The Earth has mass ME and average radius RE. The Moon has mass MM and the average distance from the center of mass of th

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The Earth has mass ME and averageradius RE. The Moon hasmass MM and the average distance fromthe center of mass of the moon to the center of mass of the Earthis DM. For this problem use the followingconstants. Mass of the Earth: 5.97E24 kg Mass of the Moon: 7.35E22kg Radius of the Earth: 6,371 km
a) Find an expression for the moment ofinertia IE of the Earth on its axisin terms of the given parameters.
b) Find an expression the moment of inertia of theMoon IM in its orbit about the Earth.You may assume the diameter of the moon is very small relative tothe Earth-Moon distance.
c) Calculate for thedistance DS in meters that the Moonwould have to be from the Earth so that the Moon’s moment ofinertia IM about the Earth is equalto the moment of inertia IE of theEarth on its axis.