
length of time of the orbital snapshot, where
and how fast object was going
tilt of an orbit with respect to the equatorial
plane of the object it orbits about
angle between two objects in orbit with respect
center of objects and along an equator
an angle
shape of the ellipse of the orbit
size of the orbit or how far away the object
is
Location of object in the orbit, with respect
to the Epoch
friction
How close will the asteroid get to Earth? To calculate this, we
need two of the orbital elements: a, the semi-major axis of the
ellipse, which measures how far away the asteroid is from the
Sun on average (for a perfect circle, the semi-major axis is equal
to the radius), and e, the eccentricity, which measures elliptical
the orbit is (a perfect circle has an eccentricity of 0).
The closest the asteroid gets to the Sun (called perihelion) is
calculated from the equation
Rperihelion = a(1 – e)
The farthest the asteroid get from the Sun (called aphelion) is
calculate similarly
Raphelion = a(1 + e)
28
How close will it come to Earth? The semi-major axis of
Earth’s orbit is 1 Astronomical Unit (AU), defined as the
average Earth-Sun distance. If either the perihelion or aphelion
is close to 1 AU, then the asteroid comes close to Earth orbit.
If the perihelion is less than 1 AU and the aphelion is greater
than 1 AU, then the asteroid actually crosses Earth’s orbit.
These are the asteroids to watch out for!
Asteroid WISE Chapter 4: How Close Will It Come?
Chapter 5
5. Spinning Space Rocks
Developed by HOU Leader, Thomas Morin
Investigation
Rotation Period Of An “AsterSpud”
Objects rotate differently in space. Planets being spherical (like a ball) for
the most part spin on an axis with simple symmetry.
Other objects such as asteroids similarly have axes
of rotation but because of their shape can be widely
different than spherical such elongated like a potato,
...or a chunk of rock....
In this investigation you use a potato
and light sensor to collect data that
can help you to determine the time it
takes a potato (acting as an asteroid)
to rotate around its axis.
SETUP—this is what you will need:
• A single light source to shine on the potato.
• A light probe and interface connected to a
computer to be used as the instrument to
collect the data while the potato is rotating.
• A back drop that is dark helps the potato to stand
out during the investigation.
This image
shows the
potato and
drill setup.
Note the black
background.
The drill is
mounted with
the spin axis
vertical.
Black background
Asterspud
Barrier to block drill
from view
Light
source
Asterspud
Drill
This image
shows the rest of
the setup using
the light probe,
light source
and computer
interface.
Light sensor
Laptop
Chapter 5: Spinning Space Rocks
Asteroid WISE
29
When you have constructed your “Astro-spud” setup, it is now time
to collect data and determine the period of rotation.
Procedure:
Part I:
Plot brightness of a rotating object to determine its period of rotation.
1. With the surrounding lights off or low turn on your single light source
SAMPLE OF THE DATA
on to the “Astro-spud”.
Time
Illumination
2. Make sure that the computer and light probe are connected and the
probe is pointing directly at the “Astro-spud” and the correct software
0
2.7
(such as Vernier’s Logger Pro or Logger Lite or similar software) is
0.05
2.5
activated.
0.1
2.1
3. Turn on the drill to a slow rate of rotation so as not to launch the
0.15
1.9
“Astro-spud” from the drill.
0.2
2.3
4. Keeping the drill turning at a constant rate (that’s where a clamp
0.25
2.5
placed on trigger works well)
0.3
3.3
5. Start to record the light fluctuations produced as the “Astro-spud”
0.35
2.9
rotates. This should be done for at least 5-6 seconds to collect a fair
0.4
2.7
sized sample. Longer times can work as well.
0.45
2.1
6. Your data and graph might look like the samples shown here.
0.5
2.3
Sample graph
9. Now that you have collected data, and
made graphs of a least two different
rotational rates, share your results with
another team and see if they have similar
wave forms as yours.
Part II:
Make a record of different rotational positions.
7. From your data and constructed graph, you
now will be able to determine the period of the
“Astro-spud”. The graph is now a signature
of what a particular orientation of a rotating
object and it can be used to determine other
objects that rotate on a similar axis.
8. Questions:
a. What do you think a graph would look
like for the “Astro-spud” if it was spun at
a faster rate?
b. What do you think a graph would look like
for the “Astro-spud” when it is spun at a
slower rate?
