Calculate the centripetal acceleration of moon towards the earth

Explanation

The centripetal acceleration is given by `a= (v^(2))/(r )` . This expression explicityly depends on Moon's speed which is non- trivial Let us work with the formula
`epsilon ^(2) R_(m) = a_(m)`
`a_(m)` is centripetal acceleration of the Moon due to Earth gravity.
`R_(m) = 604 = 60 xx 6.4 xx 10^(6)`
`= 384 xx 10^(6) m`
As we know the angular velocity `epsilon= (2pi)/(T )`
and `T = 27.3 ` days `= 27.3 xx 24 xx 60 xx 60`
second `=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))`
`=0.00272 ms^(-2)`
The centripetal acceleration of Moon towards the Earth is 0.00272 `ms^(-1)`