Question

Calculate the location xcm of the center of mass of the Earth-Moon system. Use a coordinate system in which the center of the Earth is at x=0 and the Moon is located in the positive x direction.

Answer 1

Answer:

$4.6\times 10^3 km$

Explanation:

We are given that

Mass of Earth,M=$6\times 10^{24} kg$

Mass of moon,m=$7.35\times 10^{22} kg$

$x_1=0$

Distance between Earth and moon,$x_2=3.80\times 10^5 km$

We have to find the location of the center of mass of the Earth- Moon system.

Position of center of mass of Earth-Moon system

$x=\frac{Mx_1+mx_2}{m+M}$

Using the formula

$x=\frac{6\times 10^{24}\times 0+7.35\times 10^{22}\times 3.8\times 10^5}{6\times 10^{24}+7.35\times 10^{22}}$

$x=4.599\times 10^3 Km\approx 4.6\times 10^3 km$