Modeling & Analysis of Environmental Orbit Perturbation and Budgeting Their Effect on Orbital Elements

Document Type : Research Article

Authors

Department of Aerospace Engineering, Amirkabir University of Technology, Tehran, Iran

Abstract

This paper examines the impact of orbit perturbations on satellite translational dynamics, encompassing both major and minor forces. The former category includes atmospheric drag, Earth oblateness, solar radiation, and third-body attractions. Atmospheric drag is based on a solar activity model and its rotation due to meridional and zonal winds. Earth's oblateness is considered over a high order of Earth gravity harmonics, along with direct solar radiation pressure and the effect of third-body attraction, such as the Moon and Sun gravity, utilizing a high-accuracy ephemeris. Minor force effects include Earth's solid tides resulting from the Sun and Moon attraction, the effect of reflected solar radiation pressure from the Earth (Albedo), and relativity effects. The three primary theories employed to expand equations are perturbed potential function, force components, and acceleration. An investigative study was conducted to analyze the budget of perturbations in orbital elements at various altitudes. This approach applies to high orbit injection, orbit transfer using low electrical propulsion, and high-precision missions. The research underscores the significance of possessing a precise perturbed dynamic model, which facilitates high-revolution orbit transfer.

Keywords

Main Subjects

References

[1] T. Verhoef and R. Noomen, Satellite Decay Computation and Impact Point Prediction, Advances in Space Research, 30(20) (2002) 313–319. DOI: 10.1016/s0273-1177(02)00301-0.
[2] J. Kabeláč and L. Sehnal, Atmospheric Effects on the Dynamics of the MIMOSA Satellite, Journal of Geodesy, 76 (2003) 536–542. DOI: 10.1007/s00190-002-0275-4.
[3] C. Pardini, W. K. Tobiska, and L. Anselmo,   Analysis of the Orbital Decay of Spherical Satellites Using Different Solar Flux Proxies and Atmospheric Density Models, Advances in Space Research, 37(2) (2006) 392–400. DOI: 10.1016/j.asr.2004.10.009.
[4] N. A. Saad, M. N. Ismail, and K. H. I. Khalil, Decay of Orbits due to the Drag of Rotating Oblate Atmosphere, Planetary and Space Science, 56(3) (2008) 537–541. DOI: 10.1016/j.pss.2007.11.004.
[5] C. Pardini, L. Anselmo, K. Moe, and M. M. Moe, On the secular decay of the LARES semi-major axis, Acta Astronautica, 140 (2017) 469–477. DOI: 10.1016/j.actaastro.2017.09.012.
[6] P. Kustaanheimo and E. L. Stiefel, Perturbation theory of Keplerian motion based on spinor regularization, Journal für die Reine und Angewandte Mathematik, 218 (1965) 204–219. DOI: 10.1515/crll.1965.218.204.
[7] G. Xu, Y. Xu, and J. Xu, Analytical solution of a satellite orbit disturbed by atmospheric drag, Monthly Notices of the Royal Astronomical Society, 410(1) (2011) 654–662. DOI: 10.1111/j.1365-2966.2010.17471.x.
[8] N. Ozar, S. M. H. Al-Mamury, and H. H. Selim, The Effect of Atmospheric Drag Force on the Elements of Low Earth Orbital Satellites at Minimum Solar Activity, NeuroQuantology, 19(9) (2021) 24–37. DOI: 10.14704/nq.2021.19.9.NQ21134.
[9] N. M. Harwood and G. G. Swinerd, Long periodic and secular perturbation to the orbit of a spherical satellites due to direct solar radiation pressure, Celestial Mechanics and Dynamical Astronomy, 62(1) (1995) 71–80. DOI: 10.1007/bf00692069.
[10] W. M. Kaula, Theory of Satellite Geodesy. Waltham, MA: Blaisdell Publishing Company, (1966).
[11] M. Ziebart, High Precision Analytical Solar Radiation Pressure Modeling for GNSS Spacecrafts. London, UK: University of East London, PhD Thesis (2001).
[12] Y. Bar-Sever and D. Kuang, New Empirically Derived Solar Radiation Pressure Model for Global Positioning System Satellites. Pasadena, California: Jet Propulsion Laboratory (JPL), JPL Technical Report (2004).
