Two asteroids are gravitationally attracted to

Question

Two asteroids are gravitationally attracted to each other due to their mass and the distance between each other. If they are suddenly pushed twice as far away, how many times greater or smaller will the gravitational force between them be?

Answer 1

Initially, the force is

F = Gm₁m₂ / r²

Replace r with 2r.

F' = Gm₁m₂ / (2r)² = (Gm₁m₂ / r²) / 4 = F/4

The force is reduced to 1/4 of its original value.