18 12:01.00 AM-Due Dae:i8 11:00:00 P End Date: 4 18 11-59:00 PM (10%) Problem 9:

Question

18 12:01.00 AM-Due Dae:i8 11:00:00 P End Date: 4 18 11-59:00 PM (10%) Problem 9: The Earth has mass ?? and average radius RE: The Moon has mass MM and de avenge distance from the center of mass of the moon to the center of mass of the Earth is Dyy For this problem use the following constants Mass of the Earth: 5.97124 kg Mass of the Moon: 7.35822 kg Radius of the Earth: 6371 km 33% Part (a) Find an expression for the moment of inertial, ofthe Earth on its axis in terns of Grade Summary Potent tial 100% 4 5 6 per attempo Subesit Hinis: 0% deduction per hint. Iliaiemaining: ii 33% Part (b) Find an expression the moment of incra or the Moon in its rbit about the Earth Yo moon is very small relative to the Earth-Moon distance. -&33% Part (c) Calculate for the distance Ds ly about the Earth is equal to the moment of inertia Ig of the Earth on its axis. u may assume the diameter of the in meters that the Moon would have to be from the Earth so that the Moon's moment of inertia

Explanation / Answer

a) IE = (2/5)*M_E*R_E^2

b) IM = M_M*D_M^2

c) IE = IM

(2/5)*M_E*R_E^2 = M_M*D_s^2

D_s = sqrt((2/5)*M_E/M_M)*R_E

= sqrt((2/5)*5.87*10^24/(7.35*10^22))*6371 km

= 36000 km

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