Science Olympiad 2006 Astronomy Division C Glossary

2007 Science Olympiad Glossary – Astronomy Division C
Kepler's Laws of Planetary Motion

LAW 1: The orbit of a planet/comet about the Sun is an ellipse with the Sun's center of mass at one focus.

This is the equation for an ellipse:

LAW 2: A line joining a planet/comet and the Sun sweeps out equal areas in equal intervals of time

LAW 3: The squares of the periods of the planets are proportional to the cubes of their semimajor axes:

T_a² / T_b² = R_a³ / R_b³

Square of any planet's orbital period (sidereal) is proportional to cube of its mean distance (semi-major axis) from Sun
Mathematical statement: T = kR^3/2 , where T = sideral period, and R = semi-major axis
Example - If a is measured in astronomical units (AU = semi-major axis of Earth's orbit) and sidereal period in years (Earth's sidereal period), then the constant k in mathematical expression for Kepler's third law is equal to 1, and the mathematical relation becomes T² = R³

Examples of Kepler's Third Law

Planet	P (yr)	a (AU)	T²	R³
Mercury	0.24	0.39	0.06	0.06
Venus	0.62	0.72	0.39	0.37
Earth	1.00	1.00	1.00	1.00
Mars	1.88	1.52	3.53	3.51
Jupiter	11.9	5.20	142	141
Saturn	29.5	9.54	870	868

Above is courtesy of Bill Drennon-Physics Teacher
Central Valley Christian High School
Visalia, CA USA
http://home.cvc.org/science/kepler.htm

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Also, go to this website - http://csep10.phys.utk.edu/astr161/lect/history/kepler.html At the bottom of that site are a couple of links that further illustrate Kepler's laws.