1. The Laws of Planetary Motion
Earth Science
Mr. Cloud

2. Kepler’s Quandary
Retrograde Motion

3. Geocentric Model (Ptolemy’s Model)

4. Heliocentric Model (Copernican Model)

5. A complicated relationship?
Tycho Brahe
(1546 –1601)
Johannes Kepler
( )
A complicated relationship?

6. The Law of Ellipses
Each planet orbits the sun in a path called an ellipse.
An ellipse is a closed curve whose shape is determined by two points, or foci, within the ellipse.
Think of an ellipse as a flattened circle.
Planetary Motion Simulator

7. The Law of Equal Areas
Kepler calculated that a line from the center of the sun to the center of an object sweeps through equal areas in equal periods of time.
Equal areas are covered in equal amounts of time as an object orbits the sun.

8. Retrograde Motion Solved!

9. The Law of Periods: Harmonic Law
Describes the relationship between the average distance of a planet from the sun and its orbital period.
Orbital period: is the time required for a body to complete a single orbit
The cube of the average distance (a) is always proportional to the square of its orbital period (p)
a3 = p2

10. The Law of Periods
Ex. Mars has an average distance of 1.5 AU from the sun.
AU= astronomical unit (1 AU = x 108 km)( the mean distance between Earth and the sun)
Ex. p2 = a3
P2 = (1.5)3 = 3.4
P = √3.4 = 1.8 years