The Earth has mass ME and average radius RE$.$ The Moon has mass MM and the average distance from the center of mass of the moon to the center of mass of the Earth is DM$.$ For this problem use the following constants.

Mass of the Earth: $5\mathrm{.}97$E$24$ kg

Mass of the Moon: $7\mathrm{.}35$E$22$ kg

Radius of the Earth: $6,371$ km

$-$ Part $($a$)$

Find an expression for the moment of inertia IE of the Earth on its axis in terms of the given parameters.

IE $=(2/5)$ME$$RE$2$Correct$!$

$-$ Part $($b$)$

Find an expression the moment of inertia of the Moon IM in its orbit about the Earth. You may assume the diameter of the moon is very small relative to the Earth$-$Moon distance.

IM $=$ MM$$DM$2$Correct$!$

$$ Part $($c$)$

Calculate for the distance DS in meters that the Moon would have to be from the Earth so that the Moon$$s moment of inertia IM about the Earth is equal to the moment of inertia IE of the Earth on its axis.