62 The Poetry of Physics and The Physics of Poetry
forces sum up to zero. Once it is pushed over the cliff the force of the
ground pushing up can no longer act and so the car begins to fall.
The third law is a statement of the fact that whenever two bodies
interact the forces they exert on each other are equal and opposite as was
illustrated by the recoil of a discharged gun. Since the force acting on a
body is a measure of the change of its momentum this law plus the
principle of inertia insures that momentum will be conserved. The
conservation of momentum may be stated as a law but it should be noted
that it follows from Newton’s three laws of motion and the definition of
momentum.
Newton’s three laws of motion offer a programme for describing the
universe. If one knows the position and velocity of the particles in the
universe at one given time and the mutual forces between them then one
can predict the position and velocity of these particles for all future
times. This is possible since knowledge of the forces implies knowledge
of the accelerations. Then using the differential and integral calculus
developed by Newton together with knowledge of the initial positions
and velocities, one can use the information of the accelerations to predict
all of the particles’ future positions. The key to describing a mechanical
system such as the solar system for example, therefore reduces to
describing the forces between the various components of the system as
well as their position and velocity at one given moment, which
presumably one obtains through observation.
Indeed the first problem Newton applied his new mechanics to
was the motion of the planets of the solar system. In order to solve
this problem he had to make an assumption regarding the forces
between the heavenly bodies. The notion of a universal gravitational
interaction between the Sun and the planets, which also accounts for the
Earth’s local gravitational field had already been developed by Newton’s
predecessors, Copernicus, Gilbert, Roberval and Borelli who gave a
qualitative description of the gravitational interaction.
In order to explain the interaction of the planets and the Sun using
the mechanics he had developed, Newton required a quantitative under-
standing of the gravitational interaction. It was through his studies of
Kepler’s three laws of planetary motion that Newton came to understand
the gravitational interaction quantitatively. He postulated that any two
bodies would be mutually attracted to each other with a force directly
proportional to the mass of each body and inversely proportional to the
square of the distance between them. In other words the larger the mass,