Q.Calculate the value of acceleration due to gravity on the surface of Mars if the radius of Mars = $3.4\times10^3$ km and its mass is $6.4\times10^{23}$ kg.

Applying the universal law of gravitation to an object of mass m near a large sphere of mass M (like the Earth) at distance r from its centre gives a force $F=GMm/r^2$; dividing by m (Newton's second law, $a=F/m$) gives the acceleration due to gravity, $g=GM/r^2$ -- crucially INDEPENDENT of the falling object's own mass, exactly matching Galileo's experimental finding that all bodies fall at the same rate regardless of mass. Near a planet's surface, $r\approx R$ (the planet's radius), giving the familiar surface value $g=GM/R^2\approx9.8$ m/s^2 for Earth. …