Please consult my earlier post, with timestamp 09/03/04 03:20 AM. I'll derive it more completely this time.<br /><br />Let G = universal gravitational constant<br />and Me = Gravitational mass of Earth<br />and me = Inertial mass of Earth<br />and M = gravitational mass of object<br />and m = inertial mass of object<br />and r = radius between the centers of mass of the Earth and the object.<br /><br />The magnitude of the force due to gravity on the object, which is also the magnitude of the force due to gravity on the Earth, f, is given by: f=G*Me*M/r*r.<br /><br />Since in general f=ma, then a=f/m. If we ignore all other forces, such as friction, we can solve for acceleration.<br /><br />The acceleration of the object due to Earth, a, is a=f/m, and the acceleration of the Earth due to the object, ae, is ae=f/me, towards each other's center of mass.<br /><br />Since inertial and gravitational mass are emperically equivalent, Me=me and M=m, precicely. Hence inertial mass and gravitational mass cancel out. (BTW - this is a deep mystery.)<br /><br />So a=G*Me/r*r and ae=G*M/r*r.<br /><br />Since Me is much much larger than M, a is much much larger than ae. That is to say that the Earth hardly accelerates at all, so little that it appears stationary within measurement error.<br /><br />So, although a bowling ball and feather would accelerate the same, the bowling ball would reach the Earth's suface in less time than the feather would, because the bowling ball moves the Earth more than the feather does.<br /><br />...Except in the case where they are dropped next to each other at precicely the same time!!! In this case, the acceleration of the Earth due to the bowling ball will cause the Earth to accelerate towards the feather in exactly the same way that the Earth accelerates toward the bowling ball! The Earth's motion cancels completely!<br /><br />So Gallileo was precicely correct, a bowling ball and a feather, dropped at the same time from the same height, ignoring all forces except