A satellite is placed between the Earth and the Moon, along a straight line that connects their centers of mass. The satellite has an orbital period around the Earth that is the same as that of the Moon, 27.3 days. How far away from the Earth should this satellite be placed?
The Attempt at a Solution
I used Kepler's third law with r being the distance. I took (27.3*86400)2, which is the period squared and set it equal to the expression (4∏2r3/GME). I got 19404m, which is wrong. I think the problem is the fact that r is cubed and the period is squared, that screws me.