Question

Two masses, m1 & m2 are separated by a distance of 12 m between their centers. The gravitational force attraction between the two masses is measured to be 6.0 x 10-6 N. The masses are then moved closer to one another, to a distance of 4 m between centers, and the resulting gravitational force is measured again. According to the Universal Law of Gravitation, the second measurement is

Answer 1

The universal law of gravitation says that the gravitational force between the two masses is

F₁ = G m₁ m₂ / r ² = 6.0 × 10⁻⁶ N

where r = 12 m. When the distance between the two masses is reduced to R = 4 m, i.e. 1/3 of the original distance r, we have

F₂ = G m₁ m₂ / R ² = G m₁ m₂ / (r/3)² = 1/9 G m₁ m₂ / r ² = 1/9 F₁

so that the resulting gravitational force has 1/9 the first magnitude, or

F₂ = 1/9 (6.0 × 10⁻⁶ N) ≈ 6.7 × 10⁻⁷ N