How does quadrupling the distance between two objects affect the gravitational force between them?
4 Answers

The effects of gravity between two bodies are directly proportional to the mass, and inversely proportional to the distance. If one body in a two body system has a fourth of the mass of the other, it’s gravitational pull is four times less than the larger body at any given distance between them. On the other hand, if it was moved four times ƒᴀʀтher away from the larger body, the gravitational attraction is reduced to one sixteenth of it’s former strength assuming the masses of both are unchanged.

The strength between two objects decreases with the square of the distance between their centers. We therefore say that the gravitational force (Fg) follows an inverse square law. By quadrupling the distance between two objects the gravitational force (Fg) will decrease by 1/4^2 = 4^2= 16.
Mass attracts every mass through the force of gravity. The strength of the gravitational force (Fg) is directly proportional to the product of their masses. They increase in linear fashion so gravitational force (Fg) will be twice as strong if one of the masses increases by a factor of 2.
1/3^2 = 3^2=9. The strength of gravity between two objects decreases with the square of the distance between the centers. So if the earth moved to 1/3 of its current distance from the

The gravity changes by the inverse square of the distance. So you get the current gravity G1 and the distance D and the new gravity G2 would be G2=G1/(D^2). Increasing the distance by four times would therefore decrease the gravitational force by 4^2 or 16 times, down to 6.25% of what it initially was.

Inverse of Distance Squared remember?
4 X the distance, 1/16 the gravity.