Question

Prove that the gravitational acceleration on the surface of the moon is 1/6 from the gravitational acceleration on the surface of the earth.(G=6.67x10^-11N m^-2 kg^-2,mass of the moon=7.34767309x10^22kg,radius of moon=1.74x10^6m)

Answer 1

$g_e=G\frac{M_e}{R_e^2}=9.81(m/s^2)$

$g_m=G\frac{M_m}{R_m^2}=6.67\cdot10^{-11}\cdot\frac{7.3476\cdot10^{22}}{(1.74\cdot10^6)^2}=1.62(m/s^2)$

$g_e/g_m=9.81/1.62\approx6\to g_m=\frac{1}{6}g_e$ . Answer