Question

The mass of the earth is 5.98 1024 kg, the mass of the moon is 7.36 1022 kg, and the distance between the centers of the earth and the moon is 3.82 108 m. How far is the center of mass of the earth-moon system from the center of the earth

Answer 1

x_{cm} = 4.644 10⁶ m

Step-by-step explanation:

The center of mass is given by the equation

`x_(cm)` = 1 /
`M_(total)` ∑
`x_(i) m_(i)`

Where M_{total} is the total masses of the system,
`x_(i)` is the distance between the particles and
`m_(i)` is the masses of each body

Let's apply this equation to our problem

M = Me + m

M = 5.98 10²⁴ + 7.36 10²²

M = 605.36 10²² kg

Let's locate a reference system located in the center of the Earth

Let's calculate

x_{cm} = 1 / 605.36 10²² [Me 0 + 7.36 10²² 3.82 10⁸]

x_{cm} = 4.644 10⁶ m