Local Orbital Derivatives of the Earth Potential Expressed in Terms of the Satellite Cartesian Coordinates and Velocity

Open access

Local Orbital Derivatives of the Earth Potential Expressed in Terms of the Satellite Cartesian Coordinates and Velocity

In a satellite gradiometry mission the observables will be the second order derivatives of the Earth potential in the local orbital reference frame. The conventional expansions for these derivatives contain singular factors. They depend on the functions of the orbit inclination I and their first and second order derivatives. If the orbit eccentricity is taken into account then the functions of the eccentricity also involve these expressions. In the present paper more simple alternative expansions for the orbital derivatives are constructed, depending on the spherical coordinates and cos I. They have only two sums and do not have singular factors. These expansions depend on the Legendre functions of the latitude but do not depend on their derivatives. As compared to the earlier expressions of the authors the present ones have the form which is more convenient for computations. Besides, these expressions can be applied not only for the case when the satellite orbit is circular and π / 2 ≤ I ≤ π but for the arbitrary eccentricity (0 ≤ e < 1) and inclination (0 ≤ I ≤ π). After additional transformations the final expansions for the orbital derivatives represent, for the first time, simple functions of the cartesian coordinates of the satellite and the components of its velocity. These expressions may be convenient for inverting a huge amount of the GOCE data in the geopotential coefficients.

Ditmar P., Klees R. (2002) A method to compute the Earth's gravity field from SGG/SST data to be acquired by the GOCE satellite. Delft University Press, Delft, Netherlands.

Ditmar P., Klees R., Kostenko F. (2003) Fast and accurate computation of spherical harmonic coefficients from satellite gradiometry data. Journal of Geodesy, Vol. 76, No. 11-12, pp. 690-705.

ESA (2003) ESA's gravity mission GOCE. BR-209, ESA Publication Division, Netherlands.

Holmes S. A., Featherstone W. E. (2002) A unified approach to the Clenshaw summation and the recursive computation of very high degree and order normalized associated Legendre functions. Journal of Geodesy, Vol. 76, No. 8, pp. 279-299.

Heiskanen W. A., Moritz H. (1967) Physical Geodesy. Freeman and Company, San Francisco.

Ilk K. H. (1983) Ein Beitrag zur Dynamik ausgedehnter Körper - Gravitationswechselwirkung. Deutsche Geodätische Kommission, Reihe C, Heft No. 288, München.

Kaula W. M. (1966) Theory of Satellite Geodesy. Blaisdell Publishing Company, Waltham, Massachusetts.

Klees R., Koop R., Visser P., van den IJssel J. (2000a) Efficient gravity field recovery from GOCE gravity gradient observations. Journal of Geodesy, Vol. 74, pp. 561-571.

Klees R., Koop R., Visser P., van den IJssel J. (2000b) Data analysis for the GOCE mission. International Association of Geodesy Symposia, Vol. 121, (Ed. Schwarz) Geodesy Beyond 2000 - The Challenges of the First Decade, pp. 69-74.

Koop R. (1993) Global gravity field modelling using satellite gravity gradiometry. Publ. Geodesy, New series, No. 38, Netherlands Geodetic Commission, Delft.

Pail R., Plank G. (2002) Assessment of three numerical solution strategies for gravity field recovery from GOCE satellite gravity gradiometry implemented on a parallel platform. Journal of Geodesy, Vol. 76, No. 8, pp. 462-474.

Petrovskaya M. S., Vershkov A. N. (2006) Non-singular expressions of the gravity gradients in the local north-oriented and orbital reference frames. Journal of Geodesy, Vol. 80, No. 3, pp. 117-127.

Reed G. B. (1973) Application of kinematical geodesy for determining the short wave length components of the gravity field by satellite gradiometry. Ohio State University, Dept. of Geod. Sciences, Rep. No. 201, Columbus, Ohio.

Rummel R., Sansò F., van Gelderen M., Koop R., Schrama E., Brovelli M., Migliaccio F., Sacerdote F. (1993) Spherical harmonic analysis of satellite gradiometry. Publ. Geodesy, New Series, No. 39, Netherlands Geodetic Commission, Delft.

Smart W. M. (1953) Celestial Mechanics. Longmans, Green and Co, London - New York - Toronto.

Sneeuw N. (1991) Inclination functions. Group Theoretical Background and a Recursive Algorithm, Department of Mathematical and Physical Geodesy, Rep. 91.2, Delft University of Technology.

Sneeuw N. (1992) Representation coefficients and their use in satellite geodesy. Manuscripta Geodaetica, Vol.17, pp. 117-123.

Sneeuw N. (2000) A semi-analytical approach to gravity field analysis from satellite observations. Reihe C, Heft Nr. 527, Deutsche Geodätische Kommission, München.

Sneeuw N., Dorobantu R., Gerlach C., Müller J., Oberndorfer H., Rummel R., Koop R., Visser P., Hoyng P., Selig A., Smit M. (2001) Simulation of the GOCE gravity field mission. In: Benciolini B. (ed.) IV Hotine-Marussi Symposium on Mathematical Geodesy. IAG Symposia Vol. 122, Springer, Berlin - Heidelberg - New York, pp. 14-20.

Vermeer M. (1990) Observable quantities in satellite gradiometry. Bull. Gód., Vol. 64, pp. 347-361.

Artificial Satellites

The Journal of Space Research Centre of Polish Academy of Sciences

Journal Information


CiteScore 2016: 0.33

SCImago Journal Rank (SJR) 2016: 0.179
Source Normalized Impact per Paper (SNIP) 2016: 0.560

Metrics

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 48 48 16
PDF Downloads 7 7 2