The gravitational force between two asteroids is 100N. What would the force be if the distance between the asteroids was cut in half?

The gravitational forces between two masses are inversely proportional to

the square of the distance between the centers of the masses.

So if the distance between the centers of the asteroids is multiplied by 1/2,

then the gravitational forces between them are multiplied by ...

1 / (1/2) ² = (2) ² = 4.

The new force is (100N) x (4) = 400N.