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

`4.6* 10^3 km`

Step-by-step explanation:

We are given that

Mass of Earth,M=
`6* 10^(24) kg`

Mass of moon,m=
`7.35* 10^(22) kg`

`x_1=0`

Distance between Earth and moon,
`x_2=3.80* 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=(Mx_1+mx_2)/(m+M)`

Using the formula

`x=(6* 10^(24)* 0+7.35* 10^(22)* 3.8* 10^5)/(6* 10^(24)+7.35* 10^(22))`

`x=4.599* 10^3 Km\approx 4.6* 10^3 km`