Two objects attract each other gravitationally. If the mass of each object doubles, how does the gravitational force between them change?

The gravitational force between them quadruples

Explanation:

According to law of gravitation, the force of attraction (F) between two masses m1 and m2 is directly proportional to the product of the masses and inversely proportional to the square of the distance (r) between them. Mathematically,

F1 = Gm1m2/r² ... 1

If their masses doubles, the formula becomes;

F2 = G (2m1) (2m2) / r²

F2 = 4Gm1m2/r² ... 2

Dividing equation 2 by 1, we have;

F2/F1 = {4Gm1m2/r²}:{Gm1m2/r²}

F2/F1 = 4Gm1m2/r²*r²/Gm1m2

F2/F1 = 4

F2 = 4F1

The gravitational force between the masses when they doubles quadruples.