Physics for Geologists, Second edition

3 Gravity
Universal gravity
When discussing weight, mass and density (page 14) we stated Newton's
Law of Gravitation: that every particle of mass ml attracts every particle
of mass mz with a force that is directly proportional to the product of their
masses and inversely proportional to the square of the distance between their
centres of mass; and this force acts along a straight line joining them:
where r is the distance between their centres of mass, and G is the universal
constant of gravitation, and we noted that G is not a true constant because
it has dimensions.
Fields
Fields are difficult to define. Within a body of water there is a pressure field.
If the water is of constant density and is at rest, surfaces of equal pressure
(pgz) are horizontal (that is, normal to the vector -g). When the water flows,
the pressure field changes because the energy of the water changes. Energy is
also a field. Fields may consist of scalars (magnitude), such as temperature,
pressure or energy, or of vectors (magnitude and direction), such as force;
and they can be mapped.
The space in which terrestrial gravity acts, and the space in which mag-
netism acts, are called gravity fields and magnetic fields, respectively. An
electric current in a wire sets up a magnetic field around the wire. Fields in
physics are spaces (or areas) in which some agent (commonly a force) oper-
ates. There are fields at various scales, regional and local. The local magnetic
and gravity fields are of interest to geologists because ore bodies may give
rise to anomalies. Take gravity.
On the surface of the Earth the force due to gravity acting on any object
is, as we saw on page 14,
Copyright 2002 by Richard E. Chapman