Since you're interested in the fundamental properties of gravity let's
ignore air friction, which could mess up the real experiment.
The answer is- it depends on just what you mean by 'accelerate
faster'. First, lets look In a standard Newtonian picture, where you
pretend that space and time have simple properties. The balls
accelerate at exactly the same rate when they're at the same distance
from the Earth, according to a principle discovered by Galileo.
Let's say you drop the balls one at a time and measure the time
before they hit. The heavier ball would cause the Earth to accelerate
toward it more than the light one would. That means that the distance
between the ball and the earth would shrink a tiny bit faster for the
heavy ball. Then it would be a little closer to the Earth, and so its
own acceleration would be a tiny bit greater. It and the Earth would
collide a little quicker.
Now if you drop both balls at the same time, they're BOTH pulling
the Earth up, and they still accelerate exactly the same as each other
at some height so they both hit the Earth at the same time.
If you try to use more general coordinate frames of General
Relativity, incorporating gravity as part of the properties of
space-time rather than as a 'force', the choice of how much you say
something accelerates becomes arbitrary. However, the basic fact
remains true that if the balls are dropped together, they hit at the
same time. If they are dropped separately, the heavy one hits a tiny
bit more rapidly, as measured by beats of some standard clock.
I'm not quite sure what your last question means. However, it helps
to remember Newton's third law. Whatever force the ball exerts on the
Earth (we're back in Newtonian descriptions) has exactly the same
strength as the force the Earth exerts on the ball, but pointed the
(republished on 07/12/06)