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

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

temp rises, and expansion