Question

Calculate the centripetal acceleration of the Moon towards the Earth.

Answer 1

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

ω²R_m = a_m

a_m is the centripetal acceleration of the Moon due to Earth’s gravity, ω is the angular velocity

R_m is the distance between Earth and the Moon, which is 60 times the radius of the Earth.

R_m = 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