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# Physics/Physics

Question
I am a part of a study group for my AP Physics class. We are studying for exams which are in a couple weeks. A part of that is we go over a ton of problems, situations and concepts and do them together as a group. However, we are struggling with the concept of a lunasynchronous orbit.

Assuming the moon is the only factor, how do you find the altitude of the lunasynchronous orbit? What kind of formula is used to find that altitude? (We know the mass of the moon and the gravitational constant are used, but what else?)

And if the presence of the Earth were added, what effect would it have on that orbit? (Nothing mathematical or anything here, just in general terms; we assume it would reduce the altitude; a stronger force pulling the orbiting object "away" would mean it needs to be closer to the moon to keep in a lunasynchronous orbit)?

Any help you can provide here is much appreciated; if possible, at least the formula for the first part and a general Yes/No for our theory on the second part.
Clark

Well, do you mean that the Moon is the only factor, in that you need to only account for its rotation?  The Moon rotates once a month, since it stays tidally locked to the Earth.  Therefore, you'd have to figure out an orbit with a period of a month.  But since the Moon's gravity is way less than Earth's, that orbit would be way out there beyond the Earth-Moon distance.  That orbit would be disturbed by the Earth...but calculating it is the same as calculating a geosynchronous orbit if you're ignoring the Earth.  It's just that a day on the Moon is a month long.  Formulas are identical.  Well, almost, but you can look up a sidereal lunar orbital period on google just like I can.

Involving the Earth gives you options!  They're called Lagrange points, and wikipedia has a great article on them.  Since they maintain the satellite's position relative to the Moon, they are technically lunar synchronous orbits, all five points.  Read up, someone has work all those details out for you:
http://en.wikipedia.org/wiki/Lagrangian_point

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