The moon orbits the earth once in 27.3 days in an almost circular orbit. Calculate the centripetal acceleration experienced by the earth? (Radius of the earth is 6.4×10×10×10×10 ×10×10 m )

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Solution

The centripetal acceleration can be found out only if the distance between Earth and moon is known.
Distance between earth and moon, r=3.84x10⁸
The period which the Moon orbits around the Earth is: (27.3 day)(24 hr/day)(3600 s/hr) = 2358720 s
The centripetal acceleration of the Earth in its orbit around the sun will be: a = v²/r = (2πr/T)²/r = 4π²r/T²
Then a = 4π²(3.84x10⁸m)/( 2358720 s)² = 2.72x10^-3 m/s²

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