Question

Calculate the acceleration due to gravity at the surface of Mars if its diameter is 6760 km and mass one-tenth that of earth. The diameter of earth is 12742 km and acceleration due to gravity on earth is $9.8m/s^2$

Answer 1

$g=\frac{GM}{R^2}=\frac{4GM}{D^2}$

Hence,

$\frac{g_m}{g_e}=\frac{M_m}{M_e}\times {\left(\frac{D_e}{D_m}\right)}^2$

$⟹\frac{g_m}{9.8}=\frac{1}{10}\times {\left(\frac{12742}{6760}\right)}^2$

$⟹g_m=3.48m/s^2$