Question

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 $4.67\times {10}^6\text{m}$.

Short answer

The center of mass of the Earth-Moon system from the center of the Earth is $4.67\times {10}^6\text{m}$

Step-by-step solution

Step 1. Given information

Distance between earth and moon: $384,400\text{km}$.

Earth's mass: $M=5.972\times {10}^{24}\text{kg}$

Moon's mass: $m=7.349\times {10}^{22}\text{kg}$

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.

$\begin{array}{l}{x}_{\text{cm}}=\frac{\left(5.98\times {10}^{24}\text{kg}\right)(0\text{m})+\left(7.36\times {10}^{22}\text{kg}\right)\left(3.84\times {10}^8\text{m}\right)}{5.98\times {10}^{24}\text{kg}+7.36\times {10}^{22}\text{kg}}\\ x_{\text{cm}}=4.668\times {10}^6\text{m}\end{array}$

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

$4.67\times {10}^6\text{m}$