# PHY 110 Lecture 7: Motion of the Planets

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9 Feb 2017
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Motion of the Planets
1. Erasthothenes and Aristarchus
a. Using simple tools and basic geometry to measure
i. The size of the Earth
ii. The size of the Moon and the Sun
iii. And the distances to the Moon and the Sun
2. The Greek Geocentric Model
a. An Earth-centered, or geocentric, model of the universe
3. The Problem of Retrograde Motion
a. The “merry-go-round” model doesn’t explain retrograde motion
i. Periods when the planets appear to move backwards in the constellation
4. The Ptolemaic System
a. To explain retrograde motion, Ptolemy created a complicated system of spheres
on spheres
i. In Ptolemy’s model, planets orbited Earth indirectly by moving on
epicycles which, in turn, orbited the Earth
1. If the planet moves rapidly eastward on the epicycle and the
epicycle moves slowly eastward around Earth, the planet is seen to
be moving eastward
2. If the planet moves rapidly westward along the epicycle and the
epicycle still moves slowly eastward around Earth, the planet looks
like is moving westward (retrograde motion).
5. The Heliocentric Model and Retrograde Motion
a. At a certain point, Mars appears to move eastward against the background of stars
as seen from Earth
b. As Earth passes Mars in its orbit, Mars appears to move westward against the
background of stars (retrograde motion).
c. Later, Mars again appears to move eastward against the background of the stars as
seen from Earth.
6. Copernicus and the Orbits
a. Elongation: the angle between the Sun and a planet, as viewed from Earth
b. Conjunction: a planet and the Sun lining up, as viewed from the Earth.
c. Elongation can be used to determine the size of the orbit
7. The Phases of Venus
a. Galileo’s discoveries of moons orbiting Jupiter and phases of Venus strongly
supported a heliocentric model
b. Phases of Venus could not occur in the Ptolemaic system
8. The Moons of Jupiter
a. Observations of Jupiter and its moons showed that there are objects that do not
orbit the Earth
9. Elliptical Orbits and Kepler’s First Law
a. The orbit of a planet about the Sun is an ellipse with the Sun at one focus.
b. Mercury has the most eccentric orbit at 0.207.
10. Orbital Speeds and Kepler’s Second Law
a. A line joining a planet and the Sun sweeps out equal areas in equal intervals of
time.
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