Originally posted by an0n
Ah, I get it now. You can change one object and still get the same accelerative force, but change the two and....
Right, I understand now. It's a 'between' force, not a 'from' force.
Er - sort of. There's a whole bunch of "almost correct" answers in this thread; I'm going to try to straighten it out. Bobboau was correct, but didn't tell the whole story.
Force due to gravity = G * ([M1] * [M2] / r^2), as Bobboau (and Kazan) said. R is the radius between the two masses, measured from their centers. You can do this because gravity acts on all masses as though they were point masses - a single point in space at which all the mass is concentrated.
Now let's say that [M1] is the Earth and [M2] is the Moon. You want to measure the acceleration of the moon due to Earth's gravity, so using F = ma, F = [M2] * a becomes a = F / [M2].
If you write it out on paper, the [M2]s cancel each other out. So you're left with a = G * ([M1] / r^2). The Moon's mass has no effect. So if you took a baseball and the Moon and dropped them toward the Earth from exactly the same point in space, they would fall with exactly the same acceleration.
The only way you change the acceleration is by changing [M1] or r. So gravity changes over distance, as Kazan said. But this isn't really noticeable except with very large masses, such as black holes. Here, gravity changes so quickly that if you were falling feet-first toward the black hole, your feet would be accelerating several orders of magnitude faster than your head. Your body would disintegrate.
