Answer to Question #277652 in Physics for Kristine

Question

Rhea, one of Saturn’s moons, has a radius of 764 𝑘𝑚 and an acceleration due to the gravity of 0.265 𝑚/𝑠 2 at its surface. Calculate its mass and average density. 

Answer 1

Let's first find the mass of Rhea:

$$g=\dfrac{GM}{R^2},$$ $$M=\dfrac{gR^2}{G}=\dfrac{0.265\ \dfrac{m}{s}\times(7.64\times10^5\ m)^2}{6.67\times10^{-11}\ \dfrac{N\times m^2}{kg^2}}=2.32\times10^{21}\ kg.$$

Then, we can find the volume of Rhea:

$$V=\dfrac{4}{3}\pi R^3.$$

Finally, we can find the average density of Rhea:

$$\rho=\dfrac{M}{V}=\dfrac{M}{\dfrac{4}{3}\pi R^3},$$ $$\rho=\dfrac{2.32\times10^{21}\ kg}{\dfrac{4}{3}\pi\times(7.64\times10^5\ m)^3}=1242\ \dfrac{kg}{m^3}.$$