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
= 1 / M ∑
Where M is the total mass, and
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