How will the force of universal gravitation change if the mass of one of the interacting bodies is increased by 6 times?

Given:

m1, m2 – masses of two interacting bodies;

m3 = 6 * m1 – the mass of one of the bodies was increased by 6 times.

It is required to determine F2 / F1 – how the force of gravitational interaction between bodies will change with an increase in the mass of one of the bodies.

Since it is not specified in the problem statement, we assume that the distance between the two bodies does not change and is equal to r.

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

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

In the second case, the force of interaction will be equal to:

F2 = G * m2 * m3 / r ^ 2 = G * m2 * 6 * m1 / r ^ 2 = 6 * G * m1 * m2 / r ^ 2.

Then:

F2 / F1 = (6 * G * m1 * m2 / r ^ 2) / (G * m1 * m2 / r ^ 2) = 6, that is, it will increase 6 times.

Answer: with an increase in the mass of one of the bodies by six times, the force of gravitational interaction will also increase by 6 times.