Answer to Question #277652 in Physics for Kristine

Question #277652

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


1
Expert's answer
2021-12-20T10:26:28-0500

Let's first find the mass of Rhea:


g=GMR2,g=\dfrac{GM}{R^2},M=gR2G=0.265 msΓ—(7.64Γ—105 m)26.67Γ—10βˆ’11 NΓ—m2kg2=2.32Γ—1021 kg.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=43Ο€R3.V=\dfrac{4}{3}\pi R^3.

Finally, we can find the average density of Rhea:


ρ=MV=M43Ο€R3,\rho=\dfrac{M}{V}=\dfrac{M}{\dfrac{4}{3}\pi R^3},ρ=2.32Γ—1021 kg43π×(7.64Γ—105 m)3=1242 kgm3.\rho=\dfrac{2.32\times10^{21}\ kg}{\dfrac{4}{3}\pi\times(7.64\times10^5\ m)^3}=1242\ \dfrac{kg}{m^3}.

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