. The Moon has a radius of 1.74×106m. It is orbiting the Earth at a distance of 3.84×108m, taking 27.3 days for a complete revolution. The free-fall acceleration on Moon is 1.62 m/s2 . From the information given, find the mass of the Moon and the mass of Earth.

mass of moon = 7.350 * 10²² Kg

Mass of earth = 5.98 * 10²⁴Kg

Explanation:

acceleration due to gravity = (gravitational constant * mass of the body) / (distance from the centre of mass)²

g = Gm/r²

G = 6.673 * 10^-11

g(moon) = 1.62 m/s²

r (moon) = 1.74 *10⁶

g = GM/r²

M = gr² / G

M = 1.62 * (1.74 * 10⁶)² / 6.673 * 10^-11

M = 7.350 * 10²² Kg

Mass of moon = 7.350 * 10²² Kg

Mass of earth =?

g = GM / r²

M = gr² / G

g = 9.8 m/s²

G = 6.673 * 10 ^-11

r = 3.84 * 10⁸m

M = 9.8 * (3.84 * 10⁸)² / 6.673 * 10^-11

M = 5.98 * 10²⁴ Kg

Mass of the earth = 5.98 * 10²⁴kg