The force between two masses is directly proportional to the product of their masses and inversely proportional to the square of the distance between them, according to Newton’s law of gravitation. Calculate the gravitational force by multiplying the distance between the masses by r. The force is then calculated using the distance 2r. To determine the relationship between the two forces, compare them.
Fg = G×m1×m/R2
Doubling both masses and halving distance.
Fg′ = G × 2m1 × 2m2/(R/2)2
∴Fg′ = G×4×m1×m2/1/4×R2
∴Fg′ = G×m1×m1/R2 ×16
∴Fg′ = 16Fg