Physics question over gravity

Question

Compare the gravitational force on a 44.5 kg mass at the surface of the Earth (with radius 6.4 × 10^6 m and mass 6 × 10^24 kg) with that on the surface of the Moon (with mass 1/81.3 ME and radius 0.27 RE) . What is the force on the Earth? Answer in units of N.

Answer 1

Let

m = 44.5 kg be mass of the object,

M = 6 × 10²⁴ kg be the mass of the Earth,

R = 6.4 × 10⁶ m the the radius of the Earth,

G = 6.674×10^-11 m3⋅kg^-1⋅s^-2 be the gravitational constant.

The gravitational force by the Earth on the object, and by the object on the Earth is

F = GMm/R²

= 6.674×10−11 m3⋅kg−1⋅s−2 × 6 × 10^24 kg × 44.5 kg/(6.4 × 10^6 m)²

= 435 N

Please note that the ration between the gravitation force 435 and the mass 44.5

should be gravitational acceleration

435/44.5 = 9.78

I attribute the discrepancy between 9.78 and the usual 9.81 to rounding off in the

Earth's weight and radius.

The mass of the Moon is M / 81.3.

The radius of the Moon is R × 0.27.

The gravitational force on the moon would be

G(M/81.3)m/(R×0.27)² = 0.17×GMm/R²

The gravitational force on the moon is smaller by the factor of about 0.17.