30
Asteroid WISE
1. Take your “Astro-spud” attached to the drill and
now change the position in which it will spin.
Example: Turn it towards the probe so it looks
like a propeller and collect data at different
speeds.
2. After collecting the data and constructing graphs
of each different speed, compare these graphs
with your first set of graphs and see if you can
identify unique the signatures of each.
3. Using your finished graphs, see if other teams
can determine the orientation of your “astrospud”.
Chapter 5: Spinning Space Rocks
Developed by HOU Leader, Janet Ward
Investigation
22 Kaliope Light Curve
22 Kalliope Facts:
1. Discovered in 1852, Main Belt Minor Planet with small orbiting
moon Linus
2. M-type spectrum but its low density and very low albedo
doesn’t fit it well in this model
3. possible self-gravitating rubble pile
4. Dimensions 215×180×150 km and estimated 6 to 8 E18 kg
5. Rotational period 4.148 h
6. Temperature 161K
1. Binary Asteroids and Rubble Piles:
The image below is the 25143
Itokawa asteroid imaged by the
Japanese spacecraft Hayabusa.
Examine its features and compare them
to other feature you have observed
on our moon and images of other
asteroids. Is there anything unusual
about its features in comparison?
[Prepare a worksheet to write this
question with its answer, as well as
other later questions.]
Image: Minor Planet 25143 Itokawa
Image: Structure of
a self- gravitational
rubble pile
Chapter 5: Spinning Space Rocks
Asteroid WISE
31
22 Kalliope has been designated as an M-class Minor Planet by its
spectrum, which should imply that it’s composed of metal. However, it’s
not as shiny and reflective of sunlight like a typical metallic asteroid and
the computations of density confirm that it can’t be metallic.
The most likely explanation at this time is that its composition is
similar to Itokawa, shown above, and may be a “rubble pile” asteroid.
Rubble piles are formed when an asteroid smashes apart after collision
or tidal disruptions and then the bits fall back on each other over days
and weeks in a loose self-gravitating conglomerate. So craters are not
part of the surface features. Noting its oddly bent shape, Itokawa is also
probably composed of two asteroids that collided with each other.
2. Light Curves: Shape
and Composition
SHAPE EFFECTS: Asteroid
light curves have two minimum
and maximum due to their usual
elongated potato shape and its
rotations
MATERIAL EFFECTS: Composition directs the best way to measure
the brightness of an asteroid. Darker
asteroids can be detected using
infrared techniques.
32
Asteroid WISE
Chapter 5: Spinning Space Rocks
3. How Big Is It, How Hot Is It,
How Fast Does It Spin?
The average main belt asteroid
looks something like a potato so during
each rotational period, it presents two
elongated sides, and two shortened
ends. During those times, the light
curve will show two bright peaks, and
two dim troughs. On the average, it
rotates at least once in an eight-hour
period, allowing collection of the entire
curve with one night’s data. Others
can be much more difficult and take
several days or even months to rotate
just once. So data must be collected
over a long time to build the light
curve. Light curve courtesy Minor Planet
Observer/Palmer Divide Observatory
http://www.minorplanetobserver.com/pdolc/5587_1990sb.htm
4. Light Curve of 22 Kalliope
Using intensity or the brightness of the object you
will determine:
• rotation rate
• temperature
• brightness
Example: Light curve of asteroid 201
Penelope showing one full rotation of 3.7474
hours. Courtesy Las Cumbres Observatory
Global Telescope
Chapter 5: Spinning Space Rocks
A. PLOT LIGHT CURVE: (Intensity vs. Time)
Using light curve photometry for 22 Kalliope collected from derived published literature to plot a
light curve on graph paper, and carefully sketch
a best-fit curve. Measure the length of the period
of one cycle.
Elapsed Time (h)
0.4
0.150
0.301
0.440
0.590
0.790
1.050
1.280
1.325
1.550
1.645
1.710
1.855
2.190
2.380
2.700
3.000
3.325
3.550
3.620
3.780
3.950
4.030
4.100
4.160
4.530
4.855
Change in Magnitude
0.23
0.25
0.23
0.18
0.14
0.03
-0.06
-0.14
-0.12
0.00
0.03
0.06
0.10
0.21
0.22
0.14
0.03
-0.13
-0.23
-0.25
-0.17
-0.06
-0.02
0.03
0.06
0.20
0.25
Asteroid WISE
33
B. Compute Rotation Rate From Light Curve:
ω = (2π/rotation period)
The accepted value for the rotation period of 22 Kalliope is 4.148 h. What
is the percentage error of your estimate from this value?
