Question

Where is the center of mass of the Earth-Moon system? The radius of the Earth is 6378 km and the radius of the Moon is 1737 km. Select one of the answers below: Choose the correct description of the location of the center of mass of the Earth-Moon system. Choose the correct description of the location of the center of mass of the Earth-Moon system. The center of mass is exactly in the center between the Earth and the Moon. The center of mass is nearer to the Moon than the Earth, but outside the radius of the Moon. The center of mass is nearer to the Earth than the Moon, but outside the radius of the Earth.

Answer 1

Answer:

r_{cm} = 4.67 10⁶ m

We see that none of the answers is correct, the closest is the third, but the center of mass is within the radius of the Earth

Explanation:

The definition of the center of mass is

      $r_{cm}$ = 1 / M ∑$r_{i} m_{i}$

Where M is the total mass, $r_{i}$ and $m_{i}$mi are the position and the mass gives each of the bodies

We must locate a reference system for the calculation, we will locate it with the origin in the center of the Earth, the data we have are

Mass of the Earth Me = 5.98 1024 kg

Moon mass m = 7.36 1022 kg

Earth to Moon Distance r = 3.84 108 m

Let's apply this to our case

      r_{cm} = 1 / (Me + m) (Me 0 + m R)

      r_{cm} = 1 / (598 +7.36) 10²² (0 + 7.36 10²² 3.84 10⁸)

     r_{cm} = 4.67 10⁶ m

We can see that this distance is less than the radius of the Earth

We see that none of the answers is correct, the closest is the third, but the center of mass is within the radius of the Earth