Keppler's Third Law

## Question:

Mr. Jones,

Having a problem using Kepler's third law to solve a physics problem. If given the period of two moons, and the mean orbital radius of one of the moons, how do you solve for the other orbital radius of the moon, and the mass of the planet.

## Answer:

Hi Laurie,
Keppler's third law for the satellites of any planet is:

T^2=Kp*r^3 where T is the satellite period and r is the length of the semi-major axis of the elliptical orbit of the satellite. Kp is a constant for that planet. Kp=(4*pi^2)/(G*Mp) where G is the universal gravitation constant and Mp is the mass of the planet. If the eccentricity of the moon's orbits is not too great we may replace the semi-major axis with the mean radius and use the period of the moon whose orbital radius we know to calculate Kp and from that the mass of the central planet. Knowing Kp we may calculate the orbital radius of the other moon from its period.

This information is brought to you by M. Casco Associates, a company dedicated to helping humankind reach the stars through understanding how the universe works. My name is James D. Jones. If I can be of more help, please let me know.

JDJ