Question

Compare the gravitational force on a 4 kg

mass at the surface of the Earth (with radius 6.4 × 106 m and mass 6 × 1024 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 Moon?
Answer in units of N.

Answer 1

• 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.