Another Planetary Mechanics Question

[NDiggity]

Homework Statement

A NASA spaceship is orbiting the moon at an altitude of 111 km. How long does it take the ship to make one orbit around the moon?

This was a question on the test I had today, just wondering if I'm out to lunch or not. So he gave us all the info on the moon on an overhead. I used the mass of the moon 7.36*10^22 kg and the radius 1,737,000m added to the altitude.

Homework Equations

I used the equation mp=4π²R³/GT²

The Attempt at a Solution

So I plugged in 7.36*10^22=4π²(1848000)³/6.67*10¯¹¹(T²) and solved for t.

I got with sig figs 7120 seconds or something like that on the test. His numbers might have been slightly different. Did I do this completely wrong?

 

[Mindscrape]

I'm not familiar with the equation that you are using, that is to say that it must be derived from a couple of other equations, but it could be correct.

I would have used potential energy to find the angular velocity, and then the period. Just approximating in my mind, I think you are right or close to right.

 

[NDiggity]

Alright well thank you for your help. We have not learned about potential energy yet but if you think my answer is in the ballmark, that makes me worry a lot less!