Space methods - Physical Geodesy - page 268

reference orbit, and gravitational parameters; in addition, other unknowns
must be included to take into account nongravitational forces acting on the
satellite, such as air drag. An appropriate computational tool is least-squares
collocation with parameters (Moritz 1980 a: Sect. 16).
To get a strong solution, observations should be evenly distributed both
in space (with respect to the inclination of the satellites used) and in time.

Present results
At present (2005), several determinations of tesseral harmonics up to the
degree 360 are available from a combination of satellite and terrestrial data.
Soon the degree 1800 will be achieved. These coecients represent the large-
scale features of the disturbing potential T and, hence, of the geoid, since
the geoidal height is given by N = T/γ . There is a general agreement be-
tween the essential aspects of these determinations as expressed in geoidal
maps, although the details of these maps, and even more so the individual
coecients, are rather different.
As an example we take the first nonzonal coecients, C 22 and S 22 ,which,
according to Sect. 2.6, Eq. (2-95), express the inequality of the earth's prin-
cipal equatorial moments of inertia or, somewhat loosely speaking, its triax-
iality. According to Groten (2004), we have C 22 = (1574 . 5 ± 0 . 7) · 10 − 9 and
S 22 =(

10 − 9 .
Concerning the order of magnitude, J 2 is on the order of magnitude of
10 − 3 , where all the other coecients are of order 10 − 6 . This is why the earth
can be approximated by an ellipsoid so well.

− 903 . 9 ± 0 . 7) ·

7.6 New satellite gravity missions

7.6.1 Motivation and introductory considerations

Accuracy requirements in geodesy, geophysics, and oceanography for detailed
gravity field information amount to 1 mgal for gravity anomalies. The related
accuracy for the geoid ranges from 1 to 2 cm. In the presatellite era, the
earth's gravity field was known with high accuracy only in a few regions
of the world. Primarily, the available accurate gravity field information was
based on terrestrial and airborne measurements. This implied that in large
parts of the world there were virtually no gravity data available.
Why do we need the earth's gravity field at all? Following Pail (2003),
first, the gravity field reflects the mass inhomogeneities in the earth's interior
and on the earth's surface. Second, it is fundamental for the determination
of the geoid (see Chap. 11) which, in its turn, may be regarded as a physical