<font color="yellow">So.. shouldn't a bowling ball actually fall faster than a feather in a vaccuum? Every object exerts gravitational influence, and a bowling ball has more mass than a feather.. so shouldn't it fall faster? </font><br /><br />Yes, the force of gravity is greater on the bowling ball than it is on the feather, because the bowling ball has more "gravitational mass" (M) than the feather.<br /><br />However, the "inertial mass" (m) of the bowling ball is also greater than the mass of the feather. It takes more force to accelerate a bowling ball than it does to accelerate a feather, when accelerated in the same way.<br /><br />Now consider any object with gravitational mass M and inertial mass m, in a gravitational field where the force of gravity equals Mg. Let's find out how fast will this object accelerate?<br /><br />Newton's law says f=ma.<br />From Gravitation, since f=Mg in this case, Mg=ma.<br />Solving for acceleration, we find that (M/m)g=a.<br /><br />Now, it just so happens that every time anyone has ever measured them, the gravitational mass and the inertial mass have been found to be EXACTLY EQUAL IN ALL CASES. Why is this so? Nobody knows! Turns out this is a very deep mystery!<br /><br />Knowing this, we realize that M=m, so (M/m)g=g=a.<br /><br />The inertial and gravitational masses cancel out!! That's why the feather and the bowling ball fall at the same speed (on the moon).<br /><br /><font color="yellow">How can 9.81xxxx be *THE* number in all circumstances on earth?</font><br /><br />It isn't! This is just an approximation that works pretty well for most stuff. Variations come from changes in the local geology.<br /><br /><font color="yellow">What if I took a cup-full of nuetron star and dropped it- wouldn't the 9.81 number be much, much higher in that case? - and if it is indeed higher, than why not in all cases- including bowling balls and feathers?</font><br /><br />Again, the variations come from the local geolo