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) = 6.36∗106m
Radius of orbit (r)=60.1∗R=60.1∗6.36∗106
Value of g = ?
We have,
T=2πrR√rg
By Solving,
g = 4π2r3T2R2 = 4π2∗(60.1)3R3T2R2 = 4π2∗(60.1)3∗6.36∗1062361600 = 9.77m/s2
∴ The required value of g from the motion of the moon is 9.8m/s2
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