This was a rough technique to extract the rotation period. What factor
accounted for the greatest error in your value and how could that be
resolved better using an alternate technique?
C. Determine Temperature from a best fit curve of brightness vs.
wavelength for four observations:
TA4 = LS (1 – A) / (16π εσSB rSA2)
Parameter
LS
A
ε
σSB
rSA
Describes
How to Find
Measured Values
Value
solar luminosity
3.827×1026 Watts
asteroid albedo,
amount of sunlight
reflected
emissivity
measured, a default
value for an unknown
is 0.1
0.9
Stefan-Boltzmann
constant
Sun-asteroid
distance
5.6704×10-8 W/m²K4
Measured Value
JPL small-body database
“Physical Parameter” table for
specific asteroid
measured
JPL small- body database
“Orbit Diagram” on observation date
TEMPERATURE PARAMETER TABLE
a. Open the JPL Small-Body Database browser:
http://ssd.jpl.nasa.gov/sbdb.cgi and enter “22
Kalliope” in SEARCH.
d. Compute the estimated temperature by taking
the fourth root of the quotient. The unit will be
in degrees Kelvin:
b. Scroll down to the PHYSICAL PARAMETER
table and look for the Geometric Albedo value
and record it in the Temperature Parameter
Table above.
TA4 = LS (1 – A) / (16π εσSB rSA2)
c. Click on the Orbit Diagram Tab and shape the
orbit using the date arrows for the observation
date February 8, 2007.
[write the following on worksheet]
The Sun distance is ___________ AU
Convert the value to meters using the conversion
factor 1 AU = 1.4958 E11 meters
The Sun to 22 Kalliope distance on Feb 8, 2007
was _________________m. Record this
value in the table above.
34
Asteroid WISE
[write on worksheet:]
The estimated temperature value, TA, for 22 Kalliope on the observation night was
____________ K or ______________ o C.
Is this a hot or cold asteroid by definition using
your estimated value? NASA states that the average surface temperature
of an asteroid is -100oC. How does your computed value compare? What was your percentage
deviation from NASA’s average value?
Chapter 5: Spinning Space Rocks
D. Derive Asteroid Albedo From Light Curve: A = Lv/(Lth + Lv)
Lv = πRA2 LS/4πrSA2 A /4πrEA2
Lth = Pin = πRA2 LS (1 – A)/4πrSA2
ALBEDO PARAMETER TABLE
Parameter
A
Lv
Lth
Describes
albedo- brightness of
reflected sunlight
visible light observation
How to Find
Measured Values
Value
derive
Measured Value
derive
RA
thermal infrared brightness
radius of asteroid
derive
measured
LS
rSA
Solar luminosity
Sun-asteroid distance
3.827×1026 Watts
measured
rEA
Earth- asteroid distance
measured
JPL small- body database
“Physical Parameter” table
for specific asteroid
JPL small- body database
“Orbit Diagram” on observation date
JPL small- body database
“Orbit Diagram” on observation date
a. Open the JPL Small-Body Database browser
http://ssd.jpl.nasa.gov/sbdb.cgi: and enter “22
Kalliope” in SEARCH.
b. Scroll down to the PHYSICAL PARAMETER
table and look for the Diameter value, which
is in kilometers. Convert to radius in meters
and record it in the Albedo Parameter Table
above.
c. Click on the Orbit Diagram Tab and shape the
orbit using the date arrows for the observation
date February 8, 2007. [write on worksheet:]
The Sun distance is ___________ AU
The Earth distance is __________ AU
Convert the value to meters using the conversion
factor 1 AU = 1.4958 E11 meters
The Sun to 22 Kalliope distance on Feb 8, 2007
was _________________m. Record this
value in the table above.
The Earth to 22 Kalliope distance on Feb 8,
2007 was _________________m. Record
Chapter 5: Spinning Space Rocks
this value in the table above.
d. Compute the Visible Light parameter and place
in the Albedo Table.
Lv = πRA2 LS/4πrSA2 A /4πrEA2
e. Compute the Thermal Infrared Brightness
parameter and place in the Albedo Table.
