00:01
Well, this is a problem dealing with something in a circular orbit, and those are always fun.
00:05
Whenever you have a problem that talks about a circular orbit, you should immediately think of whether you can use the centripetal acceleration as part of the problem.
00:17
For something going in a circular path at a constant velocity, the acceleration of that thing is equal to v squared divided by r, where v is the speed and r is the radius of the orbit.
00:28
And we can use that here.
00:31
We can say that the force of gravity, which is the force that is keeping this spacecraft in orbit, is equal to the mass of the object times its centripetal acceleration, which is v squared divided by r, since we're going to assume it's going in a circular path.
00:51
But we already know the formative for the force of gravity.
00:54
The magnitude of the force of gravity is going to be equal to big g times the mass, of the moon times the mass of the object divided by the radius of the orbit squared.
01:09
That's a distance away from the center of the moon that the object is at.
01:14
And that's going to be equal to the mass of the object times b squared divided by the radius of its orbit.
01:22
So we can simplify this by dividing both sides by little m.
01:25
The mass of the object does not matter.
01:28
And we can also multiply both sides of our equation by the radius of the orbit...