Question

g HW 5.6.The Moon and the Earth both orbit the center of mass of the Earth-Moon system.Earth is 81 times more massive than the Moon. Assume that the distance between the centerof the Earth and the Moon is 384,400.0 km. Determine the distance of the center of mass of theEarth-Moon system from the center of the Earth. Does it lie inside or outside the Earth with theradius of 6,371.0 km

Answer 1

`R_(cm)` = 4.688 106 m

Step-by-step explanation:

The expression for the center of mass is

R cm = 1 / M ∑
`r_(i)`
`m_(i)`

Where M is the total mass of the system, ri and m1 are the distance and mass of each particle from a defined origin

Let's look for the total mass, the mass of the moon is m and that of the earth Me

M =
`M_(e)` + m

M = 81m + m

M = 82 m

The distance from the earth to the moon is R = 384.4 106 m

`R_(cm)` = 1 / M (M R1 + m R)

`R_(cm)` = 1 / 82m (0 + m R)

`R_(cm)` = R / 82

`R_(cm)` = 384.4 106/82

`R_(cm)` = 4.688 106 m

The radius of the earth is

`R_(e)` = 6371 103 m

`R_(e)` = 6.371 106 m

We can see that the center of mass of the system is within the beating radius