The force of gravity acts between the bodies. If the mass of each body is doubled, and the distance between

The force of gravity acts between the bodies. If the mass of each body is doubled, and the distance between the bodies is preserved, then the gravitational force between the bodies is

Given:

m3 = 2 * m1 – the mass of the first body was doubled;

m4 = 2 * m2 – the mass of the second body was doubled;

r1 = r2 – the distance between the bodies has not changed.

It is required to determine F2 / F1 – how the gravitational force will change.

The force of gravity in the first case will be equal to:

F1 = G * m1 * m2 / r1 ^ 2, where G is the gravitational constant.

The force of gravity in the second case will be equal to:

F2 = G * m3 * m4 / r2 ^ 2 = G * 2 * m1 * 2 * m2 / r12 = 4 * G * m1 * m2 / r12.

Then:

F2 / F1 = (4 * G * m1 * m2 / r12) / (G * m1 * m2 / r12) = 4 times.

Answer: the force of gravity will increase by 4 times.