Basic regularities of the Sun's gravity effect on the satellites motion on almost circular low-Earth orbits
Heading:
| 1Pirozhenko, AV, 1Maslova, AI, 1Pyrozhenko, OO 1Institute of Technical Mechanics of the National Academy of Sciences of Ukraine and the State Space Agency of Ukraine, Dnipro, Ukraine |
| Space Sci. & Technol. 2026, 32 ;(1):03-12 |
| https://doi.org/10.15407/knit2026.01.003 |
| Publication Language: English |
Abstract: The effect of the Sun’s gravity on satellite motion in nearly circular low-Earth orbits (with eccentricity around 10-3 and altitudes up to 1000 km) is examined. These types of orbits are commonly used for satellites that conduct remote sensing of Earth. Although the Sun's gravitational effect on satellite motion is minor compared to the non-centrality of the Earth’s gravitational field, modern requirements for remote sensing missions make such studies relevant.
To date, many studies have focused on how the gravity of a third body (the Moon and the Sun) influences the motion of artificial satellites of the Earth. Different approaches have been used to address the problem, yielding profound and meaningful results. At the same time, in these studies, the primary focus is on the orbits of satellites with significant eccentricity, and rather cumbersome approaches and formulas make it difficult to extend the results to the case of nearly circular low-Earth orbits. Therefore, it is of interest to use simpler approaches and
In the article, assuming that the Earth moves relative to the Sun along an unperturbed Keplerian orbit, the main regularities of changes in the parameters of almost circular orbits are determined, and analytical estimates describing changes in the orbital parameters of the satellite under the influence of the Sun’s gravitational attraction are constructed. It is shown that short-periodic oscillations with the period of orbital motion of the satellite due to the influence of the Sun’s gravitational attraction are negligibly small for the orbits under consideration. The long-periodic and secular motion of the orbital plane orientation is described by simple equations whose properties have been investigated in detail. These equations coincide with the equations of evolution of the kinetic momentum of a rotating symmetric solid body under the action of
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| Keywords: basic regularities of satellite motion, gravity of the Sun, long-period and secular motion, nearly circular low-Earth orbit |
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https://doi.org/10.15407/itm2023.01.014
3. Beletskii V. V. (1975). Motion of a satellite about the center of mass in a gravitational field. Moscow: Mosk. un-t [in Russian].
4. Beletskii V. V. (1966). Motion of an Artificial Satellite About Its Centre of Mass. I.P.S.T. ISBN-10: 0706504593.
5. Broucke R. A. (2003). Long-term third-body effects via double averaging. J. Guidance, Control, and Dynamics, 26(1), 27-32.
https://doi.org/10.2514/2.5041
6. Chao Ch.-Ch Hoots F. (2018). Applied Orbit Perturbation and Maintenance. Aerospace Press; Second edition. ISBN: 978-1-884989-27-8.
https://doi.org/10.2514/4.989278
7. Domingos R. C., Moraes R. V., Prado A. F. B. (2008). Third-body perturbation in the case of elliptic orbits for the disturbing body. Mathematical Problems in Engineering,
https://doi.org/10.1155/2008/763654
8. Ju T., Shao X., Zhang D., Wei X. (2022). Repeat Ground-Track Orbit Design Using Objective Dimensionality Reduction and Decoupling Optimization. IEEE Transactions on Aerospace and Electronic Systems, 58(6), 5741-5748.
https://doi.org/10.1109/TAES.2022.3178063
9. Kahle R., D'Amico S. (2014). The TerraSAR-X Precise Orbit Control - Concept and Flight Results. Proceedings of the 24th International Symposium on Space Flight Dynamics (ISSFD), 2014-05-05 - 2014-05-09.
10. Kozai Y. (1962). Secular perturbations of asteroids with high inclination and eccentricity. Astron. J., 67, 591-598.
https://doi.org/10.1086/108790
11. Lara M. (2021). Hamiltonian Perturbation Solutions for Spacecraft Orbit Prediction: The Method of Lie Transforms. De Gruyter; 1st edition. e- ISBN: 978-3-11-066851-3.
https://doi.org/10.1515/9783110668513
12. Lara M. (2022). On perturbation solutions in the restricted three-body problem dynamics. Acta Astronautica, 195, 596-604. doi.org/10.1016/j.actaastro.2022.01.022
https://doi.org/10.1016/j.actaastro.2022.01.022
13. Lee S. S. (2021). Closed-form solution of repeat ground track orbit design and constellation deployment strategy. Acta Astronautica, 180, 588-595.
https://doi.org/10.1016/j.actaastro.2020.12.021
14. Lidov M. L. (1962). The evolution of orbits of artificial satellites of planets under the action of gravitational perturbations of external bodies. Planetary and Space Science, 9(10), 719-759.
https://doi.org/10.1016/0032-0633(62)90129-0
15. Nie T., Gurfil P. (2021). Long-term evolution of orbital inclination due to third-body inclination. Celestial Mechanics and Dynamical Astronomy, 133(1), article number 1.
https://doi.org/10.1007/s10569-020-09997-x
16. Nie T., Zhang S., Yi T., Ren J. (2025). Analytical Solution for Third-Body Perturbations with Double Averaging. J. Guidance, Control, and Dynamics, 48(2), 384-392.
https://doi.org/10.2514/1.G008338
17. Pirozhenko A., Maslova A., Khramov D., Volosheniuk O., Mischenko A. (2020). Development of a new form of equations of disturbed motion of a satellite in nearly circular orbits. Eastern-European J. Enterprise Technologies, 4(5/106), 70-77.
https://doi.org/10.15587/1729-4061.2020.207671
18. Pirozhenko A. V. (1998). Effect of energy dissipation in thread material on the evolution of rotational motion in space cable systems. Space Science and Technology, 4(5), 116-124 [in Russian].
https://doi.org/10.15407/knit1998.05.116
19. Pirozhenko A. V., Maslova A. I., Vasilyev V. V. (2019). About the influence of second zonal harmonic on the motion of satellite in almost circular orbits. Space Science and Technology, 25(2), 3-11 [in Russian].
https://doi.org/10.15407/knit2019.02.003
20. Prado A. F. B. (2003). Third-body perturbation in orbits around natural satellites. J. Guidance, Control, and Dynamics, 26(1), 33-40.
https://doi.org/10.2514/2.5042
21. Yamamoto T., Arikawa Y., Ueda Y., Itoh H. (2016). Autonomous Precision Orbit Control Considering Observation Planning: ALOS-2 Flight Results. J. Guidance, Control, and Dynamics, 39(6), 1244-1264.
https://doi.org/10.2514/1.G001375
22. Zeng Q., Jiang Yu, Nie T., Liu X. (2024). Free and forced inclinations of orbits perturbed by the central body's oblateness and an inclined third body. Celestial Mechanics and Dynamical Astronomy, 136(3), article number 16.
https://doi.org/10.1007/s10569-024-10187-2