Download Lecture 4, PPT version

Class Etiquette
Don’t distract
your classmates
Outline - Jan. 26, 2010
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Last word on Eclipses (pgs. 45-47)
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Planetary motions (pgs. 49-51)
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Stellar parallax (pg. 52)
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Ancient Observatories (pgs. 60-65)
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Ancient Greek Astronomy (pgs. 65-68)
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Copernicus, Tycho, Kepler, Galileo (pgs. 70-78)
Cause of Eclipses
Total solar eclipse
Annular (“ring”) solar eclipse
Total lunar eclipse
Solar eclipse: new moon passes in front of the sun, shadow of the
new moon falls on the earth
Lunar eclipse: earth passes between the sun and the full moon,
shadow of the earth falls on the full moon
Why don’t we get a solar eclipse with every new moon
and a lunar eclipse with every full moon?
Moon’s orbit is inclined at 5o to Earth’s orbit. It is only when the moon is
precisely in the same plane as the earth’s orbit that eclipses can occur.
How to tell a planet from a star without a telescope
Five planets are visible
without a telescope. They
look like points of light (like
stars), with one important
difference.
“Planets” comes from the
Greek word “planetes”
meaning “wanderers”.
Planets move with respect to the (fixed) stars
Locations of Venus and Jupiter over the course
of 6 nights. All photos taken when the star
“Spica” was in the same location in the sky.
Notice how Venus has moved much farther
than Jupiter over this period of time!
The primary motion of the planets is from
WEST to EAST
Sometimes the planets reverse their motion
and travel from EAST to WEST, a phenomenon
known as “retrograde motion”
Example: Retrograde Motion of Mars
East
West
From Jan. 4, 1995 to March 25, 1995, Mars is moved “backward” in the sky (east to west)
On astronomical maps, east is on the LEFT and west is on the RIGHT. Why????
From what perspective are you viewing this picture?
West
East
Astronomers look UP at the sky!
Actual image of Mars undergoing “retrograde motion”
Do you notice anything different about Mars when it is undergoing
retrograde motion? (Assume all the individual exposures were the
same length of time.) Retrograde motion is on the TOP part of the
“loop” in the sky.
It’s all about perspective!
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We see the planets move with respect to the fixed stars
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Space is really 3-d (planets are much closer than the stars), but space
looks 2-d (when you look at a picture of the sky you don’t have a
sense of depth that tells you the planets are closer than the stars)
•
The planetary motion you see is due to combination of: (1) earth’s
motion about the sun and (2) the planet’s motion about the sun
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Retrograde motion happens when an inner planet (e.g., the earth)
catches up to and “laps” an outer planet (e.g., Mars)
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All planets orbit in the same direction about the sun continuously, they
only appear to go “backward”
Retrograde Motion of Mars
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Happens about once every 2 years
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Only occurs when Mars and Earth are near their distance of closest
approach (called “opposition” because Mars and the Sun are on
opposite sides of the sky, as seen from earth)
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Is currently going on! Mars will be at opposition on Friday (Jan. 29)
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For every 1 orbit of the Earth around the sun, Mars makes about 2
orbits around the sun
http://www.youtube.com/watch?v=72FrZz_zJFU
Does the earth really orbit the sun?
What proof do we have?
Once again, it’s all a matter of
perspective!
As the earth orbits the sun, nearby
stars appear to shift their location in
the sky compared to extremely
distant (“background”) stars.
The farther is a star, the smaller is
its parallax.
If p is measured in arcseconds, the
distance to the star is
d = 1/p
The closest star to us (other than the sun) has a
parallax of p = 0.7687 arcsec = 2.1x10-4 degree.
where d is in units of “parsecs”
This is much too small to see without a telescope!!
1 parsec = 1 pc = 3.26 ly
Ancient Observatories
Stonehenge (3000 to 5000 years old)
Salisbury Plain, west of London, England
Truly Monolithic!
