Given the mass of the moon = 7.35 × $10^{22}$ kg and the radius of the moon = 1740 km. Calculate the acceleration experienced by a particle on the surface of the moon due to the gravitational force of the moon. Find the ratio of this acceleration to that experienced by the same particle on the surface of the earth.

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Solution

Mass of the moon = 7.35 * $10^{22}$ kg,radius of the moon = 1740 km

acceleration experienced by a particle on the surface of the moon due to the gravitational force of the moon = $\frac{G M_{e a r t h}}{R^{2}}$

$\frac{G M_{m a r s}}{{R^{2}}_{m a r s}}$ = $\frac{(6.67 * 10^{- 11}) * (7.35 * 10^{22})}{{(1740 * 10^{3})}^{2}}$

= 1.61 $\frac{m}{{s e c}^{2}}$

Ratio of this acceleration to that experienced by the same particle on the surface of the earth = $\frac{1.61}{9.8}$ = 0.1642

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