How far from the center of the earth is the center of mass of the earth + moon s



Answered question


How far from the center of the earth is the center of mass of the earth + moon system? Data for the earth and moon can be found inside the back cover of the book.

Answer & Explanation

Ryan Willis

Ryan Willis

Beginner2021-11-19Added 15 answers

The center of mass of a system consists of a set of obect numbered i=1,2,3... where i has mass mi and is located at position (xi,yi) is given by:
xcm=1Mimixi (1)
ycm=1mimiyi (2)
From the back cover of the book, the mass of earth is me=5.98×1024 kg, the mass of Moon is mm=7.36×1022 kg, and the distnace between them is R=3.84×108 m
We can conisder Earth and Moon to be along a straight line, and we ca take this straight line to be the x-axis.
Also we take the origin to be at the center of Earth, so Earths position is xe=0 and Moon's position is xm=R
Since our system consists of Earrth and Moon only, we can write equation (1) for our system as follows:
Now , we enter the given values, so we get:
xcm=0+(7.36×1022 kg)(3.84×108 m)7.36×1022+5.98×1024 kg=4.67×106m
xcm=4.67×106 m
Therefore, the center of mass of the Earth-Moon system is at 4.67×106 m from the center of Earth which is less than Earth's radius 6.37×16m

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?