[13] F. Xia, Y. Shen, and Q. Zhao, Advancing the Solar Radiation Pressure Model for BeiDou-IGSO, Remote Sensing, 14(6) (2022). DOI: 10.3390/rs14061460.
[14] J. Žižka and D. Vokrouhlický, Solar radiation pressure on (99942) Apophis, Icarus, 211(1) (2011) 511–518. DOI: 10.1016/j.icarus.2010.08.011
[15] F. Delhaise, Analytical Treatment of Air Drag and Earth Oblateness Effect Upon An Artificial Satellite, Celestial Mechanics and Dynamical Astronomy, 52(1) (1991) 58–103.
[16] N. V. Emelyanov, The acting analytical theory of artificial Earth satellites, Astronomical & Astrophysical Transactions, 1(2) (1992) 119–127. DOI: 10.1080/10556799208244526.
[17] H. H. Selim, Analytical Third Order Solution for Coupling Effects of Earth Oblateness and Direct Solar Radiation Pressure on the Motion of Artificial Satellites, International Journal of Astronomy and Astrophysics, 4(3) (2014) 530–543. DOI: 10.4236/ijaa.2014.43049
[18] A. Masoud, M. Abdelkhalik, and A. Sharaf, Construction of Frozen Orbits Using Continuous Thrust Control Theories Considering Earth Oblateness and Solar Radiation Pressure Perturbations, Astrodynamics, 2(4) (2018) 329–343. DOI: 10.1007/s42064-018-0028-7.
[19] M. K. Ammar, M. R. Amin, and M. H. M. Hassan, Visibility intervals between two artificial satellites under the action of Earth oblateness, Applied Mathematics and Nonlinear Sciences, 3(2) (2018) 353–374. DOI: 10.21042/amns.2018.2.00028.
[20] A. El-Enna, Analytical Treatment of the Earth Oblateness and Solar Radiation Pressure Effect on an Artificial Satellite, Applied Mathematics and Computation, 151(1) (2004) 121–145. DOI: 10.1016/S0096-3003(03)00339-4.
[21] Y. Kozai, Second-order analytical solution of artificial satellite theory without air drag, The Astronomical Journal, 67(7) (1962) 446. DOI: 10.1086/108898.
[22] T. P. Brito, C. C. Celestino, and R. V. Moraes, Study of the decay time of a CubeSat type satellite considering perturbations due to the Earth’s oblateness and atmospheric drag, Journal of Physics: Conference Series, 641(1) (2015), 12-26. DOI: 10.1088/1742-6596/641/1/012026.
[23] I. M. Nikolkina, L. S. Ozipova, and A. V. Shatina, "The influence of the Earth’s oblateness on the image motion velocity during the electro-optical survey of the planet’s surface, Journal of Physics: Conference Series, 1705(1) (2020), 12008. DOI: 10.1088/1742-6596/1705/1/012008.
[24] Y. Kozai, On the effects of the sun and moon upon the motion of a close earth satellite, Smithsonian Astrophysical Observatory Special Report, 22 (1959).
[25] P. Musen, On the long-period lunisolar effect in the motion of the artificial satellite, Journal of Geophysical Research, 66(6) (1961) 1659–1665. DOI: 10.1029/jz066i006p01659.
[26] W. M. Kaula, Development of the lunar and solar disturbing functions for a close satellite, The Astronomical Journal, 67(5) (1962) 300–303. DOI: 10.1086/108729.
[27] G. E. Cook, Luni-solar perturbations of the orbit of an earth satellite, Geophysical Journal International, 6(3) (1962) 271–291. DOI: 10.1111/j.1365-246x.1962.tb00351.x.
[28] J. P. Murphy and T. L. Felsentreger, Analysis of lunar and solar effects on the motion of close earth satellites, NASA Technical Note, no. TN D-3559, (1966).
[29] Y. Kozai, A new method to compute lunisolar perturbations in satellite motions, Smithsonian Astrophysical Observatory Special Report, 349 (1973) 1–27.
[30] R. H. Estes, On the analytic lunar and solar perturbations of a near Earth satellite, Celestial Mechanics, 10(2) (1974) 253–276. DOI: 10.1007/BF01586857.
[31] M. T. Lane, On analytic modeling of lunar perturbations of artificial satellites of the earth, Celestial Mechanics and Dynamical Astronomy, 46(4) (1989) 287–305. DOI: 10.1007/BF00049314.
[32] F. B. A. Prado, Third-body perturbation in orbits around natural satellites, Journal of Guidance, Control, and Dynamics, 26(1) (2003) 33–40. DOI: 10.2514/2.5042.
