Temporal Variation of the Terrestrial Gravity Field due to Internal/
External Volume and Surface Forces: Functional Relations Between
Generalized Love-Shida Functions
Summary
E. W. Grafarend and J. Engels
Department of Geodetic Science
University of Stuttgart
Keplerstr. 11
D-70174 Stuttgart
Germany
and
P. Varga
Geodetic and Geophysical Research Institute
of the Hungarian Academy of Sciences
Sopron, POBS, H-9401
Hungary
The high resolution analysis of orbit perturbations of terrestrial artificial satellites
has documented that the eigengravitation of a massive body like the Earth changes
in time, namely with periodic and aperiodic constituents. Such a time variation of a
massive body's gravitational field is caused by the body's deformatl:on due to internal
and external volume as well as surface forces, recognized early by A.E.H. Love and
T. Shida. In particular, it has been shown that for a rigid body the time - variation of
its gravitational field approaches zero, manifest of gravitostatics. In contrast, due to
mass transport and the spacetime variation of the mass density the "real" gravitational field of a deformable body varies in spacetime, manifest of gravitodynamics. Up
to the present the spacetime variation of an intrinsic or eigen-gravitational field has
only been analyzed under certain constitutional symmetries of tht! deformable body,
namely spherical symmetry and cylindric (" spheroidal") symmetry.
Our first aim here is accordingly to present the spacetime field equations of gravitation, both in the Eulerian and the Lagrangean portrait of a deformable, massive
body without any symmetry assumption. We review gravitodynamics by representing
the spatial (" Eulerian") increments versus the material (" Lagrangean") increments
of the vector-valued force field, the scalar-valued gravitational potential field as well
as the scalar-valued mass-density field, the linearized, incremental gravitational field
equations and the 'jump conditions' at interfaces. In particular the material ("Lagrangean") field equations and 'jump conditions' prove to be complicated on their
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External Volume and Surface Forces: Functional Relations Between
Generalized Love-Shida Functions
Summary
E. W. Grafarend and J. Engels
Department of Geodetic Science
University of Stuttgart
Keplerstr. 11
D-70174 Stuttgart
Germany
and
P. Varga
Geodetic and Geophysical Research Institute
of the Hungarian Academy of Sciences
Sopron, POBS, H-9401
Hungary
The high resolution analysis of orbit perturbations of terrestrial artificial satellites
has documented that the eigengravitation of a massive body like the Earth changes
in time, namely with periodic and aperiodic constituents. Such a time variation of a
massive body's gravitational field is caused by the body's deformatl:on due to internal
and external volume as well as surface forces, recognized early by A.E.H. Love and
T. Shida. In particular, it has been shown that for a rigid body the time - variation of
its gravitational field approaches zero, manifest of gravitostatics. In contrast, due to
mass transport and the spacetime variation of the mass density the "real" gravitational field of a deformable body varies in spacetime, manifest of gravitodynamics. Up
to the present the spacetime variation of an intrinsic or eigen-gravitational field has
only been analyzed under certain constitutional symmetries of tht! deformable body,
namely spherical symmetry and cylindric (" spheroidal") symmetry.
Our first aim here is accordingly to present the spacetime field equations of gravitation, both in the Eulerian and the Lagrangean portrait of a deformable, massive
body without any symmetry assumption. We review gravitodynamics by representing
the spatial (" Eulerian") increments versus the material (" Lagrangean") increments
of the vector-valued force field, the scalar-valued gravitational potential field as well
as the scalar-valued mass-density field, the linearized, incremental gravitational field
equations and the 'jump conditions' at interfaces. In particular the material ("Lagrangean") field equations and 'jump conditions' prove to be complicated on their
174