The acceleration due to gravity on the surface of the moon

Question

The acceleration due to gravity on the surface of the moon is 1.62 $ms^{-2}$. The radius of the Moon is 1740 km. Find the mass of the moon.

Accepted Answer

Solution:

Acceleration due to gravity = $g_{m} = 1.62 ms^{-2}$

Radius of the moon = $R_{m}$ = 1740 km = $1740 imes1000$ m = $1.74 imes 10^{6} m$

Mass of moon = $M_{m}$ = ?

$g_{m}$ = $G M_{m}/〖R〗^{2}_m$

or

$M_{m}$ = $(\frac{gm imes〖R〗_{m})}{G}$

$M_{m}$ = $(\frac{1.62 imes(1.74 imes10^{6}))^{2}}{(6.673 imes 10^{-11})}$

= $(\frac{1.62 imes 3 imes10^{12})}{(6.673 imes 10^{-11})}$

$M_{m}$ = $7.35 imes 10^{22}$ kg