If R_m is the radius of moon orbit round the earth, a_m the acceleration of moon towards the centre of earth, and R_e the radius of earth. Then a_m is equal to (if g is acceleration due to gravity on the surface of earth)

$\left(\frac{R_e}{R_m}\right)^2 g$

$\mathrm{g}=\frac{\mathrm{GM}_{\mathrm{e}}}{\mathrm{R}_{\mathrm{e}}^2}$          ..........(1)

$\mathrm{a}_{\mathrm{m}}=\frac{\mathrm{GM}_{\mathrm{e}}}{\mathrm{R}_{\mathrm{m}}^2}$       ..........(2)

$\frac{(2)}{(1)}, \frac{a_m}{g}=\frac{\frac{\mathrm{GM}_e}{\mathrm{R}_{\mathrm{m}}^{\mathrm{e}}}}{\frac{\mathrm{GM}_{\mathrm{e}}}{\mathrm{R}_{\mathrm{e}}^2}}=\frac{\mathrm{R}_{\mathrm{e}}^2}{\mathrm{R}_{\mathrm{m}}^2} ; \mathrm{a}_{\mathrm{m}}=\left(\frac{\mathrm{R}_{\mathrm{e}}}{\mathrm{R}_{\mathrm{m}}}\right)^2 \mathrm{~g} \mathrm{f}$