Question

mass of the earth and the moon are 5.98×10^24 kg and 7.36 * 10^22 kg respectively. distance between the earth and the moon is 3.80*10^8 m . find the distance of the centre of mass of the earth moon system from the centre of the earth​

Answer 1

Explanation:

Place the origin at the center of the earth to simplify the calculations. Subscript "e" refers to earth, and subscript "m" refers to moon.

xcm = (mexe + mmxm)/(me + mm) = [me(0) + mmxm]/(me + mm)

xcm = mmxm/(me + mm) = (7.36 x 1022)(3.82 x 108)/[(5.98 x 1024) + (7.36 x 1022)] m

xcm ≅ 4.64 x 106 m

It is about 4.64 x 106 m from the center of the earth.

Answer 2

typical distance of 384,400 kilometers separating Earth and the moon's centers, that works out to a center of mass that is roughly 379,700 kilometers from the moon's center and about 4,700 kilometers from Earth's.