Lth = Pin = πRA2 LS (1 – A)/4πrSA2
f. Compute the Albedo of 22 Kalliope:
A = Lv/(Lth + Lv)
Asteroid WISE
35
Exit Ticket
Design an illustration of the following terms by creating a diagram of Earth, the Sun
and planets, the Asteroid Belt, and the Kuiper Belt.
asteroid comet
meteroid
meteor meteorite
• Note the general placement of orbits of the
objects about the Sun and with respect to the
8 planets.
• Create a “callout “ for planet Earth to explain
terms as they apply to atmospheric effects and
impacts
• Note when each is properly in use.
36
Asteroid WISE
Chapter 6: Getting Involved in the Search
Chapter 6
6. Getting Involved in the Search
Investigation
IASC Founder and Director: Patrick Miller
Asteroid Search Campaign
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
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.
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 6: Getting Involved in the Search
Asteroid WISE
37
Appendix A:
Space Rock Vocabulary
Asteroid
Naturally formed solid bodies that orbit the
sun, have no atmosphere and no signs of
gas or dust coming from them. Most are
found in orbit between the orbits of Mars
and Jupiter.
Breccia
Rock made from pieces of rocks formed
earlier.
Carbonaceous Chondrite
Stony meteorite containing chondrules and
volatiles.
Chondrite
A stony meteorite containing chondrules.
Chondrule
Round, glassy part of meteorite made from
silicates.
Coma
Comet
Roughly spherical area of vaporizing gases
and dust around the nucleus of a comet.
Small bodies of rock, iron and frozen water
and gases that orbit the sun in elliptical orbits.
As they get close to the sun the gas vaporizes
leaving a tail of dust and debris.
Comet Head
The nucleus and coma of a comet.
Dust Tail
Trail of gases, dust and debris left behind as
a comet gets close to the sun.
Ejecta
Fireball
38
Pulverized rock scattered by impacts on an
object’s surface.
A very bright meteor.
Asteroid WISE
Kuiper Belt
Small asteroids obiting the sun between the
orbits of Uranus and Neptune thought to be
the source of comets.
Light-year
The distance light travels in a year. About 1013
km or 6 trillion (thousand billion) miles.
Meteor
A bright streak of light that appears briefly
in the sky. It is sometimes called a shooting
star or falling star. It is actually caused by a
meteoroid entering the earth’s atmosphere,
heating up so much that it glows and creates
a trail of melted and vaporized meteoroid
particles.
Meteorite
Any meteor striking the ground.
Meteoroid
A solid object moving in interplanetary space,
of a size considerably smaller than an asteroid
and considerably larger than an atom. It can
be a piece of comet debris.
Meteor Shower
When the Earth enters a meteoroid stream left
by a comet it produces a meteor shower.
Oort Cloud
A spherical region outside the orbit of Pluto
thought to be the source for long-period comets with orbits of longer than 200 years.
Orbit
The path an object takes as it moves around
another object.
Rotation
An object spinning about its center.
Volatiles
Carbon compounds, frozen gases and other
materials that when heated vaporize.
Chapter 6: Getting Involved in the Search
Appendix B:
Determining Asteroid Characteristics from WISE Data
by Matt Fillingim
We’ve identified an asteroid in the WISE data. Will it hit Earth? If it were to
impact Earth, how bad would it be: a puff of smoke in the atmosphere or the
end of civilization as we know it?
The starting point will be a sequence of images from WISE. What can we
learn from the data?
POSITION:
The first thing we (and the WISE software pipeline) can determine is the position of the object. The satellite measures the right ascension and declination
of the object in space. From just three measurements at different times, the
position and orbit of the asteroid can be estimated.
In 1801, Carl Friedrich Gauss developed a method to calculate the orbits of
Ceres, the first asteroid discovered (now technically designated a dwarf planet),
using three measurements of right ascension and declination. His method was
first widely published in 1809. This method relies on Johannes Kepler’s first two
Laws of Planetary Motion published in 1609:
1. The orbit of every planet is an ellipse with the
Sun at a focus.
2. A line joining a planet and the sun sweeps out
equal areas during equal intervals of time.
