Non-singular expression for the gradient of the Earth gravitational potential in the local north-oriented ellipsoidal reference frame |
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| Authors: | Margarita S Petrovskaya Andrey N Vershkov |
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| Institution: | 1. Central (Pulkovo) Astronomical Observatory of the Russian Academy of Sciences, Pulkovskoe Shosse 65/1, 196140, St. Petersburg, Russia
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| Abstract: | In this contribution we continue our earlier research, concerning the ellipsoidal harmonic expansions of the Earth disturbing gravitational potential and its derivatives on an external reference ellipsoid confocal with respect to the normal ellipsoid and close to it. One of the results of the previous investigation is represented by a new expression for the derivative of the Jekeli’s Legendre function of the second kind, entering the ellipsoidal harmonics in the potential derivative. The derived expression depends on two Gauss hypergeometric functions which converge better than the hypergeometric functions of other authors. In the present paper we construct another expression for the derivative of the Jekeli’s Legendre function, depending on two alternative hypergeometric functions. While our earlier hypergeometric series in the expression for the derivative of this function converge better when the orders of the terms do not exceed a half of their degrees, the series constructed in the present paper converge more rapidly when the orders surpass a half of the degrees. We deduce an improved expression for the derivative of the Jekeli’s Legendre function by combining these results and then construct a corresponding new expression for the derivative of the disturbing potential. This expression is applied for constructing non-singular expressions for the components of the gradient of the potential in the local north-oriented ellipsoidal reference frame. The new expressions for these components have no these deficiencies and the expression for the potential gradient depends on very quickly convergent hypergeometric series. |
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