[33] R. C. Domingos, R. Vilhena de Moraes, and A. F. B. A. Prado, Third-Body Perturbation in the Case of Elliptic Orbits for the Disturbing Body, Mathematical Problems in Engineering, 763654, (2008). DOI: 10.1155/2008/763654.
[34] M. Lara, J. F. San-Juan, and L. M. López, On the third-body perturbations of high-altitude orbits, Celestial Mechanics and Dynamical Astronomy, 113(4) (2012) 435–452. DOI: 10.1007/s10569-012-9433-z.
[35] C. W. T. Roscoe, S. R. Vadali, and K. T. Alfriend, Third-Body Perturbation Effects on Satellite Formations, The Journal of the Astronautical Sciences, 60(3-4) (2013) 408–433. DOI: 10.1007/s40295-015-0057-x.
[36] T. Nie, P. Gurfil, and S. Zhang, Semi-analytical model for third-body perturbations including the inclination and eccentricity of the perturbing body, Celestial Mechanics and Dynamical Astronomy, 131(6) (2019) 29. DOI: 10.1007/s10569-019-9905-5.
[37] Q. Zeng, Y. Zheng, and J. Liu, Free and forced inclinations of orbits perturbed by the third-body gravity, Celestial Mechanics and Dynamical Astronomy, 136(2) (2024) 16. DOI:10.1007/s10569-024-10187-2.
[38] Y. Kozai, Effect of the Tidal Deformation of the Earth on the Motion of Close Earth Satellite, Publications of the Astronomical Society of Japan, 17(4) (1965) 395–402.
[39] W. M. Kaula, Tidal Friction With Latitude-Dependent Amplitude and Phase Angle, The Astronomical Journal, 74(9) (1969) 1108–1114. DOI: 10.1086/110912.
[40] L. Iorio, Earth Tides and Lense–Thirring Effect, Celestial Mechanics and Dynamical Astronomy, 79(3) (2001) 201–230. DOI:10.1023/A:1011168615758.
[41] P. Tourrenc, M. C. Angonin, and X. Ovido, Tidal Gravitational Effects in a Satellite, General Relativity and Gravitation, 36(10) (2004) 2237–225. DOI: 10.1023/B:GERG.0000046181.95611.06.
[42] V. G. Gurzadyan, A. Paolozzi, C. Bianco, and et al., On the Earth’s tidal perturbations for the LARES satellite, The European Physical Journal Plus, 132(12) (2017) 548. DOI: 10.1140/epjp/i2017-11839-3.
[43] H. Lass and C. B. Solloway, On the Comparison of the Newtonian and General Relativistic Orbits of a Point Mass in an Inverse Square Law Force Field, AIAA Journal, 7(6) (1969) 1029–1031. DOI: 10.2514/3.5271
[44] A. Ghaffar, On Some Applications of Approximate Methods in Relativistic Celestial Mechanics. Washington D.C.: NASA Goddard Space Flight Center, Technical Report TR R-341, (1970).
[45] D. Robincom, General Relativity and Satellite Orbits, Celestial Mechanics, 15(1) (1977) 21–33. DOI: 10.1007/bf01229045.
[46] M. Gulklett, Relativistic Effects in GPS and LEO. Copenhagen, Denmark: The Niels Bohr Institute, University of Copenhagen, (2003).
[47] K. Sośnica, R. Zajdel, and G. Bury, General relativistic effects acting on the orbits of Galileo satellites, Celestial Mechanics and Dynamical Astronomy, 133(4) (2021) 14. DOI: 10.1007/s10569-021-10014-y.
[48] D. Vokrouhlický and P. Farinella, Diurnal Yarkovsky effect as a source of mobility of meter-sized asteroidal fragments, Astronomy and Astrophysics, 335 (1998) 1093–1100.
[49] W. F. Bottke, D. Vokrouhlický, and M. Brož, The Effect of Yarkovsky Thermal Forces on the Dynamical Evolution of Asteroids and Meteoroids, in Asteroids III, W. F. Bottke, A. Cellino, P. Paolicchi, and R. P. Binzel, Eds. Tucson: University of Arizona Press, (2002) 395–408.
[50] D. Capek and D. Vokrouhlický, Accurate model for the Yarkovsky effect, in Dynamics of Populations of Planetary Systems, Z. Knežević and A. Milani, Eds. Cambridge: Cambridge University Press, (2005) 1–6.
[51] S. N. Deo and B. S. Kushvah, Yarkovsky effect and solar radiation pressure on the orbital dynamics of the asteroid (101955) Bennu, Astronomy and Computing, 21 (2017) 64–77. DOI: 10.1016/j.ascom.2017.07.002.
[52] T. N. Sannikov, Central Field Motion with Perturbing Acceleration Varying by the Inverse Square Law: Application to the Yarkovsky Effect, Solar System Research, 55(4) (2021) 321–331. DOI: 10.1134/s1063772921040053.
 