We can estimate the object’s position in space
by making some assumptions that simplify the
mathematics. Our three observation times will be
called t1, t2, and t3. We can approximate the area
swept out by the object between times t1 and t2 and
between times t2 and t3 as triangles rather than
sections of an ellipse so that the ratio of the times
between observations is equal to the ratio of the
areas of the triangles (approximately) swept out by
the object. Using this simplification, we can estimate
the Sun-object and Earth-object distances. We need
these distances to calculate the temperature and
size of the asteroid later on.
[ISpreadsheet “example_ceres.xls” calculates
these distances – it uses cross products and linear algebra which may be beyond most students.
It is derived from the notes of Dr. J. B. Tatum at
the University of Victoria (http://www.astro.uvic.
ca/~tatum/celmechs.html). Minor Planet Ephemeris
Service (http://www.cfa.harvard.edu/iau/MPEph/
MPEph.html) at the Minor Planet Center will also
give these numbers; “r” is the Sun-object distance
and “Delta” is the Earth-object distance.]
Asteroid WISE
Oct 2009
To completely describe the orbit of an object, we
need six variables known as the orbital elements.
These six orbital elements describe the size, shape,
and orientation of the orbit. The complete process
of calculating an orbit is a mathematically intensive process. One of the jobs of the Minor Planet
Center (http://www.cfa.harvard.edu/iau/mpc.html)
is to calculate the orbits of asteroids and other
objects based on observations from professional
and amateur astronomers alike. Many observations are necessary to make better estimates of
the orbit and to refine the orbit. Also, gravitational
interactions with planets and other asteroids can
slightly change the orbit of asteroids over time. So
even for well known objects, new observations are
important to continue to refine their orbits.
The WISE software pipeline will identify all of the
known objects in the images, which will be most
of the objects in the images. The orbital elements
for known objects can be found using the Minor
Planet Ephemeris Service (http://www.cfa.harvard.
edu/iau/MPEph/MPEph.html) at the Minor Planet
Center (http://www.cfa.harvard.edu/iau/mpc.html).
Just type in the name or number of the asteroid in
the box and be sure to click the MPC 8-line button
near the bottom of the page.
39
[Note: I also have a black-box program that calculates the orbital elements that I got online and rewrote in IDL (Interactive Data Language).
I don’t think that the full calculation is spreadsheet-able.]
So from observations we’ve computed the Sun-asteroid and Earthasteroid distances. With the help of the Minor Planet Center, we know
the orbit of the asteroid. How close will the asteroid get to Earth? To
calculate this, we need two of the orbital elements: a, the semi-major
axis of the ellipse, which measures how far away the asteroid is from
the Sun on average (for a perfect circle, the semi-major axis is equal to
the radius), and e, the eccentricity, which measures elliptical the orbit
is (a perfect circle has an eccentricity of 0).
The closest the asteroid gets to the Sun (called perihelion) is calculated
from the equation
Rperihelion = a(1 – e)
The farthest the asteroid get from the Sun (called aphelion) is calculate
similarly
Raphelion = a(1 + e)
How close will it come to Earth? The semi-major axis of Earth’s orbit is
1 Astronomical Unit (AU), defined as the average Earth-Sun distance.
If either the perihelion or aphelion is close to 1 AU, then the asteroid
comes close to Earth orbit. If the perihelion is less than 1 AU and the
aphelion is greater than 1 AU, then the asteroid actually crosses Earth’s
orbit. These are the asteroids to watch out for!
INTENSITY:
We can also learn a lot about the asteroid (rotation
rate, temperature, size, etc) from its intensity – how
bright it appears in the WISE images.
Rotation Rate:
The light curve can be created by plotting the
intensity of an object as a function of time from a
sequence of images. If the object is not spherical
(for example, potato-shaped), the brightness of
the object will changes as it rotates. If the object
rotates quickly enough (a typical asteroid has an
8-hour rotation period, some have periods that are
shorter and some have periods that are considerably longer), the rotation rate can be measured
from the brightness variations of the light curve.
The ratio of the maximum to minimum brightness
is equal to the ratio of the maximum to minimum
area facing the Earth as it rotates. This ratio is a
measure of the “potato-ness” of the object.
