Calculate the centripetal acceleration of moon towards the earth

Explanation

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
`omega^2 R_m = a_m`
`a_m` is centripetal acceleration of the Moon due to Earth.s gravity.
`omega ` is angular velocity
`R_m` is the distance between Earth and the Moon, which is 60 times the radius of the Earth.
`R_m = 60 R = 60 xx 6.4 xx 10^6 = 384 xx 10^6 m`
As we know the angular velocity `omega = (2pi)/(T)` and
`T = 27. 3 days = 27.3 xx 24 xx 60 xx 60 sec = 2.358 xx 10^6 sec `
By substituting these values in the formula for acceleration
`a_m = ((4pi^2) (384 xx 10^6) )/((2.358 xx 10^6)^2) = 0.00272 ms^(-2)`
The centripetal acceleration of Moon towards the Earth is` 0.00272 ms^(-2)`