The Use of Ellipsoidal Harmonics for the Representation of the Geopotential
The potential of the Earth is developed in ellipsoidal harmonics, and the mathematical tools required, which are the generation of Lame’s functions and the relationship between rectangular and ellipsoidal coordinates, are compiled. Brief reference is made to a procedure utilized for the determination of the gravity coefficients in the expansion ot the geopotential in ellipsoidal harmonics when precise satellite tracking data is available.
With the aim of carrying out a numerical integration of the Lagrangian equations of planetary motion, the functional dependence of the disturbing earth potential on the orbital elements for elliptic motion is given. In particular, formulae for the partial derivatives of the disturbing potential with respect to the orbital elements are derived, thus making possible the numerical calculation of these partial derivatives from orbital elements.
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