physics, rotational motion, gravitation, question is in the description

Question

According to the equation for gravitational force, what happens to the force between two bodies if the mass of one of the bodies is double? If both masses are double?

Answer 1

The equation for gravitational force between two objects is GmM/r^2

G- is the gravitational constant

m- is the mass of the first object

M- is the mass of the second object

r- is the distance between the two objects

with this being shown if you where to double the mass of object one (m) then the new mass would be 2m

and the force would go from GmM/r^2 -> G2mM/r^2 effectively doubling the force.

if you also doubled the mass of object two (M) then 2GmM/r^2 (the equation we got from doubling small m)

would become 4GmM/r^2 (since we now also doubled big M).

this would effectively become 4 times the original force (GmM/r^2)