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Question
Calculate the centripetal acceleration of the Moon towards the Earth.
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Solution
The centripetal acceleration is given by a = `v^2/r` This expression explicitly depends on Moon’s speed which is nontrivial. We can work with the formula
ω2Rm = am
am is the centripetal acceleration of the Moon due to Earth’s gravity, ω is the angular velocity
Rm is the distance between Earth and the Moon, which is 60 times the radius of the Earth.
Rm = 60R = 60 x 6.4 x 106 = 384 x 106 m
As we know the angular velocity ω = `(2π)/T` and T =
27.3 days = 27.3 x 24 x 60 x 60 second = 2.358 x 106 sec.
By substituting these values in the formula for acceleration
a6 = `((4π^2)(384×10^6))/(2.358×10^8)^2` = 0.00272 ms-2
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