Journal of Astronomy and Space Sciences

  • 제41권2호
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  • Pages.87-106
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  • 2024
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  • 2093-5587(pISSN)
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  • 2093-1409(eISSN)
한국우주과학회 (The Korean Space Science Society)
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Perturbations of Zonal and Tesseral Harmonics on Frozen Orbits of Charged Satellites

  • Fawzy Ahmed Abd El-Salam (Department of Astronomy, Faculty of Science, Cairo University) ;
  • Walid Ali Rahoma (Department of Astronomy, Faculty of Science, Cairo University) ;
  • Magdy Ibrahim El-Saftawy (Department of Space Science and Astronomy, Faculty of Science, King Abdulaziz University) ;
  • Ahmed Mostafa (Department of Mathematics, Faculty of Science, Ain Shams University) ;
  • Elamira Hend Khattab (Department of Astronomy, Faculty of Science, Cairo University)
  • 투고 : 2023.12.23
  • 심사 : 2024.03.25
  • 발행 : 2024.06.15
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초록

The objective of this research is to address the issue of frozen orbits in charged satellites by incorporating geopotential zonal harmonics up to J6 and the initial tesseral harmonics. The employed model starts from the first normalized Hamiltonian to calculate specific sets of long-term frozen orbits for charged satellites. To explore the frozen orbits acquired, a MATHEMATICA CODE is developed. The investigation encompasses extensive variations in orbit altitudes by employing the orbital inclination and argument of periapsis as freezing parameters. The determined ranges ensuring frozen orbits are derived from the generated figures. Three-dimensional presentations illustrating the freezing inclination in relation to eccentricity, argument of periapsis, and semi-major axis parameters are presented. Additional three-dimensional representations of the phase space for the eccentricity vector and its projection onto the nonsingular plane are examined. In all investigated scenarios, the impacts of electromagnetic (EM) field perturbations on the freezing parameters of a charged satellite are demonstrated.

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과제정보

The authors would like to express their profound gratitude to the reviewers and the editorial team for their constructive criticism and highly productive discussions, which significantly contributed to the improvement of the manuscript.

