Effectiveness of KS elements in satellite orbit prediction using earth's gravity, drag and solar radiation pressure


  • T. R. Saritha Kumari Vikram Sarabhai Space Centre
  • M. Xavier James Raj Applied Mathematics Division, Vikram Sarabhai Space Centre, Thiruvananthapuram






Orbit Prediction, Solar Radiation Pressure, Semi-Major Axis, KS Elements.


Satellite moving under the gravitational field of Earth deviates from its two-body elliptic orbit, due to the combined effects of the gravitational field of Earth, atmospheric drag, solar radiation pressure, third-body gravitational effects, etc. This paper utilizes the KS regular element equations to solve Newtonian equations of motion to obtain numerical solution with respect to perturbing forces, like, Earth's gravity (includes zonal, sectorial and tesseral harmonics terms), atmospheric drag and solar radiation pressure. Effectiveness of the theory is illustrated by comparing the results with some of the existing theories in literature.



[1] P.Kustaanheimo and E.L.Stiefel, “Perturbation Theory of Kepler Motion Based on Spinor regularization†J Reine Angew Math 218: 204-19, 1965.

[2] E.L.Stiefel.G.Scheifele, “Linear and Regular celestial Mechanicsâ€, New York, Springer-Verlag, 1971.

[3] Graf, Jr. O.F., Mueller, A., and Starke, S., “The Method of Averages Applied to the KS Differential Equationsâ€, NASA-CR-151607, (1977).

[4] T.R.Saritha Kumari and M.Xavier James Raj, “Orbit Predictions using KS element equations with Earth's Oblateness", Journal of Aerospace Sciences and Technologies, ISSN 0972-950X, V.68, No.1, pp.1-7, Paper code: V68 N1/947-2017.

[5] Lemoine, F. G., S. C. Kenyon, J. K. Factor, R.G. Trimmer, N. K. Pavlis, D. S. Chinn, C. M. Cox, S. M. Klosko, S. B. Luthcke, M. H. Torrence, Y. M. Wang, R. G. Williamson, E. C. Pavlis, R. H. Rapp and T. R. Olson (1998).The Development of the Joint NASA GSFC and the National Imagery and Mapping Agency (NIMA) Geopotential Model EGM96. NASA/TP-1998-206861, July 1998.

[6] Chobotov, Vladimir; Przemieniecki, J S , “Orbital mechanicsâ€, Virginia AIAA 1996. AIAA 1996.AIAA, 1996.

[7] Valledo, David A, “Fundamentals of Astrodynamics and applicationsâ€, Dordrecht Kluwer Academic Publishers 2001, 2001.

[8] Escobal, Pedro Ramon., “Methods of orbit determination†, New York John Wiley 1965New York, John Wiley, 1965.

[9] NRL NRLMSISE-00 websiteNRL NRLMSISE-00 website. NRL NRLMSISE-00 website NRL NRLMSISE-00 website

[10] Hany R. Dwidar ,"Prediction of Satellite Motion under the Effects of the Earth's Gravity, Drag force and Solar Radiation Pressure in terms of the KS-regularized variables", IJACSA,Vol.5, No. 5, 2014.

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