Environmental Engineering Reference
In-Depth Information
9
Gravitation
Throughout Part I of this topic, we focused our attention on the basic principles
of motion as articulated by Newton. On occasion we invoked the force of grav-
ity in order that we might consider interesting physical applications of Newton's
laws. However in most cases we assumed that the motion was taking place in
a sufficiently small region of space that the gravitational field could be assumed
constant. However, thanks again to Newton, we now understand that gravity is a
force that acts between all bodies such that the force between any two bodies is
directly proportional to the product of their masses and inversely proportional to
the square of the distance between them. Of course we know that gravity is not
the only force at work in the natural world. Electricity and magnetism, unified
by Faraday, Ampere and Maxwell into the theory of electromagnetism are also
abundantly evident and are ultimately responsible for light itself. In addition, we
now know that the atomic nucleus is prevented from exploding under the repulsive
influence of the Coulomb force which acts between its proton constituents by a
further force, the strong nuclear force, which acts only over very tiny distances.
Finally, the burning of the Sun can only be understood once we recognise the
existence of a fourth fundamental force: the weak force, responsible also for the
process of nuclear beta decay. So it seems that physical phenomena throughout the
Universe can be thought of as arising out of the interactions of matter which occur
as a result of these four fundamental forces. All other forces, such as the tension
in a spring or the force which drives forwards a sailing boat, are none other than
complicated consequences of one or more of these fundamental forces.
Of all the forces in nature, Newton's Law of Gravity sits alongside Coulomb's
Law of electrostatics (which is also described by an inverse square law and is a
part of the electromagnetic theory) in being simple enough that we can make very
significant progress in understanding its consequences without too much hard work.
It is for that reason that we focus our attention in this chapter on gravity and over
the next few pages we shall use Newton's theory of gravity in order to understand
fully gravitational systems containing two bodies. That will be sufficient for us to