Largest stones
weigh 50 tons
Rising and setting points of sun
and moon from various alignments
Heel Stone
Aubry holes used to predict eclipses
Sunrise on summer solstice
Heaven on Earth?
Pyramids of and near Giza Plateau
“Great Pyramid” of Giza (Cheyops Pyramid)
built for Khufu between 2589 BC ad 2566
BC; first pyramid on the Giza plateau
Looking through shaft from King’s
chamber around 2600 BC would have
seen Orion’s belt when it first appeared
in the winter sky
Osiris, god of death and resurrection, resided in Constellation of Orion
A scale model of Orion in Egypt?
These were Master Builders!
Why are the other 2 pyramids at Giza smaller than the first and “not quite” in a straight line?
Milky Way = Nile
No pyramids at
locations of
“Betelguese” or “Rigel”
Ancient Observatories
North America
Caracol Temple, Yucatan Peninsula, built by
Mayan Indians around 1000 AD
Big Horn Medicine Wheel (Wyoming), built
by Plains Indians
Windows aligned with celestial events,
particularly rising and setting of Venus
(associated with deity Kulkulkan), as well as
rising and setting of sun on solstices and
equinoxes
27 “spokes” and other features aligned
with astronomical events (rising and
setting of sun and stars)
Largest and most complete example
Heliocentric vs. Geocentric
(sun-centered vs. earth-centered)
We know that we live in a heliocentric (sun-centered)
system. The ancient Greeks (for the most part) were
completely convinced that we lived in a geocentric system.
The ancient Greeks weren’t stupid people!
They had reasons for their beliefs.
They also didn’t have telescopes.
Ancient Greek Rationale for Stationary Earth
If Earth does revolve/orbit about the sun, what would you expect the
consequence to be for the locations of stars observed 6 months apart?
If Earth does rotate on its axis once per day, what would you naively
expect to observe/experience on this “moving” body?
If Earth were not at the center of the universe, then why do all objects fall
toward earth?
Note: Ancient Greeks knew the earth was spherical for a variety of reasons
(heights of specific constellations seen from different latitudes, apparent sizes
of ships sailing away from harbor don’t shrink proportionately, shadow of earth
on the moon during a lunar eclipse is always curved).
Ancient Greek “Philosophy”
(not based on observation)
Earth was the realm of the unpure (non-eternal, constantly changing, decay)
Heavens were the realm of the pure (eternal, absolutely unchanging)
Heavenly objects must be made of pure/perfect geometrical forms
(flawless spheres), and must travel on the purest of orbits (perfect circles)
Built up a geocentric model of the solar system based upon this philosophy
(explained transient phenomena such as comets and meteors as forms of
“weather”; i.e., they were earthly phenomena)
Note: most of the above assertions are untestable without telescopic observations!
Retrograde Motion in a Geocentric System
Impossible to explain the observed planetary motions
(especially retrograde motion) just by putting each planet on a
circular orbit, centered on the earth
Result: circular “epicyles” that made the planets literally
move backward in their orbits!
Resulting orbit: “loop-de-loops” in the sky;
planet swings backward on the inner part of
the little loops
Claudius Ptolemy
(about 100 to 170 AD)
Extraordinarily complicated geocentric model (epicycles on top of
epicycles, centers of primary orbits offset from the location of the earth)
Needed 80+ circles just to explain the motion of the sun, moon and 5
planets
Incredibly accurate - was still working well for predicting locations of
planets and occurrences of eclipses in the late-16th century!
There must be a simpler way…
Nicolaus Copernicus (1473-1543)
Sun-centered, planets placed at correct relative distances from the sun,
inner planets moving more quickly than outer planets
Motivation was simplicity (not greater accuracy compared to Ptolemy)
Retrograde motion caused by inner planets catching up to and “lapping”
outer planets
Eventually had to add epicycles to make sun-centered model as accurate
as Ptolemaic geocentric system
The heavens can change!
