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.