Astrophysics and Space Science

, Volume 133, Issue 2, pp 339–353 | Cite as

Prediction of satellite motions in the Earth's gravitational field with axial symmetry by the KS regularized theory

  • Mohamed Adel Sharaf
  • Mervat El-Sayed Awad
  • Mona A. Banaja
Article

Abstract

In this paper, economical and stable recurrence formulae for the Earth's zonal potential and its gradient for the KS regularized theory will be established for any numberN of the zonal harmonic coefficient. A general recursive computational algorithm based on these formulae is also established for the initial value problem of the KS theory for the prediction of artificial satellites in the Earth's gravitational field with axial symmetry. Applications of the algorithm for the problem of the final state prediction are illustrated by numerical examples of three test orbits each for two geopotential models corresponding toN=2 andN=36. A final state of any desired accuracy is obtained for each case study, a result which shows the flexibility of the algorithm.

Keywords

Axial Symmetry Gravitational Field Computational Algorithm Zonal Potential State Prediction 

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References

  1. Engles, R. C. and Junkins, J. L.: 1981,Celes. Mech. 24, 3.Google Scholar
  2. Lerch, F.et al.: 1979, Proceeding of the 1978 Spring Annual Meeting of the American Geophysical Union, Miami, Floria.Google Scholar
  3. Stiefel, E. L. and Scheifele, G.: 1971,Linear and Regular Celestial Mechanics, Springer-Verlag, New York.Google Scholar

Copyright information

© D. Reidel Publishing Company 1987

Authors and Affiliations

  • Mohamed Adel Sharaf
    • 1
  • Mervat El-Sayed Awad
    • 1
  • Mona A. Banaja
    • 2
  1. 1.Dept. of AstronomyCairo UniversityEgypt
  2. 2.Dept. of MathematicsGirls College of EducationJeddahSaudi Arabia

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