The mass of the Earth is 5.98 times 10^24 kg, the mass of the Moon is 7.35 times

Question

The mass of the Earth is 5.98 times 10^24 kg, the mass of the Moon is 7.35 times 10^22 kg. The distance between the center of the Earth and the center of the Moon is 3.84 times 10^8 m. and the diameter of the Earth is 1.27 times 10^7. Where is the center of mass of the Earth-Moon system located relative to the surface of the Earth? What distance would the Moon need to be at relative to the center of the Earth for the center of mass of the Earth-Moon system to be exactly at the surface of the Earth? Draw the path of the Earth around the sun using the information from part (a) (not

Explanation / Answer

Mass of earth M = 5.98X1024kg

Mass of moon m = 7.35X1022kg

distance between the centers of moon and earth is d = 3.84X108m

Radius of the earth R = 1.27X107m/2 = 0.635X107m

a) Let us suppose that the center of mass or CM is located at a distance D from the center of the earth.

then we have:

D = md/(M+m) = d/(M/m + 1) = (3.84X108m)/[(598/7.35 + 1)] = 0.466X107m

So the CM is located at a distance = 0.635X107m - 0.466X107m = 1.69X106m below the earth's surface.

b) Here D = R, So,

D = R = md/(M+m) = d/[(598/7.35 + 1)] = d/82.36

So d = 82.36R =  82.36(0.635X107m) = 52.298X107m

So for the CM to be at surface of earth the distance between the center of moon and earth should be

d = 52.298X107m

This concludes the answers. Check the answer and let me know if it's correct. If you need anymore clarification I will be happy to oblige...

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