# How far does the center of mass lie from the center of the earth?

• rmarkatos

#### rmarkatos

The Earth and moon are separated by a center-to-center distance of 3.85x10^8m. The mass of the Earth is 5.98x10^24kg and that of the moon is 7.35x10^22kg. How far does the center of mass lie from the center of the earth?

I know you have to use the equation
Xcm=m1x1+m2x2/m1+m2

I don't know what x1 or x2 and i am not exactly sure what you measure x1 and x2 from and that is probably why i can't figure out how to use the equation.

rmarkatos said:
The Earth and moon are separated by a center-to-center distance of 3.85x10^8m. The mass of the Earth is 5.98x10^24kg and that of the moon is 7.35x10^22kg. How far does the center of mass lie from the center of the earth?

I know you have to use the equation
Xcm=m1x1+m2x2/m1+m2

I don't know what x1 or x2 and i am not exactly sure what you measure x1 and x2 from and that is probably why i can't figure out how to use the equation.
Draw a line through the Earth and the moon. Pick any point you want on that line to call x = 0. Then do your calculation. When you find the CM, find the distance from there to the center of the earth. Some choices for x = 0 are more convenient than others, but you are free to make any choice you want.

the line you drawn is in between the Earth and moon? and you pick a point that is on line in between the moon and earth?

I really do not understand what you mean by that, my textbook does not do a good job of explaining it

rmarkatos said:
the line you drawn is in between the Earth and moon? and you pick a point that is on line in between the moon and earth?
The point you pick on the line is completely arbitrary. In this problem you are asked to find how far the center of mass is from the center of the earth, so a convenient choice would be the make x = 0 the center of the earth. That choice also makes the calculation a bit simpler than it would be for most other choices. x1 and x2 are the displacements (distance and + or - direction) of m1 and m2 from the point you choose to call x = 0.