Physics for Geologists, Second edition

Gravity 29
g being a vector, the negative sign indicating that it acts downwards. The
gravity field is -g and the force acting on any mass in the field is simply that
mass multiplied by the value of the field in that position.
Regionally, it may be sufficient to consider the gravity field as being every-
where -9.8 m s-2 directed towards the centre of the Earth, approximately;
but in detail, -g is constant neither in quantity nor direction. We have noted
earlier that there is a latitude effect. A formula for the sea-level value for g
in latitude 4 is
which is not considered to be quite correct but was nevertheless the standard
until artificial satellites led to the better formula
The discrepancy is very small, and of no significance over the limited area
of many surveys. Indeed, merely changing the equatorial value of g in the
old formula would have given results within about 1$ parts in 10 000 of
the new. But the more we learn about the earth, the better we can and must
describe it. As we have already noted, the acceleration on the Equator due
to the centrifugal force, v~/R, is about 34 x loF3 m s-~.
The practical unit of g is the gal, which is acceleration in units of cm sP2,
so multiply Equation 3.3 by 100 if you want to use gals - but beware! The
milligal is the common unit. The SI unit is the Gravity Unit, or g.u. One
milligal equals 10 g.u.
The rotation of the Earth about the Sun also affects the value of g, as does
the Moon's rotation about the Earth, both of which we see in tides (which
will be examined more closely below). On a local scale, the topography and
elevation above sea level must also be taken into account because hills distort
the local gravitational field, as do valleys, and elevation implies extra mass
beneath a gravimeter - the instrument for measuring the value of g. When all
these effects have been taken into account, there are still local variations that
Copyright 2002 by Richard E. Chapman