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

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

Abstract

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).

Keywords

Gravitational field Lorentz forces Orbital elements Charged satellites Perturbations 

References

  1. Abd El-Salam, F.A., Abd El-Bar, S.E., Rassem, M.: Fully analytical solution of the electromagnetic perturbations on the motion of the charged satellites in Earh’s magnetic field. Eur. Phys. J. Plus 132, 198 (2017).  https://doi.org/10.1140/epjp/i2017-11500-3 CrossRefGoogle Scholar
  2. Abdel-Aziz, Y.A.: Lorentz Force Effects on the Orbit of a Charged Artificial Satellite: A New Approach, Vol. 1. Applied Mathematical Sciences, vol. 31, pp. 1511–1518. Hikari, Rousse (2007) zbMATHGoogle Scholar
  3. Abdel-Aziz, Y.A., Khalil, K.I.: Electromagnetic effects on the orbital motion of a charged spacecraft. Res. Astron. Astrophys. 14(5), 589–600 (2014).  https://doi.org/10.1088/1674-4527/14/5/008 ADSCrossRefGoogle Scholar
  4. Aghav, S.T., Gangal, S.A.: Simplified orbit determination algorithm for low Earth orbit satellite using spaceborne GPS navigation sensor. Artif. Satell. 49(2), 81–99 (2014).  https://doi.org/10.2478/arsa-2014-0007 ADSGoogle Scholar
  5. Ahmed, M.K.: On the normalization of perturbed Keplerian systems. Astron. J. 107(5), 1900 (1994) ADSCrossRefGoogle Scholar
  6. Al-Bermani, M.J.F., Ali, A.A.H., Al-Hashmi, A.M., Baron, A.S.: Effects of atmospheric drag and zonal harmonic on Cosmos1484 satellite orbit. J. Kufa Phys. 4(2), 1 (2012) ADSGoogle Scholar
  7. Atchison, J.A., Peck, M.A.: Lorentz-augmented jovian orbit insertion. J. Guid. Control Dyn. 32(2), 418–423 (2009) ADSCrossRefGoogle Scholar
  8. Bell, W.W.: Special Functions for Scientists and Engineers. Van Nostrand, London (1968) zbMATHGoogle Scholar
  9. Bezděk, A., Vokrouhlický, D.: Semianalytic theory of motion for close-Earth spherical satellites including drag and gravitational perturbations. Planet. Space Sci. 52, 1233–1249 (2004) ADSCrossRefGoogle Scholar
  10. Bhardwaj, R., Sethi, M.: Resonance in satellite’s motion under air drag. Am. J. Appl. Sci. 3(12), 2184–2189 (2006) CrossRefGoogle Scholar
  11. Chen, W.Y., Jing, W.X.: Differential equations of relative motion under the influence of J2 perturbation and air drag. In: AIAA Space 2010 Conference & Exposition, Anaheim, CA, USA (2010) Google Scholar
  12. Delhaise, F.: Analytical treatment of air dragand Earth oblateness effects upon an artificial satellite. Celest. Mech. Dyn. Astron. 52, 85–103 (1991) ADSCrossRefzbMATHGoogle Scholar
  13. Gangestad, J.W., Pollock, G.E., Longuski, J.M.: Lagrange’s planetary equations for the motion of electrostatically charged spacecraft. Celest. Mech. Dyn. Astron. (2010).  https://doi.org/10.1007/s10569-010-9297-z MathSciNetzbMATHGoogle Scholar
  14. Hassan, I.A., Hayman, Z.M., Basha, M.A.F.: Pre-solution of the perturbed motion of artificial satellite. In: Proc. First Middle East Africa IAU-Regional Meet, vol. 1, p. 1 (2008).  https://doi.org/10.10107/977403330200167 Google Scholar
  15. Khalil, K.H.I.: The drag exerted by an oblate rotating atmosphere on an artificial satellite. Appl. Math. Mech. 23, 1016 (2002) MathSciNetCrossRefzbMATHGoogle Scholar
  16. Laplace, P.S.: Traitede Mecanique Celeste, Tom IV, Par 2. Courcier, Paris (1805) Google Scholar
  17. Lee, D., Springmann, J.C., Spangelo, S.C., Cutler, J.W.: Satellite dynamics simulator development using Lie group variational integrator. In: Proc. AIAA Modeling and Simulation Technologies Conference, Portland, Oregon, 08–11 August, 2011 Google Scholar
  18. Li, L.-S.: Perturbation effect of the Coulomb drag on the orbital elements of the Earth satellite in the ionosphere. Acta Astronaut. 68, 717–721 (2011) ADSCrossRefGoogle Scholar
  19. Li, L.-S.: Influence of the electric induction drag on the orbit of a charged satellite moving in the ionosphere (solution by the method of the average value). Astrophys. Space Sci. 361, 1 (2016).  https://doi.org/10.1007/s10509-015-2583-1 ADSMathSciNetCrossRefGoogle Scholar
  20. Newton, I.: Philosophiae Naturalis Principia Mathematica, Book II, Section IV, London (1687). English translation by F. Cajori, Newton’s Principia, University of California Press, Berkeley (1934) Google Scholar
  21. Peck, M.A.: Prospects and challenges for Lorentz-augmented orbits. In: AIAA Guidance, Navigation, and Control Conference, San Francisco, CA, AIAA Paper 2005-5995 (2005) Google Scholar
  22. Peck, M.A., Streetman, B., Saaj, C.M., Lappas, V.: Spacecraft formation flying using Lorentz forces. J. Br. Interplanet. Soc. 60, 263–267 (2007) ADSGoogle Scholar
  23. Pollock, G.E., Gangestad, J.W., Longuski, J.M.: Analysis of Lorentz spacecraft motion about Earth using the Hill-Clohessy-Wiltshire equations. In: AIAA/AAS Astrodynamics Specialist Conference and Exhibit, Honolulu, HI, AIAA Paper 2008-6762 (2008) Google Scholar
  24. Pollock, G.E., Gangestad, J.W., Longuski, J.M.: Analytical solutions for the relative motion of spacecraft subject to Lorentz-force perturbations. Acta Astronaut. 68, 204 (2011) ADSCrossRefGoogle Scholar
  25. Reid, T., Misra, A.K.: Formation filght of satellites in the presence of atmospheric drag. J. Aero. Eng. Sci. Appl. III, 64 (2011) Google Scholar
  26. Streetman, B., Peck, M.A.: Gravity-assist maneuvers augmented by the Lorentz force. In: AIAA Guidance, Navigation, and Control Conference, Hilton Head, SC, AIAA Paper 2007-6846 (2007a) Google Scholar
  27. Streetman, B., Peck, M.A.: New synchronous orbits using the geomagnetic Lorentz force. J. Guid. Control Dyn. 30(6), 1677–1690 (2007b) ADSCrossRefGoogle Scholar
  28. Streetman, B., Peck, M.A.: Gravity-assist maneuvers augmented by the Lorentz force. J. Guid. Control Dyn. 32(5), 1639–1647 (2009) ADSCrossRefGoogle Scholar
  29. Xu, G., Tianhe, X., Chen, W., Yeh, T.: Analytical solution of a satellite orbit disturbed by atmospheric drag. Mon. Not. R. Astron. Soc. 410, 654 (2011) ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

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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