Kepler's laws
by Bill Drennon (Well, the laws are by Johannes Kepler!)
Physics Teacher
Central Valley Christian High School
Visalia, CA USA
Though originally stated to describe the motion of planets around the sun,
Kepler's Laws also apply to comets.
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
Click here to see larger
animation
LAW 3: The squares of the periods of the
planets are proportional to the cubes of their semimajor axes:
Ta2 / Tb2 = Ra3
/ Rb3
- Square of any planet's orbital period (sidereal) is proportional to cube
of its mean distance (semi-major axis) from Sun
- Mathematical statement: T = kR3/2 , 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 |
