The evaluation of a complete 360 × 360 geopotential model at every satellite location of interest represents a substantial computational effort that is usually both undesirable and unnecessary. This section explains how an adequate truncation level of the expansion series may be selected for a satellite orbit of interest, based on two elementary observations.
The first observation is
that the term 
in equations (D-1) and (4‑4) leads to a rapid attenuation of the gravity
potential with orbit radius r, so
that the details of the geopotential become less and less notable at increasing
height (in other words, the Earth rapidly turns into a point mass with
increasing distance).
The second observation is that the expansion series may always be safely truncated at a degree l that provides contributions of lower order of magnitude than the inherent noise level of the model itself.
Considering these
observations, an adequate truncation degree can be determined on the basis of
Kaula’s rule ([RD.31] and equation D.6). This is briefly illustrated via an
example that selects a suitable truncation degree l for the orbit height of GNSS constellations, which have a radius r of about 4 times the equatorial radius
(i.e. an altitude of
H≈25 000 km).
In theory, the degree N of the expansion should be infinite to model the exact variability of the geopotential surface. In practice the maximum degree remains finite. This leads to truncation errors in the expansion series, and thus in a quantification error of the gravity acceleration. In order to get an impression of the truncation effect, Kaula (see [RD.31]) formulated a rule-of-thumb that provides the order of magnitude of normalized expansion coefficients as a function of the degree l:
|
|
(D-6) |
This estimate has turned out to be remarkably accurate, even for modern day models that expand up to degree and order 360 or higher.
Table D-1 shows for increasing degree l the signal power in the harmonic components for that degree
according to the Kaula rule, the attenuation factor for that degree, and
the product of these two, which represents the remaining signal power at the
orbit height of interest.
The inherent noise level of a 360 × 360 degree model can be approximated by the signal power for l = 360, which is 7,7x10-11.
Looking in the last column of Table D-1, it appears that the attenuating effect of the 25 000 km orbit height already reduces the degree 8 terms of the model to an order of magnitude that is below the noise level of the model.
In practice, one should account for the fact that Kaula’s rule is just an approximation, albeit an accurate one. Instead of applying the estimated 8 × 8 resolution, one can choose to apply e.g. a 12 × 12 resolution for GPS orbits, especially because the effort of evaluating a 12 × 12 field is still trivial in comparison to the evaluation of the full 360 × 360 model.
The above selection process for a suitable truncation degree does not account for cases where the orbital motion of the satellite, in combination with the rotation of the Earth, leads to a resonance situation where certain harmonic components are continuously sensed by the satellite in exactly the same way. This is particularly likely to happen for so called repeat orbits, where the ground track of the spacecraft returns to the same point on the Earth surface after M orbital revolutions, which take exactly the same amount of time as N revolutions of the Earth (= days). This is, for instance, the case for geosynchronous, GNSS, and Earth observation satellites. Even very small harmonic components that are in exact phase with orbital motion may then result in significant orbital perturbations after sufficient propagation time intervals.
For Earth-orbiting satellites, the only tide generating bodies of interest are the Sun and the Moon. This leads to the following main conclusions:
• The tidal effects of the Moon are more pronounced than those due to the Sun, because the effect of distance is stronger than that of mass.
•
The main gravity harmonic
perturbation is the zonal harmonic 
which is of order 10-3,
while further gravity harmonics are of order 10-6 or smaller. Consequently,
tidal effects can only be ignored in cases where the gravity field is truncated
at degree 2 (Earth oblateness only) or 1 (central body gravity only).
Hence, luni-solar tide effects become non negligible when modelling harmonic perturbations of the gravity field for degrees 3 or higher.
Table D-2 gives the coefficients of the EIGEN-GLO4C model up to degree and order 8x8.
Figure D-1 shows a graphical representation of the EIGEN-GLO4C Geoid (greatly exaggerated).