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).
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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
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)
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
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
Ahmed, M.K.: On the normalization of perturbed Keplerian systems. Astron. J. 107(5), 1900 (1994)
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)
Atchison, J.A., Peck, M.A.: Lorentz-augmented jovian orbit insertion. J. Guid. Control Dyn. 32(2), 418–423 (2009)
Bell, W.W.: Special Functions for Scientists and Engineers. Van Nostrand, London (1968)
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)
Bhardwaj, R., Sethi, M.: Resonance in satellite’s motion under air drag. Am. J. Appl. Sci. 3(12), 2184–2189 (2006)
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)
Delhaise, F.: Analytical treatment of air dragand Earth oblateness effects upon an artificial satellite. Celest. Mech. Dyn. Astron. 52, 85–103 (1991)
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
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
Khalil, K.H.I.: The drag exerted by an oblate rotating atmosphere on an artificial satellite. Appl. Math. Mech. 23, 1016 (2002)
Laplace, P.S.: Traitede Mecanique Celeste, Tom IV, Par 2. Courcier, Paris (1805)
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
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)
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
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)
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)
Peck, M.A., Streetman, B., Saaj, C.M., Lappas, V.: Spacecraft formation flying using Lorentz forces. J. Br. Interplanet. Soc. 60, 263–267 (2007)
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)
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)
Reid, T., Misra, A.K.: Formation filght of satellites in the presence of atmospheric drag. J. Aero. Eng. Sci. Appl. III, 64 (2011)
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)
Streetman, B., Peck, M.A.: New synchronous orbits using the geomagnetic Lorentz force. J. Guid. Control Dyn. 30(6), 1677–1690 (2007b)
Streetman, B., Peck, M.A.: Gravity-assist maneuvers augmented by the Lorentz force. J. Guid. Control Dyn. 32(5), 1639–1647 (2009)
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)
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Abd El-Bar, S.E., Abd El-Salam, F.A. Modelling of charged satellite motion in Earth’s gravitational and magnetic fields. Astrophys Space Sci 363, 89 (2018). https://doi.org/10.1007/s10509-018-3310-5
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DOI: https://doi.org/10.1007/s10509-018-3310-5