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At what altitude off the surface of the Moon would a satellite be in a sta- tionary orbit over the Moon?

This is a neat question, but one which does not have a simple answer. For an isolated planet we can work out the read radius of a circular orbit with a certain period. To be motionless, stationary, the period must be 24 hours for Earth, while for the Moon the period must be 28 days. The longer the period the farther away is the orbit from the planet. For an orbit far away from the Moon our satellite would encounter the gravity of the Earth and that would alter the orbit and make a stationary orbit unlikely. Because of the Earth's presence such an orbit is not possible. If it were, you could use the value of the radius for Earth and multiply it by the one-third power of the ratio of the Moon to the Earth masses and multiply by the two-thirds power of the number 28. That should give the value without the presence of the Earth.


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