The acceleration of an object does not change regardless of the mass of that object.
However the force exerted does. Also, the acceleration of the Earth towards the object does change with mass. So a large rock would pull more on the earth than a small feather. In both cases, the pull is so small, it's considered non-existant. Also, the acceleration of gravity changes with your distance from the surface. All this can be proven quite easily.
G m
1 m
2
F = ----------
r
2
This is the gravitational law equation, which gives the force two objects exert on each other due to gravity. G is the
Universal gravitational constant, and equals 6.67259
E-11. Next, we have
Newton's Second Law, which is:
F = ma
or force is mass times acceleration. Now, let m be the mass of one of the objects, say m
1. Substitute the second for the first equation.
G m
1 m
2
m
1a = ----------
r
2
and cancel. units to get:
G m
2
a = ----------
r
2
Something to think about is that weight and mass are often mislabled. This mistake occurs just as much in
metric as
imperial units. In imperial (
english) units, pounds is often incorrectly referred to as a measure of mass. The correct unit for mass is the
slug. In metric, the kilogram is often miscorrectly referred to as a unit of weight. The unit of weight for metric is the
newton.
Mass is a collection of particles,
Weight is the force exerted on a body by gravity.
Another common misinterpretation of the gravity law is, if your stand on a chair, x distance from the surface of the earth, then stand on a chair twice as tall, or 2x, you should weight a fourth as much. (since r is increased by two, then the term r
2 should decrease the force by four). While this is mathmatically correct, the distance r is measured not to the surface of an object, but to the distance between the two
center of gravities for the objects object. For spheres, such as the earth, the
center of gravity is the same as the center of the sphere. So in reality, r has only increased by an very small amount.