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Obtain the value of g from the motion of moon assuming that its period of rotation around the earth is 27 days 8 hours and the radius of its orbit is 60.1 times the radius of the earth.

Given,

T = 27 days 8 hours = (27 * 24 + 8) hours = 656 hours = 2361600 Sec
Radius of Earth (R) = 6.36106m
Radius of orbit (r)=60.1R=60.16.36106
Value of g = ?

We have,
T= 2πrRrg

By Solving,
g = 4π2r3T2R2 = 4π2(60.1)3R3T2R2 = 4π2(60.1)36.361062361600 = 9.77m/s2

∴ The required value of g from the motion of the moon is 9.8m/s2
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