Question

What is the effect on the force of gravity between two objects if the mass of one object remains unchanged while the distance to the second object and the second object's mass are both doubled?

Answer 1

The force of gravity after you double the mass and the distance is half of the initial force:
`F_(2)=(1)/(2)F_(1)`

Step-by-step explanation:

The initial force of gravity is:

`F_(1)=(Gm_(1)m_(2))/(r^2)`

where
`G` is the universal gravitational constant,
`m_(1)` is the mass of the first object,
`m_(2)` is the mass of the second object, and
`r` is the distance between the objects.

If the mass of the second object is doubled, now we have
`2m_(2)`, and if the distance between the objects is also doubled instead of
`r` now we have
`2r`.

So the force of gravity now is:

`F_(2)=(Gm_(1)(2m_(2)))/((2r)^2)\\ F_(2)=(2Gm_(1)m_(2))/(4r^2) \\F_(2)=(1)/(2) (Gm_(1)m_(2))/(r^2)`

and we know that
`F_(1)=(Gm_(1)m_(2))/(r^2)`

so the new force of gravity is:

`F_(2)=(1)/(2)F_(1)`

The force of gravity after you double the mass and the distance is half of the initial force.