This is one of the most fascinating subjects in physics! The question:
"Why is the gravitational mass of an object exactly equal to its
inertial mass" has given rise to a great many interesting lines of
Here's what that means:
Newton's second law says F = m*a, where F is the sum of all the forces on an object, m is its mass, and a is its acceleration.
Newton also found out that F = m*g expresses the force gravity
exerts on an object (there may be other forces, but when you drop
something, these other forces are temporarily not playing a role. Air
resistance gums things up a little bit, but let's ignore that for now).
The quantity g is just 9.81 meters/sec^2 near the earth's surface, and
it gets weaker as you go away from the earth.
If gravity's the only force on a book, then its acceleration is
just g. The mass divides out! You can drop anything, and as long as you
don't have air resistance, it will fall at the same rate as if you
dropped anything else.
This is one consequence of Einstein's equivalence principle, that
a gravitational field and an accelerated reference frame (think:
standing in an elevator that starts going up -- you feel momentarily as
if gravity is turned up in the room a bit) are indistinguishable. Then
all objects should accelerate the same in a gravitational field. But I
still cannot answer the "why" part of why this is so.
(published on 10/22/2007)