a resolution of 60 km we require however an ex
pansion to degree 180 or more than 32,000 coeffi
cients. New methods of analysis will obviously be
required, but the most suitable approach is not yet
clear. Perhaps some form of direct mapping is
preferable to a mathematical treatment. The first
altimeters to be flown will probably have an ac
curacy of one or two meters and provide a spatial
resolution, using the present methods of data
analysis, of perhaps 500 km. At this accuracy and
resolution we do not yet run into the serious prob
lems of the departures of sealevel from the geoid,
yet the results will provide a major improvement on
what is possible by the classical methods.
Another method for improving our understanding
of the earth's gravity field is by a technique known
as satellite-to-satellite tracking. One of the satellites
would be in a geostationary orbit while the second
satellite circles the earth at a low altitude, perhaps
as low as 300 km. This low satellite is tracked from
the stationary satellite by a highly accurate Doppler
tracking system while it itself is being tracked from
the ground by perhaps laser or radio interfero-
metry. If we have a constellation of three such geo
stationary satellites we would have a complete
orbital coverage and we can observe some of the
short wavelength features in the geopotential. The
low altitude will also enhance the satellite's suscepti
bility to the short wavelength features although
the atmospheric drag forces will now become im
portant and the only way in which we can eliminate
this is to use drag-free satellites. Now the whole
program becomes sufficiently complicated for it to
be relegated well into the future.
Conclusion
The determination of the earth's gravity field is the
most important result obtained from satellite
geodesy and has provided an extremely valuable
boundary condition for the problem of determining
the structure of the earth's interior. Improvements
in the gravity field can only come from the very
precise tracking of satellites and laser range obser
vations will be of the utmost importance for this.
It is perhaps necessary to stress that such improve
ments can only come from a truly international
cooperative observing program. The solution dis
cussed in the preceding section is an expression of
this international cooperation since the data was
collected with the support of national agencies and
universities on six continents.
We have seen also, that there is a limit to the infor
mation that can be obtained from the now used
methods and that if we want to improve the resolu
tion of the solution we have to look towards the
new methods. The recommendations made by the
NASA study group on solid-earth and ocean phy
sics [29] and the recent results by McKenzie [27]
certainly indicate the desirability of determining
this detail.
Of the new methods, satellite altimetry is the most
promising and it is difficult to see any future pro
gress in satellite geodesy without the altimeter
playing a dominant role. This does not mean the end
of laser tracking: Far from it, as accurate laser
data will be absolutely necessary for providing the
precise reference orbits and for calibrating the
altimeter system. Thus any global altimeter system
will also require a fully international tracking
program.
Whereas the gravity field has now brought us into
close contact with the solid earth physics, the alti
metry satellites will eventually bring us into close
contact with physical oceanography. For accuracies
of about a meter sea level in the open ocean will
approximate the geoid with a sufficient accuracy
and we can consider both as static. For accuracies
of 10-20 cm - and these are possible in the near
future - the ocean surface and the geoid must be
considered as dynamic surfaces: The former being
constantly remoulded by currents, waves, winds and
variations in atmospheric pressure and salinity
while the geoid is constantly changing shape due
to the lunar and solar tides. The interpretation of
the results will therefore require a thorough under
standing of these various forces at work on the
ocean surface.
We have talked about precise laser data being
necessary and we have hinted at accuracies of 10 or
20 cm. Recent progress in laser technology has
indicated that such accuracies are indeed possible
now.
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