40
Oct 2009
From the rotation rate, we can also get an estimate
of the lower limit of the asteroid’s density. An object
held together by its own gravity (a “pile of rubble”
as opposed to a giant rock), will fly apart if spins
too fast – that is, when its centrifugal acceleration
is larger than its surface gravity:
ω2R > GM/R
where ω is the rotation rate (2π/rotation period), R
is the asteroid’s radius, G is the universal gravitational constant, and M is the asteroid’s mass. After
a little algebra,
ρ < (3.3/P)2
where ρ is density in g/cm3 and P is the rotation
period in hours. If the density is lower than this
number, the asteroid will spin itself apart. In most
cases, this will give a very low number (much less
than 1 g/cm3 which is the density of water). This
is the lower limit of the density; it can certainly be,
and usually is, much higher.
Asteroid WISE
Temperature:
By equating the solar energy reaching the asteroid to the thermal energy
emitted by the asteroid, the temperature of the asteroid can be calculated. As
shown below, in general, the temperature of the asteroid only depends upon
its distance from the Sun (with some simple assumptions).
The incident solar energy is
Pin = πRA2 x LS/4πrSA2
where RA is the radius of the asteroid and πRA2 is the cross-sectional area of
the asteroid; LS is the solar luminosity (the power output of the Sun) and is
equal to 3.827×1026 Watts; rSA is the Sun-asteroid distance (determined above),
so LS/4πrSA2 is the solar power per unit area at rSA. The incident solar energy,
then, is the solar power intercepted by the asteroid.
For a blackbody (an object that is a perfect absorber of radiation), the thermal
power radiated is
Pout = 4πRA2σSBTA4
where σSB is the Stefan-Boltzmann constant (5.6704×10-8 W/m²K4), and TA
is the temperature of the asteroid in Kelvins. This is known as the StefanBoltzmann Law.
Setting Pin = Pout and solving for TA gives
TA4 = LS/(16π σSB rSA2)
However, in reality, asteroids are not blackbodies,
they are graybodies (not quite perfect absorbers
of radiation), so Pin and Pout must be slightly modified:
Pin = πRA2 x LS x (1 – A)/4πrSA2
where A is the asteroid albedo (the amount of sunlight reflected), so (1 – A) is the amount of sunlight
absorbed by the asteroid.
Pout = 4πRA2εσSBTA4
where ε is the asteroid’s emissivity, a measure of
how well the asteroid radiates energy (a perfect
blackbody has an emissivity of exactly 1).
The refined temperature estimate is
TA4 = LS (1 – A)/(16π εσSB rSA2).
In general, the emissivity, ε, is often assumed to
be 0.9. Measured asteroid albedos vary between
0.023 and 0.63. If the albedo is unknown, a common assumed value is 0.1, so (1 – A) is 0.9. In this
case, the blackbody temperature and the greybody
temperature are the same, and the only measured
quantity is the Sun-asteroid distance, rSA.
Asteroid WISE
Oct 2009
[An alternate way to try to calculate the temperature
is to use the intensities of the asteroid as observed
by (up to) four wavelengths observed by WISE.
The brightness as a function of wavelength of a
blackbody follows Planck’s Law:
where λ is wavelength, h is the Planck constant
(6.62606896×10−34 Joule-second), c is the speed
of light (299,792,458 meters/second), and k is the
Boltzmann constant (1.3806504×10−23 Joule/Kelvin). The temperature of a blackbody determines
its intensity (I), or brightness, as a function of wavelength. The measured brightness at four different
wavelengths can be used to determine the “best fit”
temperature. This temperature can be compared
to the one calculated using the distance only.
41
Size:
By using the infrared brightness from the WISE images with the Sun-asteroid and
Earth-asteroid distances, the size of the asteroid can be calculated. How bright
the asteroid looks to us as observers on Earth, depends on how big the asteroid is
and how away it is from us. Since we already computed how far it is from us from
its position, how bright the asteroid is depends on its size.
As stated above, the solar power incident on the asteroid is
Pin = πRA2 LS (1 – A)/4πrSA2
If the object is in thermal equilibrium (which is probably reasonable if it is a relatively
slow rotator), then the incident solar power is equal to the total thermal radiation
emitted by the asteroid, the thermal luminosity, Lth.
Pin = Lth
Since the thermal radiation is emitted in all directions, the brightness WISE observes,
Bth, is decreased by 1/4 πrEA2, where rEA is the Earth-asteroid distance.
