Posted by daniel on Tuesday, July 5, 2011 at 8:41pm.
Well, you know the Gravitational Field Strength at Earth's surface, 9.8N/kg, and that this is reduced by distance squared, so at the moons location, it is...
field strength= 9.8N/kg * (re/d)^2 where re is the radius of Earth, and d is the distance from the EArth cneter to the Moon center.
This field strength is also equal to the acceleration falling toward EArth, so at the moon...
9.8(re/d)^2=V^2/d=(2PId/period)^2/d
9.8 re^2=4PI^2 d^3/period
Solve for d change period in days to seconds first, and re to meters
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