Parts a b and c please. The Earth has mass M_E and average radius R_E. The Moon
ID: 1452244 • Letter: P
Question
Parts a b and c please.
The Earth has mass M_E and average radius R_E. The Moon has mass M_M and the average distance from the center of mass of the moon to the center of mass of the Earth is D_M. For this problem use the following constants. Mass of the Earth: 5.97E24 kg Mass of the Moon: 7.35E22 kg Radius of the Earth: 6,371 km Find an expression for the moment of inertia I_E of the Earth on its axis in terms of the given parameters. Find an expression the moment of inertia of the Moon I_M in its orbit about the Earth. You may assume the diameter of the moon is very small relative to the Earth-Moon distance. Calculate for the distance D_S in meters that the Moon would have to be from the Earth so that the Moon's moment of inertia I_M about the Earth is equal to the moment of inertia I_E of the Earth on its axis.Explanation / Answer
a)
for Re radius and Me mass of the earth
MOI = sphere = 2/5 Me Re ^2
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part B :
for a point object MOI becmes
Im =- Mm * Dm)^2
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c)Given Mm *(Dm^2=2/5 Me * (RI)^2.
Therefore
Dm = (2/5 * Me/Mm)^0.5 *RI