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A Numerical Approach to GPS Satellite Perturbed Orbit Computation

Published online by Cambridge University Press:  09 August 2007

Stelian Cojocaru
Stelian Cojocaru
Affiliation:
(NATO Maritime Component Command, Naples) (Email: cojocarus@yahoo.com)
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Abstract

This paper proposes a numerical algorithm designed to integrate the GPS satellite perturbed orbit. The numerical solution is applied to integrate the differential equation of perturbed motion that frames the significant perturbing accelerations. Perturbing potentials are given and the corresponding accelerations in Cartesian coordinates are subsequently deduced. The C++ program that implements a fourth-order Runge-Kutta algorithm is described and comment is made on the perturbed orbit integration results. The paper offers a set of conclusions that will hopefully create a quantitative and qualitative image of GPS orbital perturbations and open a few ways ahead.

Keywords

GPS satelliteOsculating elementsNumerical integration
Type
Research Article
Information
The Journal of Navigation , Volume 60 , Issue 3 , September 2007 , pp. 483 - 495
Copyright
Copyright © The Royal Institute of Navigation 2007

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References

REFERENCES

Broucke, R. A. (1994). Numerical integration of periodic orbits in the main problem of artificial satellites. Celestial Mech. and Dyn. Astron., 58, 99–123.CrossRefGoogle Scholar
Brouwer, D., Clemence, G. M. (1961). Methods of Celestial Mechanics. Academic Press, New York and London.Google Scholar
Cojocaru, S. (1996). Period Changes Of Satellite Circular Motion Due To Odd Zonal Harmonics of Geopotential, Romanian Astronomical Journal, 6, 2, 179–183.Google Scholar
Cojocaru, S. (1999). GPS Satellite Dynamics, Romanian Naval Academy Press (Ed. Academiei, Navale), ISBN 973-979-13-8-7.Google Scholar
Cojocaru, S. (2001). Influence Of The Even Zonal Harmonics Of The Geopotential On GPS Satellite Orbits, Romanian Astronomical Journal, 11, 1, 69–76.Google Scholar
Ferraz-Mello, S. (1964). Sur le problème de la pression de radiation dans la thèorie de satellites artificial. C.R. Acad. Sc., Paris, 285, p.463.Google Scholar
Ferraz-Mello, S. (1973). Analytical Study of the Earth's Shadowing Effects on Satellite Orbits. Celest. Mechanics, 5.Google Scholar
Gaposchkin, G. M. (1973). Smithsonian Standard Earth III. Smithsonian Astrophysical Observatory Special report 353, Cambridge, Mass.Google Scholar
Giacaglia, G. E. O. (1973). Lunar Perturbation on Artificial Satellites of the Earth, SAO Special Report 352.CrossRefGoogle Scholar
Heiskanen, and Moritz, (1967). Physical Geodesy', Technical University of Graz.CrossRefGoogle Scholar
Hofmann-Wellenhof, B., Lichtenegger, H., Collins, J. (1993). GPS – Theory and Practice. Second edition, Springer-Verlag, New York.Google Scholar
Kaula, W. M. (1966). Theory of satellite geodesy. Blaisdell Publ.Co., Waltham.Google Scholar
Kovalevsky, J., Mueller, I. I., Kolaczeck, B. (1989). Reference frames in Astronomy and Geophysics. Kluwer Academic Publ., Dordrecht.CrossRefGoogle Scholar
Kozai, Y. (1961). Effects of Solar Radiation Pressure on the motion of an artificial Satellite, SAO Special Report 56.Google Scholar
Kozai, Y. (1962). Numerical Results from Orbits. Smithsonian Astrophysical Observatory, Special Report 101.Google Scholar
Leick, A. (1995). GPS Satellite Surveying', 2nd Edition, John Wiley & Sons.Google Scholar
Seeber, G. (1993). Satellite Geodesy. W. de Gruyter.Google Scholar
Zhang, J., Zhang, K, Grenfell, R, Deakin, R. (2006). GPS Satellite Velocity and Acceleration Determination using the Broadcast Ephemeris. The Journal of Navigation, 59, 293–305.CrossRefGoogle Scholar