Geoscience Reference
In-Depth Information
1. The vertical axis of the reference ellipsoid is parallel to the earth's
axis of rotation, but it need not be in an absolute position, its center
coinciding with the earth's center of gravity. To repeat the reason:
the earth axis is accessible to (astronomical) observation, whereas the
geocenter is physically defined and inaccessible to direct geometrical
observation.
2. The geocenter is accessible in two physically defined ways: (1) gravi-
metrically through Stokes' formula and (2) physically by the first Kep-
ler law applied to satellite motion and responsible for the geocentricity
of GPS orbits.
Note that unless otherwise stated, we always assume that our observa-
tions are made at sea level. This is not so unnatural for an inhabitant of a
large plain region but causes headache to a geodesist working in the Alps
or in the Rocky Mountains. We have already been confronted with this sit-
uation before, in gravity reduction, and will meet it repeatedly later, most
prominently under the heading of Molodensky's problem.
It should also be mentioned that the ellipsoidal azimuth
α
in (5-102)
refers to the actual target, which does not in general lie on the ellipsoid.
For the conventional method of computation on the ellipsoid, one wishes the
azimuth to refer to a target on the ellipsoid, which is the point at the foot of
the normal through the actual target. Furthermore,
α
refers to what is called
a normal section of the ellipsoid, rather than to a geodesic line, which is used
in computation. In either case very small azimuth reductions are necessary;
since these reductions are purely problems in ellipsoidal geometry, the reader
is referred to any appropriate textbook.
Effect of polar motion
The direction of the earth's axis of rotation is not rigorously fixed, neither
in space nor with respect to the earth, but undergoes very small, more or
less periodic variations. Astronomers know it by the name of
nutation
(with
respect to inertial space), geodesists know it by the name of
polar motion
(with respect to the earth's body). This phenomenon arises from a minute
difference between the axes of rotation and of maximum inertia, the angle
between these axes being about 0
.
3
, and is somewhat similar to the preces-
sion of a spinning top. This motion of the pole has a main period of about
430 days, the Chandler period, but is rather irregular, presumably because
of the movement of masses, atmospheric variations, etc. (Fig. 5.13).
The International Earth Rotation Service (IERS), initially International
Latitude Service and then Polar Motion Service, which is maintained by
the International Astronomical Union and by the International Union of
