Geoscience Reference
In-Depth Information
2 Gravity field of the earth
2.1
Gravity
The total force acting on a body at rest on the earth's surface is the resultant
of gravitational force and the centrifugal force of the earth's rotation and is
called gravity.
Take a rectangular coordinate system whose origin is at the earth's center
of gravity and whose
z
-axis coincides with the earth's mean axis of rotation
(Fig. 2.1). The
x
-and
y
-axes are so chosen as to obtain a right-handed
coordinate system; otherwise they are arbitrary. For convenience, we may
assume an
x
-axis which is associated with the mean Greenwich meridian (it
“points” towards the mean Greenwich meridian). Note that we are assuming
in this topic that the earth is a solid body rotating with constant speed
around a fixed axis. This is a rather simplified assumption, see Moritz and
Mueller (1987). The centrifugal force
f
on a unit mass is given by
f
=
ω
2
p,
(2-1)
where
ω
is the angular velocity of the earth's rotation and
p
=
x
2
+
y
2
(2-2)
is the distance from the axis of rotation. The vector
f
of this force has the
z
!
P
p
f
x
y
p
y
x
Fig. 2.1. The centrifugal force
