Non-Singular Expressions for the Gravity Gradients in the Local North-Oriented and Orbital Reference Frames |
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| Authors: | M S Petrovskaya A 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: | The conventional expansions of the gravity gradients in the local north-oriented reference frame have a complicated form, depending on the first- and second-order derivatives of the associated Legendre functions of the colatitude and containing factors which tend to infinity when approaching the poles. In the present paper, the general term of each of these series is transformed to a product of a geopotential coefficient  and a sum of several adjacent Legendre functions of the colatitude multiplied by a function of the longitude. These transformations are performed on the basis of relations between the Legendre functions and their derivatives published by Ilk (1983). The second-order geopotential derivatives corresponding to the local orbital reference frame are presented as linear functions of the north-oriented gravity gradients. The new expansions for the latter are substituted into these functions. As a result, the orbital derivatives are also presented as series depending on the geopotential coefficients  multiplied by sums of the Legendre functions whose coefficients depend on the longitude and the satellite track azimuth at an observation point. The derived expansions of the observables can be applied for constructing a geopotential model from the GOCE mission data by the time-wise and space-wise approaches. The numerical experiments demonstrate the correctness of the analytical formulas.An erratum to this article can be found at |
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| Keywords: | Geopotential models Gravity gradient expansions Associated Legendre functions GOCE satellite gradiometry mission |
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