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Question
Find the acceleration of the moon with respect to the earth from the following data:
Distance between the earth and the moon = 3.85 × 105 km and the time taken by the moon to complete one revolution around the earth = 27.3 days.
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Solution
Distance between the Earth and the Moon:
r = 3.85 × 105 km = 3.85 × 108 m
Time taken by the Moon to revolve around the Earth:
T = 27.3 days
= 24 × 3600 × 27.3 s
= 2.36 × 106 s
Velocity of the Moon:
`v = (2pir)/T`
= `(2 × 3.14 × 3.85 xx 10^8)/(2.36 × 10^6)`
= 1025.41 m/s
Acceleration of the Moon:
`a = v^2/r`
= `(1025.42)^2/(3.85 xx 10^8)`
= 0.00275 m/s2
⇒ a = 2.73 × 10−3 m/s2
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