Bth = Lth/4 πrEA2 = Pin/4 πrEA2 = πRA2 LS (1 – A)/(4πrSA2 4πrEA2)
RA2 = 16π rSA2 rEA2 Bth/[LS (1 – A)]
RA = 4 rSA rEA {πBth/[LS (1 – A)]}1/2
If there is a large variation in the light curve, that is, if the asteroid is potato shaped,
an average radius can be calculated from the average brightness. Similarly, the
maximum and minimum dimensions can be calculated from the maximum and
minimum brightness of the light curve.
The WISE software pipeline should also automatically compute the size of the asteroid. This size can
be compared to the size computed above.
From coordinated visible light observations, the
albedo can be measured. The asteroid brightness
in the visible is simply the reflected sunlight.
Lv = πRA2 LS/4πrSA2 A /4πrEA2
The ratio of the visible to thermal infrared brightness is
Lv/Lth = A/(1 – A)
So the albedo is
A = Lv/(Lth + Lv)
Once the albedo is measured rather than assumed,
the size calculation above can be refined.
The albedo can also give an indication of the
composition of the asteroid. Asteroids with very
low albedos ~ 0.03, that is, very dark asteroids,
are called C-type and are typically rocky. Brighter
asteroids with albedos between 0.1 and 0.2 are
either S-type – metallic (nickel-iron) mixed with
rock (silicate) – or M-type – purely metallic.
The composition also gives an indication of the
density of the asteroid. The densities of C, S, and
M class asteroids are 1.38, 2.71, and 5.32 g/cm3,
respectively. There is a wide range of asteroid
densities, but if albedo or composition is unkown,
a density of 2 kg/m3 can be assumed.
42
Oct 2009
[If it is not feasible to calculate the albedo with
visible measurements (which it is quite possible
that it won’t be), then an albedo and density or a
range of albedos and densities can be assumed.
Albedos range from 0.023 to 0.64 with a typical
value being 0.1. Densities range from 1.38 to 5.32
g/cm3 with a typical value of 2 g/cm3 (or so says
Wikipedia, at least).]
Mass:
From size of the asteroid and its density, the mass
of the asteroid can be calculated. The volume of
the asteroid is
VA = 4/3 π rA3
The mass is simply the volume multiplied by the
density from above.
Asteroid WISE
Lastly, the kinetic energy of the asteroid can be computed.
The kinetic energy is
KE = 1/2 x mass x (velocity)2
The velocity (at least the transverse velocity parallel to Earth’s
orbital motion – there is no measurement of the line of sight
velocity away from or toward Earth) can be measured from
the sequence of WISE images. The angular distance the
asteroid moves between the first image and last image in a
sequence can be measured from the WISE images. Using
the measured right ascensions (RA) and declinations (DEC)
the angular distance, theta, is
theta = cos-1[sin(DEC1) x sin(DEC2) + COS(DEC1) x
COS(DEC2) x COS(RA1 – RA2)]
where all angles are in radians.
The actual distance the asteroid travels is
distance = rEA x theta
The velocity is then this distance divided by the time between
the first and last image in the sequence.
[Alternately, with another black-box, the orbital elements can
be converted into state vectors – instantaneous position and
velocity vectors – then the magnitude of the velocity vector
can be used.]
In SI units, the kinetic energy is in Joules (the mass is in
kilograms and the velocity is in meters per second). For
comparison, a typical stick of dynamite contains about 2×106
Joules. The largest nuclear bomb ever detonated was about
2×1017 Joules.
Asteroid WISE
Oct 2009
43
Appendix C: Web Resources
Astronomical Research Institute
http://ari.home.mchsi.com/index.htm
Hands-On Universe website
http://www.handsonuniverse.org/
Image Processing Software
http://astro.uchicago.edu/yerkes/outreach/activities/ipsoftware.html
International Astronomical Search Campaign (IASC) website
http://iasc.hsutx.edu/
JPL Horizons Web Interface
http://ssd.jpl.nasa.gov/horizons.cgi
Minor Planet Center
http://www.cfa.harvard.edu/iau/mpc.html
WISE website
http://wise.ssl.berkeley.edu/
Materials for HOU-WISE workshops
http://www.handsonuniverse.org/hs/wise/index.html
Yerkes Education Website
http://astro.uchicago.edu/yerkes/outreach/activities.html/
44
Asteroid image sets from Yerkes 24 inch
http://astro.uchicago.edu/yerkes/outreach/activities/Explorations/images/Asteroids/
Oct 2009
Asteroid WISE
Asteroid WISE
Oct 2009
45