Determination of the coefficients of the Earth's gravitational
potential expansion in solid spherical functions.
M. S. Petrovskaya
Institute of Theoretical Astronomy
Kutuzov Quay 10, St. Petersburg, Russia
New compact relations are derived for the determination of the
Earth's external gravitational potential, basing on the terrain
surface gravity data (the gradient of the potential), with due
regard for the Earth's figure nonsphericity. A closed analytical
formula is provided which, as compared with the earlier known ones,
does not involve strongly singular integrals in the correction
terms to the spherical approximation. Two compact relations are
obtained, as well, for evaluating the harmonic coefficients (Stokes
constants) of the geopotential. One of them is an explicit
analytical expression for a harmonic coefficient as a function of
the coefficients of the gravity expansion at the Earth's surface.
The other formula represents a linear combination between the whole
set of Stokes constants and the coefficents of the gravity
expansion. This relation allows to evaluate the Earth's dynamical
constants from simultaneous treatment of satellite perturbations
and surface gravity data.