The Journal of the Astronautical Sciences

, Volume 65, Issue 4, pp 448–469 | Cite as

Construction of Frozen Orbits Using Continuous Thrust Control Theories Considering Earth Oblateness and Solar Radiation Pressure Perturbations

  • Akram Masoud
  • W. A. RahomaEmail author
  • E. H. Khattab
  • F. A. El-Salam


The problem of the artificial frozen orbits around the Earth is investigated. To design such orbits with arbitrary orbital parameters, six control strategies are discussed taking into account the main zonal harmonics up to J4 and solar radiation pressure (SRP). The effect in the argument of periapsis due to the main zonal harmonics is revealed to be about three orders of magnitude greater than that of SRP. Two comparisons are given. To obtain longer lifespan of the spacecraft, continuous variable low-thrust control is implemented. Radial and/or transverse thrusts are used to achieve these orbits. Furthermore, explicit formulas for refinement of the control thrusts are given in order to overcome errors due to approximations arising from long and short periodic variations of a and e. Some concluding remarks can be inferred from the presented simulation; e.g. the energy consumed is saved efficiently when using the root mean squares rather than using averages, also when using coupled radial and transverse thrusts instead of using single radial or transverse thrust. To minimize the fuel consumption more efficiently, three new techniques are suggested. The calculations illustrated that AFOT-F Technique, where the transverse control thrust is constant, has the minimum control thrust required.


Frozen orbit Solar radiation pressure Control design Low-thrust-perturbations 


  1. 1.
    Wang, G.B., Meng, Y.H., Zheng, W., et al.: Artificial frozen orbit control scheme based on J2 perturbation. Sci. China Technol. Sci. 53, 3138–3144 (2010). CrossRefzbMATHGoogle Scholar
  2. 2.
    Pardal, P.C., Kuga, H.K., de Moraes, R.V.: Study of orbital elements on the neighbourhood of a frozen orbit. J. Aerosp. Eng. Sci. Appl. 1(2), 23–32 (2008)Google Scholar
  3. 3.
    Perry, M.E., Alea, P., Cully, M.J., McCullough, M., Sanneman, P., Teti, N., Zink, B.: Earth observing-1 spacecraft bus. In: 15th Annual/USU Conference on Small Satellites, SSC01-V-6 (2001)Google Scholar
  4. 4.
    Wu, Z., Jiang, F., Li, J.: Artificial Martian frozen orbits and Sun-Synchronous orbits using continuous low-thrust control. Astrophys. Space Sci. 352(2), 503–514 (2014). CrossRefGoogle Scholar
  5. 5.
    Weeden, B., Shortt, K.: Development of an architecture of sun-synchronous orbital slots to minimize conjunctions. In: SpaceOps 2008 Conference, AIAA, pp. 2008–3547 (2008),
  6. 6.
    Macdonald, M., McKay, R., Vasile, M., Frescheville, F.B.: Extension of the sun-synchronous orbit. J. Guid. Control Dynam. 33(6), 1935–1940 (2010). CrossRefGoogle Scholar
  7. 7.
    Folcik, Z.J.: Orbit determination using modern filters/smoothers and continuous thrust modeling. M.S. Thesis. Department of Aeronautics and Astronautics. MIT (2008)Google Scholar
  8. 8.
    Yan, Q., Kapila, V.: Analysis and control of satellite orbits around oblate earth using perturbation method. In: Proceedings of the 40th IEEE Conference on Decision and Control, pp. 1517–1522. IEEE (2001)Google Scholar
  9. 9.
    Wang, G., Meng, Y., Tang, W.Z.: Artificial Sun synchronous frozen orbit control scheme design based on J2 perturbation. Acta Mech. Sin. 27(5), 809–816 (2011). MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Zhou, J.B., Yuan, J.P., Luo, J.J.: Study of control strategy for frozen orbits with arbitrary orbital element by using radial low-thrust. J. Astronaut. 29(5), 1536–1539 (2008). (In Chinese)Google Scholar
  11. 11.
    Wu, Z,. Jiang, F., Li, J.: Extension of frozen orbits and Sun-synchronous orbits around terrestrial planets using continuous low-thrust propulsion. Astrophys. Space Sci. 360, 12 (2015). CrossRefGoogle Scholar
  12. 12.
    Brouwer, D.: Solution of the problem of artificial satellite theory without drag. Astron. J. 64(1274), 378–396 (1959)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Yang, W.L.: A first-order solution for frozen orbit. Chin. Space Sci. Technol. 20, 45–50 (2002)Google Scholar
  14. 14.
    Wilkins, C., Kapila, V.: Eliminating Perigee rotation in J2 perturbed orbits with a constant radial acceleration. In: AIAA Guidance, Navigation, and Control Conference, Hilton Head, SC AIAA-2007-6844 (2007)Google Scholar
  15. 15.
    Kozai, Y.: The motion of a close earth satellite. Astron. J. 64(9), 367–377 (1959)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Lantukh, D., Russell, R.P., Broschart, S.: Heliotropic orbits at oblate asteroids: balancing solar radiation pressure and J2 perturbations. Celest. Mech. Dyn. Astron. 121 (2), 171–190 (2015). MathSciNetCrossRefGoogle Scholar

Copyright information

© American Astronautical Society 2018

Authors and Affiliations

  1. 1.Department of Astronomy and Space Science, Faculty of ScienceCairo UniversityCairoEgypt
  2. 2.Lille Laboratory of AstronomyLille University of Science and TechnologyLilleFrance
  3. 3.IMCCE, Observatoire de Paris, UMR 8028 du CNRSUniversité Pierre et Marie CurieParisFrance
  4. 4.Department of Mathematics, Faculty of ScienceTaibah UniversityAl-MadinahKingdom of Saudi Arabia

Personalised recommendations