Centripetal force problem ( not enough givens?)

[saikisen]

Hey guys, I could not understand this question. There weren't enough givens for myself to understand how to get the period.

1. Earth and the Moon are separated at their centres by a distance of 3.4x10^8m. Determine the period of the Moon's rotation about Earth.



2. mv^2/r=Fc



3. I wasn't sure if MG applies in this question since the mass of the moon wasn't stated although Earth does have gravity that keeps the moon in its orbit. I'm assuming something like mass is supposed to be canceled in the formulas, I just don't know how or which one.

The supposed answer is supposed to be 22.8 days

 

[Brilliant]

You're exactly right, one of the masses will cancel.
There's a pretty straight forward way to do this problem with an application of Newton's Second Law and the formula a_cp = v²/r

Just do a force summation for the Moon. Look for a velocity, then consider the circumference.

Good Luck!

EDIT: Also, you mentioned that the problem did not give the mass of the Earth or Moon. Typically physics problems like this assume that you look the masses up in the tables in your book.

 

[AtticusFinch]

Also, you may need to do a center of mass calculation because the Moon does not orbit around the Earth's center but rather the systems center of mass.

 

[Brilliant]

This is true, however I don't believe this problem expects that. I calculated the answer using the R value that he gave and got the answer: 22.8 days

 

[AtticusFinch]

This is true, however I don't believe this problem expects that. I calculated the answer using the R value that he gave and got the answer: 22.8 days

Ok then, also if you ignore the center of mass you don't need to look up the mass of the moon (which is what the problem seems to want).