Mechanics, Planetary Motion and the Modern Science Revolution 63
the stronger the force and the greater the distance, the weaker the force.
When calculating the distance between two bodies to compute the
strength of the gravitational force, one measures the distance from the
center of one body to the center of the other as shown in Fig. 6.5.
The mathematical description of Newton’s law of gravitation attraction
is F = Gm 1 m 2 /R^2.
Fig. 6.5Newton was able to show mathematically that only a force, which
was inversely proportional to the square of the distance, could explain
Kepler’s law. However, the most convincing evidence he presented for
his postulate was his comparison of the acceleration of an object at the
Earth’s surface with that of the Moon. Since the distance to the Moon
was known, it was a simple matter to calculate the acceleration it
experiences as it circles the Earth once a month. The acceleration of a
body at the surface of the Earth is the same for all bodies as will be
explained below and is easily measured. When one compares this
acceleration with the lunar acceleration and the distances from the center
of the Earth to its surface and to the Moon, one easily verifies that the
gravitational force is inversely proportional to the distance between the
two bodies squared.
Newton’s result depended on the fact, which had been experimentally
verified, that the acceleration a body undergoes as a result of the Earth’s
gravitational pull, is independent of its mass. In other words, the fact is
that a five-pound stone falls as rapidly as a fifty pound stone. One can
cite a counter example such as the comparison of a stone and a feather, in
which case the stone falls faster than the feather. This example is more
complicated than the example with the two stones because the air
resistance encountered by the feather produces an effective force, which