참고문헌

  1. Abd El-Bar SE, Abd El-Salam FA, 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
  2. Abd El-Salam FA, Abd El-Bar SE, Families of frozen orbits of lunar artificial satellites, Appl. Math. Model. 40, 9739-9753 (2016). https://doi.org/10.1016/j.apm.2016.06.036
  3. Abd El-Salam FA, Abd El-Bar SE, Rassem M, Fully analytical solution of the electromagnetic perturbations on the motion of the charged satellites in Earth's magnetic field, Eur. Phys. J. Plus. 132, 198 (2017). https://doi.org/10.1140/epjp/i2017-11500-3
  4. Abd El-Salam FA, Alamri SZ, Abd El-Bar SE, Seadawy AR, Frozen apsidal line orbits around tiaxial Moon with coupling quadrupole nonlinearity, Results Phys. 10, 176-186 (2018). https://doi.org/10.1016/j.rinp.2018.05.029
  5. Abdel-Aziz YA, Khalil KI, Electromagnetic effects on the orbital motion of a charged spacecraft, Res. Astron. Astrophys. 14, 589-600 (2014). https://doi.org/10.1088/1674-4527/14/5/008
  6. Abdel-Aziz YA, Lorentz force effects on the orbit of a charged artificial satellite: a new approach, AIP Conf. Proc. 888, 385-391 (2007). https://doi.org/10.1063/1.2711134
  7. Ahmed MKM, On the normalization of the perturbed Keplerian systems, Astron. J. 107, 1900-1903 (1994). https://doi.org/10.1086/117001
  8. Atchison JA, Peck MA, Lorentz-augmented Jovian orbit insertion, J. Guid. Control Dyn. 32, 418-423 (2009). https://doi.org/10.2514/1.38406
  9. Carvalho JPS, Vilhena de Moraes R, Prado AFBA, Some orbital characteristics of lunar artificial satellites, Celest. Mech. Dyn. Astron. 108, 371-388 (2010). https://doi.org/10.1007/s10569-010-9310-6
  10. Circi C, D'Ambrosio A, Lei H, Ortore E, Global mapping of asteroids by frozen orbits: the case of 216 kleopatra, Acta Astronaut. 161, 101-107 (2019). https://doi.org/10.1016/j.actaastro.2019.05.026
  11. Delhaise F, Morbidelli A, Luni-solar effects of geosynchronous orbits at the critical inclination, Celest. Mech. Dyn. Astron. 57, 155-173 (1993). https://doi.org/10.1007/BF00692471
  12. Delsate N, Robutel P, Lemaitre A, Carletti T, Frozen orbits at high eccentricity and inclination: application to Mercury orbiter, Celest. Mech. Dyn. Astron. 108, 275-300 (2010). https://doi.org/10.1007/s10569-010-9306-2
  13. Haberman R, Rand R, Yuster T, Resonant capture and separatrix crossing in dual-spin spacecraft, Nonlinear Dyn. 18, 159-184 (1999). https://doi.org/10.1023/A:1008393913849
  14. Kamel AA, Perturbation method in the theory of nonlinear oscillations, Celest. Mech. 3, 90-106 (1970). https://doi.org/10.1007/BF01230435
  15. Khattab EH, Radwan M, Rahoma WA, Frozen orbits construction for a lunar solar sail, J. Astron. Space Sci. 37, 1-9 (2020). https://doi.org/10.5140/JASS.2020.37.1.1
  16. Lanchares V, Pascual AI, San Juan JF, Frozen orbits around a prolate body, Monogr. Real Acad. Ci. Zaragoza. 35, 73-81 (2011).
  17. Lara M, Palacian JF, Russell RP, Mission design through averaging of perturbed Keplerian systems: the paradigm of an Enceladus orbiter, Celest. Mech. Dyn. Astron. 108, 1-22 (2010a). https://doi.org/10.1007/s10569-010-9286-2
  18. Lara M, Palacian JF, Yanguas P, Corral C, Analytical theory for spacecraft motion about mercury, Acta Astronaut. 66, 1022-1038 (2010b). https://doi.org/10.1016/j.actaastro.2009.10.011
  19. Li LS, 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, 1-8 (2016). https://doi.org/10.1007/s10509-015-2583-1
  20. Li X, Qiao D, Li P, Frozen orbit design and maintenance with an application to small body exploration, Aerosp. Sci. Technol. 92, 170-180 (2019). https://doi.org/10.1016/j.ast.2019.05.062
  21. Liu X, Baoyin H, Ma X, Analytical investigations of quasi-circular frozen orbits in the Martian gravity field, Celest. Mech. Dyn. Astron. 109, 303-320 (2011). https://doi.org/10.1007/s10569-010-9330-2
  22. Liu X, Baoyin H, Ma X, Five special types of orbits around Mars, J. Guid. Control Dyn. 33, 1294-1301 (2010). https://doi.org/10.2514/1.48706
  23. Masoud A, Rahoma WA, Khattab EH, El-Salam FA, Construction of frozen orbits using continuous thrust control theories considering Earth oblateness and solar radiation pressure perturbations, J. Astronaut. Sci. 65, 448-469 (2018). https://doi.org/10.1007/s40295-018-0135-y
  24. Nie T, Gurfil P, Lunar frozen orbits revisited, Celest. Mech. Dyn. Astron. 130, 61 (2018). https://doi.org/10.1007/s10569-018-9858-0
  25. Oliveira AC, Domingos RC, Silva LM, Prado AFBA, Sanchez DM, Perturbation of the Sun on frozen orbits around mars, J. Phys. Conf. Ser. 1365, 1-8 (2019). https://doi.org/10.1088/1742-6596/1365/1/012028
  26. Parke ME, Stewart RH, Farless DL, Cartwright DE, On the choice of orbits for an altimetric satellite to study ocean circulation and tides, J. Geophys. Res. 92, 11693-11707 (1987). https://doi.org/10.1029/JC092iC11p11693
  27. Peck MA, Prospects and challenges for Lorentz-augmented orbits, in AIAA Guidance, Navigation, and Control Conference (AIAA 5995), San Francisco, CA, 15-18 Aug 2005.
  28. Quinn D, Rand R, Bridge J, The dynamics of resonant capture, Nonlinear Dynamics 8, 1-20 (1995). https://doi.org/10.1007/BF00045004
  29. Rahoma WA, Abd El-Salam FA, The effects of Moon's uneven mass distribution on the critical inclinations of a lunar orbiter, J. Astron. Space Sci. 31, 285-294 (2014). https://doi.org/10.5140/JASS.2014.31.4.285
  30. Rahoma WA, Investigating exoplanet orbital evolution around binary star systems with mass loss, J. Astron. Space Sci. 33, 257-264 (2016). https://doi.org/10.5140/JASS.2016.33.4.257
  31. Rahoma WA, Khattab EH, Abd El-Salam FA, Relativistic and the first sectorial harmonics corrections in the critical inclination, Astrophys. Space Sci. 351, 113-117 (2014). https://doi.org/10.1007/s10509-014-1811-4
  32. Rahoma WA, Orbital elements evolution due to a perturbing body in an inclined elliptical orbit, J. Astron. Space Sci. 31, 199-204 (2014). https://doi.org/10.5140/JASS.2014.31.3.199
  33. Sehnal L, The Motion of a Charged Satellite in the Earth's Magnetic Field, SAO Special Report, No. #271, 1969.
  34. Singh SK, Robyn W, Taheri E, Junkins J, Feasibility of quasi-frozen, near-polar and extremely low-altitude lunar orbits, Acta Astronaut. 166, 450-468 (2020). https://doi.org/10.1016/j.actaastro.2019.10.037
  35. Streetman B, Peck M, Gravity-assist maneuvers augmented by the Lorentz force, J. Guid. Control Dyn. 32, 1639-1647 (2009). https://doi.org/10.2514/6.2007-6846
  36. Streetman B, Peck MA, Gravity-assist maneuvers augmented by the Lorentz force, in AIAA Guidance, Navigation, and Control Conference, Hilton Head, SC, 20 Aug 2007a.
  37. Streetman B, Peck MA, New synchronous orbits using the geomagnetic Lorentz force, J. Guid. Control Dyn. 30, 1677-1690 (2007b). https://doi.org/10.2514/1.29080
  38. Tealib SK, Abdel-Aziz Y, Awad ME, Khalil KI, Radwan M, Semi-analytical solution for formation flying spacecraft subject to electromagnetic acceleration, Univ. J. Mech. Eng. 8, 41-50 (2020). https://doi.org/10.13189/ujme.2020.080106
  39. Tzirti S, Tsiganis K, Varvoglis H, Effect of 3rd-degree gravity harmonics and Earth perturbations on lunar artificial satellite orbits, Celest. Mech. Dyn. Astron. 108, 389-404 (2010). https://doi.org/10.1007/s10569-010-9313-3
  40. Tzirti S, Tsiganis K, Varvoglis H, Quasi-critical orbits for artificial lunar satellites, Celest. Mech. Dyn. Astron. 104, 227-239 (2009). https://doi.org/10.1007/s10569-009-9207-4
  41. Zotos EE, Classifying orbits in the restricted three-body problem, Nonlinear Dyn. 8, 1233-1250 (2015). https://doi.org/10.1007/s11071-015-2229-4