Question

Let F equal the gravitational force between the Earth and Moon. If the distance between (centers of) Earth and Moon is halved, what would the gravitational force between them equal ?

Answer 1

The universal law of gravitation states that:
Every object in the universe pulls every other object with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
The Gravitational force formula is given by
F = Gm1m2/r²
Where,
G is universal gravitational constant, m1 and m2 are mass of bodies r is the radius between the two masses.
if r is halved i.e r' = r/2
then F' = Gm1m2/r'² = Gm1m2/(r/2)² = 4Gm1m2/r² = 4F
So, If the distance between (centers of) Earth and Moon is halved, then the gravitational force will be 4 times.