How far from the center of the earth is the center of mass of the earth + moon system? Data for the earth and moon can be found inside the back cover of the book.

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Ryan Willis · Accepted Answer

The center of mass of a system consists of a set of obect numbered i=1,2,3... where i has mass mi and is located at position (xi,yi) is given by:xcm=1M∑imixi (1)ycm=1m∑imiyi (2)GivenFrom the back cover of the book, the mass of earth is me=5.98×1024 kg, the mass of Moon is mm=7.36×1022 kg, and the distnace between them is R=3.84×108 mCalculationsWe can conisder Earth and Moon to be along a straight line, and we ca take this straight line to be the x-axis.Also we take the origin to be at the center of Earth, so Earths position is xe=0 and Moon&#039;s position is xm=RSince our system consists of Earrth and Moon only, we can write equation (1) for our system as follows:xcm=mexe+mmxmme+mmNow , we enter the given values, so we get:xcm=0+(7.36×1022 kg)(3.84×108 m)7.36×1022+5.98×1024 kg=4.67×106mxcm=4.67×106 mTherefore, the center of mass of the Earth-Moon system is at 4.67×106 m from the center of Earth which is less than Earth&#039;s radius 6.37×1−6m

How far from the center of the earth is the center of mass of the earth + moon s

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