The masses of the Earth and Moon are approximately M_e = 6.0 times 10^24 kg and
ID: 1523456 • Letter: T
Question
The masses of the Earth and Moon are approximately M_e = 6.0 times 10^24 kg and M_m = 7.4 times 10^22 kg. The center to center distance is approximately 3.8 times 10^5 km. Where is the center of mass if we assume the center of the Earth is the origin of the coordinate system. b) The Earth's distribution of mass is not symmetrical. One way to approximate this effect is to add a third body. Assume that along the direction of the Moon, we add a third body halfway with a mass which is a tenth of a percent of Earth's mass. What is the new center of mass of this system? Additionally, express this change in center of mass as a percentage (i.e. Two body system/Three body system). How significant is this correction?Explanation / Answer
If we assume that the center of Earth is an origin of coordinate system, then the center of mass will be given as :
using a formula, we have
Xcm = Me x1 + Mm x2 / (Me + Mm)
Xcm = [(6 x 1024 kg) (0 m) + (7.4 x 1022 kg) (3.8 x 108 m)] / [(6 x 1024 kg) + (7.4 x 1022 kg)]
Xcm = (2.81 x 1031 kg.m) / (6.074 x 1024 kg)
Xcm = 4.62 x 106 m
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