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

May 29, 2016

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.

$\mu = G M = 3.793 \cdot {10}^{16} {m}^{3} {s}^{- 2}$

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 $a = 1.87 \cdot {10}^{8} m$.
${T}^{2} = \frac{4 {\pi}^{2}}{\mu} {a}^{3}$

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

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