(a) What is the acceleration due to gravity on the surface of the Moon?

(b) On the surface of Mars? The mass of Mars is \({\bf{6}}.{\bf{418}} \times {\bf{1}}{{\bf{0}}^{{\bf{23}}}}{\bf{kg}}\) and its radius is\({\bf{3}}.{\bf{38}} \times {\bf{1}}{{\bf{0}}^{\bf{6}}}{\bf{m}}\).

Gravity is a universal phenomenon and is introduced by Newton and Derived the expression for gravitational force.

Moon’s radius\({{\rm{R}}_{\rm{m}}}{\rm{ = 1}}{\rm{.737 x 1}}{{\rm{0}}^{\rm{6}}}{\rm{ m}}\)

Moon’s mass\({{\rm{M}}_{\rm{m}}}{\rm{ = 7}}{\rm{.3477 x 1}}{{\rm{0}}^{{\rm{22}}}}{\rm{ kg}}\)

Mars’s radius\({{\rm{R}}_{{\rm{mars}}}}{\rm{ = 3}}{\rm{.38 x 1}}{{\rm{0}}^{\rm{6}}}{\rm{ m}}\)

Mars’s mass\({{\rm{M}}_{{\rm{mars}}}}{\rm{ = 6}}{\rm{.418 x 1}}{{\rm{0}}^{{\rm{23}}}}{\rm{ kg}}\)

Gravitational acceleration on the moon\({{\rm{a}}_{\rm{m}}}{\rm{ = }}{{\rm{?}}^{}}\)

Gravitational acceleration on mars \({{\rm{a}}_{{\rm{mars}}}}{\rm{ = ?}}\)

Gravitational acceleration on the moon given by

\({{\rm{a}}_{\rm{m}}}{\rm{ = G}}\frac{{{{\rm{M}}_{\rm{m}}}}}{{{{\rm{R}}_{\rm{m}}}^{\rm{2}}}}\)

Here, G is the gravitation constant.

\({{\rm{a}}_{\rm{m}}}{\rm{ = 6}}{\rm{.673x1}}{{\rm{0}}^{{\rm{ - 11}}}}\frac{{{\rm{7}}{\rm{.3477x1}}{{\rm{0}}^{{\rm{22}}}}}}{{{{{\rm{(1}}{\rm{.737x1}}{{\rm{0}}^{\rm{6}}}{\rm{)}}}^{\rm{2}}}}}\)

\({{\rm{a}}_{\rm{m}}}{\rm{ = 1}}{\rm{.63 m/}}{{\rm{s}}^{\rm{2}}}\)

Gravitational acceleration on mars given by

\({{\rm{a}}_{{\rm{mars}}}}{\rm{ = G}}\frac{{{{\rm{M}}_{{\rm{mars}}}}}}{{{{\rm{R}}_{{\rm{mars}}}}^{\rm{2}}}}\)

We get what we want by swapping values.

\({{\rm{a}}_{{\rm{mars}}}}{\rm{ = 6}}{\rm{.673x1}}{{\rm{0}}^{{\rm{ - 11}}}} \times \frac{{{\rm{6}}{\rm{.418x1}}{{\rm{0}}^{{\rm{23}}}}}}{{{{{\rm{(3}}{\rm{.38x1}}{{\rm{0}}^{\rm{6}}}{\rm{)}}}^{\rm{2}}}}}\)

\({{\rm{a}}_{{\rm{mars}}}}{\rm{ = 3}}{\rm{.75 m/}}{{\rm{s}}^{\rm{2}}}\)

The values of acceleration due to gravity on moon and mars are \({\rm{1}}{\rm{.63 m/}}{{\rm{s}}^{\rm{2}}}\) and \({\rm{3}}{\rm{.75 m/}}{{\rm{s}}^{\rm{2}}}\) respectively.