Question

How does gravity change with mass?

Answer 1

Newton's gravitational law,
`F_G = (GMm)/r^2`

`F_G =` Force of gravity between two objects
`G =`Universal Gravitational constant
`M =` mass of first object
`m =`mass of second object
`r =`distance between the object's centers of mass

So force of gravity is directly proportional to mass of object. If you double the mass of something, gravity acts with twice as much force on it.

It's usually reasonable to simply think of the gravitational force between objects as a function of the distance between their centers of mass. Newton held up publication of his laws of universal gravitation because, though they did explain the motion of the planets really well, his solutions postulated that the planets could be thought of as simply point masses. He knew that he would be criticized for not using a theory which described them as large extended objects. He didn't want to be criticized. So he invented calculus and proved that they could be considered to be point masses.