The masses of the Earth and Moon are 5.98×1024kg and 7.35×1022kg respectively, and their centers are separated by 3.84×108m. At what distance from the center of the Earth is the CM of the Earth-Moon system located?
What can you say about the motion of the Earth-Moon system about the Sun, and of the Earth and Moon separately about the Sun?
A) The Earth-Moon CM follows the orbit around the Sun. Earth and Moon rotate around their CM. The radius of rotation of Earth around the CM is much greater than radius of rotation of Moon around the CM.
B) The Earth and Moon follow separate circular orbits around the Sun.
C) The Earth-Moon CM follows the orbit around the Sun. Earth and Moon rotate around their CM. The radius of rotation of Moon around the CM is much greater than radius of rotation of Earth around the CM.

C) The Earth-Moon CM follows the orbit around the Sun. Earth and Moon rotate around their CM. The radius of rotation of Moon around the CM is much greater than radius of rotation of Earth around the CM.

Explanation:

At first we assume that both Earth and Moon can be treated as particles, the center of mass of the Earth-Moon system is obtained by using this formula:

(Eq. 1)

Where:

- Location of the center of the Earth, measured in kilometers.

- Location of the Moon, measured in kilometers.

- Location of the center of mass, measured in kilometers.

- Mass of the Earth, measured in kilograms.

- Mass of the Moon, measured in kilograms.

If we know that , , and , the location of the center of mass respect to the Earth is:

The Earth has a radius of meters, we notice that center of mass in located inside the Earth and the radius of rotation of the Earth around the center of mass is much greater than the radius of rotation of the Moon around the center of mass. That center of mass follows an orbit around the sun.

In consequence, correct answer is C.

the average speed is 24.57 km/hr