Mimas, a moon of Saturn has an orbital radius of #1.87 * 10^8# #m#. What is the orbital period?

1 Answer
May 29, 2016

Answer:

The orbital period of Mimas is 0.942 days.

Explanation:

One other piece of information is required to perform the calculation. That is the standard gravitational parameter #mu# for Saturn.

#mu = GM = 3.793*10^(16) m^3s^(-2)#

Where #G# is the gravitational constant and #M# is the mass of Saturn.

Using Kepler's third law which relates the orbital period to the semi-major axis distance #a=1.87*10^8m#.
#T^2=(4pi^2 )/mu a^3#

Substituting the values for #mu# and #a# and taking the square root gives #T=82499s#. Dividing by #60*60*24# gives #T=0.954# days.

This is close to the observed orbital period of Mimas of #0.942# days.