[Jack Simth]

Originally posted by Imperator Fyron:
Yes, but objects falling within the atmosphere don't behave the same as two large objects in space attracting each other... The reason why objects fall at the same rate is that he gravitational acceleration caused by the earth's gravity is constant (at the same point on the surface of the earth, relative to two different objects). This is in part because the falling objects have infintesimal mass compared to that of the earth (though technically they do actually move the earth an infintesimal distance closer to themselves as they fall ). Objects in space are governed by the relation F = G * M1 * M2 / r^2, where F is force, G is a constant, M1 and M2 are the masses of the two objects, and r is the distance between them. A more massive object causes more gravitational force between the objects, and thus greater acceleration.

They only accelerate faster relative to each other, because both are accelerating at a rate dependant only on the other's mass. When both are massive; from a "fixed" perspective, the acceleration a body recieves depends only on the mass and distance of the bodies affeting it (until you get into relativity; but that takes extreme circumstances e.g. black holes vs. rotating black holes). You can get this fairly simply by recalling that Acceleration = F/M. For mass 1, A1 = F/M1 = (G * M1 * M2 / r^2)/M1 = (G * M2 / r^2); for mass 2, A2 = F/M2 = (G * M1 * M2 / r^2)/M2 = (G * M1 / r^2). If you are on M1 and using M2 as your referance, your acceleration = A1 + A2 = (G * M1 / r^2) + (G * M2 / r^2) = G(M1 + M2)/r^2.