The Earth has mass M_E and average radius R_E. The moon has mass M_M and the ave

Question

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

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

b)    Find an expression for the moment of intertia for 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.

c) 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 inertia I_E of the earth on it's axis.

Explanation / Answer

Earth is like as olid sphere

So

A) I_E = 0.5*M_E*R_E^2

B) I_M = M_M*D_M^2

C) given that

I_M = I_E

M_M*D_M^2 = 0.5*M_E*R_E^2

D_M^2 = (0.5*5.97*10^24*6.371*6.371*10^6)/(7.35*10^22) = 16.48 *10^8 m

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