Question

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

Answer 1

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.