maining undisturbed unless upset by a bulldozer or
by earthquakes. In the geophysical applications, on
the other hand, time becomes an active dimension
and both the coordinates and the gravity field are
considered as dynamic quantities: The modern
counterpart of continental drift - the "new global
tectonics" - has divided the earth into large, rigid
plates that move relative to each other at rates of
10 cm/year or perhaps even more. The earth's
geopotential is constantly being deformed by the
gravitational attraction of the sun and moon and
by seasonal variations in the earth's atmosphere.
The observations of those time dependencies be
come one of the most important means of under
standing the physics of the earth.
What 1 wish to explore here a little is the nature of
the geophysics that we can hope to observe using
the methods of satellite geodesy and to try to indi
cate what these observations will lead us to conclude
about the physics of our planet. For example, what
geodetic results are required to detect certain sus
pected behaviour characteristics of our dynamic
earth. In the case of the large scale motions of the
"plates" the answer is fairly straightforward: we
need a technique that gives us accuracies for relative
station positions of a centimeter or so in as short a
time span as possible. Can this be done with the
long baseline radio interferometry, or is it merely
idle speculation?
More difficult is the question as to what observation
al accuracies are ideally required for the earth's
rotational speed and for the variations of the direc
tion of the earth's axis. What geophysical conclu
sions can we obtain from such observations. Some
possible examples are perhaps interesting in this
respect. Is the well-known and rather broad
Chandler Wobble peak in the polar motion the con
sequence of several sharp peaks close together and
arising from a differential rotation between dif
ferent layers in the earth's upper mantle? Can the
nearly diurnal nutation term resulting from a free
oscillation of the liquid core be detected? Is there
indeed a long period term in the polar motion arising
from the coupling between the earth's solid inner
core and its liquid outer core?
These are just some of the questions that can be
asked, based on various geophysical models of the
earth. To test these methods we require the appro
priate observations of the earth's motion about its
center of mass and the present indications are that
the classical astronomical methods are inadequate
for this. But can laser ranging to the moon or laser
or doppler tracking of satellites give better results?
In the present discussion we will limit ourselves to
the question of the earth's gravity field mainly
because it is one with which I have had the most
experience and also because it is one which has
benefitted most significantly from the developments
of this space age. We will first discuss the results
obtained followed by a geophysical discussion.
Finally we will discuss what future developments
may be expected. I hope that I can return to some
of the other geophysical aspects of geodesy in the
future.
Determination of the earth's gravity
As the satellite moves around the earth its motion
is influenced by all the variations in the gravity
field at satellite heights. If we observe these irregu
larities, or perturbations, in the motion we can
obtain important information on the earth's poten
tial or alternatively on the shape of the geoid and
the gravity field. To extract this information we
expand the geopotential into spherical harmonics,
that is:
V=~~ 1+X I -y f'imfsin <p)
(Clm cos mX S/msin ml)
0)
where GM is the product of the gravitational con
stant and the earth's mass, ae is the equatorial
radius, Plm (sin <pare the associated Legendre poly
nomials and Clm, Slm, for the moment, are related
to the mass distribution of the earth.
In terms of the orbital elements (a, e, i, w, Q, M)
this potential can be written as:
X X AVlm(a,e,i,a>,Q,M)
where
l=lm 0\
V
GM
42
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