[53] T. N. Sannikov, Accounting for the Yarkovsky Effect in Reference Frames Associated with the Radius Vector and Velocity Vector, Solar System Research, 56(4) (2022) 268–278. DOI: 10.1134/s1063772922070058.
[54] D. G. King-Hele, Satellite Orbits in an Atmosphere: Theory and Applications. Glasgow, UK: Blackie & Son Ltd., (1987).
[55] D. A. Vallado, Fundamentals of Astrodynamics and Applications, 2nd ed. El Segundo, CA: Microcosm Press, (2001).
[56] K. Aksnes, Short-period and long-period perturbations of a spherical satellite due to direct solar radiation, Celestial Mechanics, 13(1) (1976) 89–104. DOI: 10.1007/bf01228536.
[57] A. Ghaffar, Integration of the Relativistic Equations of Motion of an Artificial Earth Satellite. Washington D.C.: NASA Goddard Space Flight Center, Technical Report R-346, (1970).
[58] J. P. Vinti, Orbital and Celestial Mechanics, G. J. Der and N. L. Bonavito, Eds. Reston, VA: American Institute of Aeronautics and Astronautics, (1998).
[59] G. H. J. and F. L. Hoods, Applied Orbit Perturbation and Maintenance, 2nd ed. El Segundo, CA: Aerospace Press, (2005).
[60] C. Rizos and A. Stolz, Force modeling for GPS satellite orbits, in Proceedings of the First International Symposium on Precise Positioning with the Global Positioning System, Rockville, MD, (1985) 87–98.
[61] A. F. Bogorodskii, Relativistic Effects in the Motion of an Artificial Earth Satellite, Soviet Astronomy, 3(5) (1959) 857–862.
[62] H. D. Curtis, Orbital Mechanics for Engineering Students, 3rd ed. Oxford, UK: Butterworth-Heinemann, (2013).
[63] M. J. Sidi, Spacecraft Dynamics and Control: A Practical Engineering Approach. Cambridge, UK: Cambridge University Press, (1997).
AUT Journal of Mechanical Engineering
Volume 10, Issue 1
January 2026
Pages 3-28

Files

Share

How to cite

Statistics