Tycho Brahe (1546-1601)
Decided to become astronomer at age 13 after witnessing partial eclipse of the sun (Aug. 21,
1560) predicted by Ptolemaic tables from 150 AD
Observed supernova in 1572 (did not move in the sky, so it had to part of the heavens)
Measured parallax of a comet in 1577 and proved that distance to comet was greater than
distance to the moon (so comets weren’t “weather”)
Tycho on the 1572 Supernova
“Amazed, and as if astonished and stupefied, I stood still,
gazing for a certain length of time with my eyes fixed intently
upon it and noticing that same star placed close to the stars
which antiquity attributed to Cassiopeia. When I had satisfied
myself that no star of that kind had ever shone forth before, I
was led into such perplexity by the unbelievability of the thing
that I began to doubt the faith of my own eyes.”
Such an event was simply inconceivable in the ancient Greek view of the heavens.
Correct Model of the Solar System
Johannes Kepler (1571-1630)
using Tycho Brahe’s lifetime’s worth of planetary motion data
First Law: The orbit of each planet around the
sun is an ellipse with the sun at one focus.
Second Law: As a planet moves around its
orbit, it sweeps out equal areas in equal time.
Third Law: The relationship between a planet’s
period of orbit about the sun (P) and the semimajor axis of its orbit (a) is
P2 = a3
where P is measured in (earth!) years, and a is
measured in AU
Purely empirical laws; they only tell you “what”, not “why”
Kepler’s First Law
planets move on elliptical orbits
An ellipse is a geometric figure
with two symmetry axes: major
axis (= long axis) and minor axis
(= short axis). Half the length of
the major axis is called the “semimajor axis”.
The farther apart are the two
foci, the “flatter” the ellipse is.
The closer together are the two
foci, the “rounder” the ellipse is.
A circle is a special case of an
ellipse in which the two foci are
on top of each other (in the
center of the circle).
Kepler’s Second Law
equal areas in equal time
The areas (“square footage”)
of each of the blue triangles
are identical. The time (t) is
also identical for each triangle.
Consequence of Kepler’s
second law: planets move
faster when they are close
to the sun than when they
are far from the sun.
Kepler’s Third Law
P2 = a3
P = the time it takes a planet to orbit once around the sun,
measured in EARTH years
a = half the length of the long axis of the planet’s orbit,
measured in AU
Galileo Galilei
(1564-1642)
First person known to use a telescope to
make detailed study of the sky
Observations provided strong proof that
the Aristotelian (= ancient Greek)
philosophy of the heavens was wrong
Observations provided direct proof that not
all objects orbited the earth and at least
one (Venus) orbited the sun
Sun, Moon and Jupiter are not “Flawless Orbs”
Galileo observed that sun has black spotches (sunspots), moon has craters
and mountains (very “earth-like” terrain), and Jupiter has big red spot
Galilean Moons of Jupiter
(not all objects orbit the earth)
Galileo discovered the 4 largest moons of Jupiter, and
showed that they orbit Jupiter, not the earth
Venus Orbits the SUN!
Venus could not show “full” phase in Ptolemy’s model
According to Ptolemy, Venus would
never show the “full” phase
because it could never be on the
opposite side of the sky as the sun
(as seen from earth).
Phases of planets can only be seen using a
telescope. Venus shows the full range of phases
(full, gibbous, crescent, new) just like the moon.
Venus is smallest (and dimmest) in its full phase.
Phases of Venus in the “Keplerian” Model
(Venus orbits the sun, and is always closer to the sun than Earth)
Venus is in the “full” phase when it is at its farthest distance from the earth,
therefore it appears very small in the sky.
Venus is in the “new” phase with it is at its closest distance to the earth, so
the “narrow crescent” Venus looks very large (and very bright)!
Minute Paper
A few sentences on one of the following:
* something you found particularly interesting today
* something you found particularly confusing today
* questions on things from today that you would like to know more about
Be sure to PRINT your name legibly