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Suppose you were an alien living on the fictitious
warlike planet Myrmidon and you wanted to measure
its size. The planet’s “sun” is shining directly down a
missile silo 1000 miles to your south, while at your
location, it is 54 degrees up from your horizon. What
is the circumference of Myrmidon?
a.
b.
c.
d.
e.
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36,000 mi
3,600 mi
10,000 mi
6,670 mi
1,590 mi
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Announcements:
• Homework #3: due NEXT Tuesday!!
• Reading: 2.1-2.5
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Review:
• Shape of the Earth
• Size of the Earth: Eratosthenes
• Distances/Sizes in Solar System
Today:
• Geocentric versus Heliocentric universe
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Astronomy Through the Ages:
Classical
All that is required to measure the
diameter of the Earth is a person with
stick and a brain.
-adapted from Big Bang, Simon Singh, p.13
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How do we know the Earth is round?
1. Watch a ship sail away.
2. Location of Sun in sky is a function of longitude
(shadows, time zones, etc).
3. Earth’s shadow during lunar eclipse is always circular.
4. People in southern hemisphere see different stars than we
do (e.g. Southern Cross, not Big Dipper…).
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Size of the Earth:
7
5000 stadia
 
360
Circumference
To Sun
7°
360
Circumference =   5000 stadia
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Circumference = 250,000 stadia
7°
Distance between
Syene and Alexandria:
5000 stadia (800 km)
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7°
Size of the Earth
7°
Size of the Moon
Distance to the Moon
Distance to the Sun
Size of Sun
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Ancient Cosmologies
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Geocentric model by Eudoxus (350 BC)
Virtual planetarium…
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A planet’s
eastward drift
10
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Problem with Eudoxus’ Model:
Retrograde Motion of the Planets
In Eudoxus’ Model, all celestial bodies should be
moving gradually eastward with respect to the stars.
This is not always the case! Planets make
occassional jaunts backwards (westward with
respect to the stars). This westward motion of the
planets is called retrograde motion.
Virtual planetarium…
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Ptolemy’s epicycles
(150 AD)
Publication:
Syntaxis
(the greatest)
Model survived until 1500’s
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Most of the time, the planets move _____ to _____ in
the sky with respect to the background stars.
During times of retrograde motion, however, they
move ______ to_______.
a)
b)
c)
d)
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East to West; West to East
East to West; North to South
West to East; East to West
West to East; North to South
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Astronomy During the
Renaissance
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The Geocentric vs. Heliocentric Debate
De Revolutionibus
Orbium Coelestium,
Nicolai Copernicus,
1543
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Retrograde Motion is a
natural consequence of
a heliocentric system.
Animation…
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Stellar parallax
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Stellar Parallax
Parallax angle of the nearest star is less than
1/3600 of one degree.
Ancient astronomers tried to measure
parallax via careful naked-eye observations
but failed.
Finally detected in 1830 by F. Bessel using
telescope.
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A species living on Europa uses telescopes similar to
ours to measure parallaxes of stars in our galaxy.
Which of the following statements best describes their
results:
a. Because they are further from the Sun, they
are only able to measure parallax angles to the closest
of stars.
b. Because they have a longer baseline, they
are able to measure parallax angles to more distant
stars.
c. Because they have a longer baseline, they are
only able to measure the parallax angles to the closest
of stars.
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The Renaissance
N. Copernicus (1473-1543):
• As the “giver of life”, he believed Sun
should be placed at the center of the
Universe.
• Believed that the Ptolemaic model had
become too clumsy and complicated.
G. Galilei (1564-1642):
• Conducted experiments on the nature
of motion.
• Observed celestial objects with
telescope.
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Galileo’s Findings
• More stars!
• Is the universe infinite?
•Moon craters
• Earth-like surface?
•Sun spots
• Celestial bodies not perfect!
•Moons of Jupiter
• A mini solar system?
•Phases of Venus
•Ptolemaic model could not explain.
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Venus’ cycle of phases
Figure 1.29
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Tycho Brahe (1546-1601)
Johannes Kepler (1571-1630)
Brahe was a meticulous
observer. His greatest
contribution to astronomy
was a catalog of planetary
positions. Like his
predecessors, he tried to
measure stellar parallax.
Kepler had the ingenuity
necessary to interpret Brahe’s
observations. Came up with
three empirical laws
describing planetary motion.
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Which two fundamental misconceptions made
Ptolemy’s geocentric model very complicated and
prevented it from adequately describing the
movements of bodies in the solar system?
I) The Sun is at the center of the Universe
II)All heavenly bodies move in combinations of
perfect circles
III)The Earth is at the center of the Universe
IV)The stars never move
a) I and IV
b) II only
c) III only
d) II and III
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