Question

Find the magnitude of the free-fall acceleration at the orbit of the Moon (a distance of 60RE from the center of the Earth with the radius of RE). Use the gravitational acceleration on the surface of the Earth is 9.8m/s^2 

Answer 1

Acceleration due to gravity is given by, $g = \frac{GM}{R_E^2}$

Free fall acceleration, $g' = \frac{GM}{(60R_E)^2}$

Dividing equations,

$\frac{g'}{g} = \frac{R_E^2}{(60R_E)^2} = \frac{1}{3600}$

$g' = \frac{1}{3600} \times 9.8 = 0.0027 m/s^2$