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Chapter 12: Q. 5 (page 330)

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.

The center of mass of the Earth-Moon system from the center of the Earth is 4.67脳106m.

Short Answer

Expert verified

The center of mass of the Earth-Moon system from the center of the Earth is 4.67脳106m

Step by step solution

01

Step 1. Given information

Distance between earth and moon: 384,400km.

Earth's mass: M=5.972脳1024kg

Moon's mass: m=7.349脳1022kg

02

Step 2. Explanation

In a two dimensional co-ordinate system, Assume the center of mass of the Earth is at origin, and the Moon on the x- axis

The center of mass the Earth-Moon system.

xcm=5.98脳1024kg(0m)+7.36脳1022kg3.84脳108m5.98脳1024kg+鈥�7.36脳1022kgxcm=4.668脳106m

Therefore, the center of mass of the Earth-Moon system from the center of the Earth is .

4.67脳106m

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