Modelling of charged satellite motion in Earth’s gravitational and magnetic fields

  • S. E. Abd El-Bar
  • F. A. Abd El-Salam
Original Article


In this work Lagrange’s planetary equations for a charged satellite subjected to the Earth’s gravitational and magnetic force fields are solved. The Earth’s gravity, and magnetic and electric force components are obtained and expressed in terms of orbital elements. The variational equations of orbit with the considered model in Keplerian elements are derived. The solution of the problem in a fully analytical way is obtained. The temporal rate of changes of the orbital elements of the spacecraft are integrated via Lagrange’s planetary equations and integrals of the normalized Keplerian motion obtained by Ahmed (Astron. J. 107(5):1900, 1994).


Gravitational field Lorentz forces Orbital elements Charged satellites Perturbations 


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Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceTaibah UniversityAl-MadinahKingdom of Saudi Arabia
  2. 2.Department of Mathematics, Faculty of ScienceTanta UniversityTantaEgypt
  3. 3.Department of Astronomy, Faculty of ScienceCairo UniversityCairoEgypt

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