physics
posted by daniel on .
given that the radius of the earth is 6.37×10^3km and the period of revolution of the moon round the earth is 27.3 days, calculate the average distance from the earth to the moon.

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