Question

The earth and moon are seperated by a

centerto cent distance of 3.85 * 108 m. The mass of
theearth is 5.98 * 1024 kg. and that of the moon is7.35
* 1022 kg. How far does the center of themass lie of the
center of the earth?

Answer 1

4674568 m or 4675 km

Step-by-step explanation:

Let x be the distance from the center of the mass system to the center of the earth. This means the distance from the center of the mass system to the center of the moon is
`3.85*10^8 - x`. For the masses to balance out, we have the following equation:

`m_e*x = m_m*(3.85*10^8 - x)`

where
`m_e` is the mass of Earth, and
`m_m` is mass of the moon

`5.98 * 10^(24)x = 7.35*10^(22)(3.85*10^8 - x)`

We can divide both sides by
`10^(22)`

`598x = 7.35*3.85*10^8 - 7.35x`

`605.35x = 2829750000`

`x = 2829750000/605.35 \approx 4674568 m` or 4675 km