Analytical model of satellite motion in almost circular orbits under the influence of zonal harmonics of geopotential
Heading:
| 1Pirozhenko, AV, 1Maslova, AI, 2Vasyliev, VV 1Institute of Technical Mechanics of the National Academy of Sciences of Ukraine and the State Space Agency of Ukraine, Dnipro, Ukraine 2Earth Observing System Data Analytics, Menlo Park, USA |
| Space Sci. & Technol. 2022, 28 ;(4):18-30 |
| https://doi.org/10.15407/knit2022.04.018 |
| Publication Language: English |
Abstract: The article deals with the movement of satellites in low near-circular orbits of the Earth. An analytical model is constructed, which consists of formulas describing the change of the osculating elements and averaged equations. An algorithm for constructing a second approximation of the influence of zonal harmonics of the geopotential on the movement of satellites in almost circular orbits is presented. For the second and third zonal harmonics, formulas are given for the osculating and average elements describing the motion of the satellite in the second approximation in small parameters. The introduction of special variables for almost circular orbits made it possible to significantly simplify the procedure for constructing the second approximation of the influence of zonal harmonics. The article provides a justification for the accuracy of the analytical model for the considered orbits. The constructed model of changes in the average elements of the orbit describes the basic principles of motion. With a sufficiently high accuracy, this model describes the changes in the average elements of the orbit with simple analytical formulas and is convenient for analyzing the properties of orbits and pre-selecting a reference orbit for a specific mission.
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| Keywords: almost circular orbits, analytical model, average elements, laws of motion, zonal harmonics |
References:
1. Beutler G. (2005). Methods of celestial mechanics. Vol. II: Application to planetary system geodynamics and satellite geodesy. Berlin: Springer. ISBN 3-540-40750-2.
https://doi.org/10.1007/b137725
2. Brouwer D. (1959). Solution of the problem of artifical satellite theory without drag. Astron. J., 64, 378-396.
https://doi.org/10.1086/107958
doi.org/10.1086/107958.
3. Cook R. A. (1992). The long-term behavior of near-circular orbits in a zonal gravity field. Proceedings of the AAS/AIAA Astrodynamics Conference (Durango, CO, August 19-22, 1991), 2205-2221.
4. Cutting E. E., Frautnick J. C., Born G. H. (1978). Orbit analysis for Seasat-A. J. Astronautical Sci., 26, 315-342.
5. Deprit A. (1981). The elimination of the parallax in satellite theory. Celestial mechanics, 24, 111-153.
https://doi.org/10.1007/BF01229192
doi.org/10.1007/BF01229192.
6. Di Carlo M., Graça Marto S. D., Vasile M. (2021). Extended analytical formulae for the perturbed Keplerian motion under low-thrust acceleration and orbital perturbations. Celestial Mechanics and Dynamical Astronomy, 133, 1-39.
https://doi.org/10.1007/s10569-021-10007-x
doi.org/10.1007/s10569-021-10007-x.
7. Dong W., Chang-yin Z. (2010). An Accuracy Analysis of the SGP4/SDP4 Model. Chinese Astron. and Astrophys., 34 (1), 69-76.
https://doi.org/10.1016/j.chinastron.2009.12.009
doi.org/10.1016/j.chinastron.2009.12.009.
8. El'yasberg P. E. (1965). Introduction to the theory of flight of artificial earth satellites. Мoskow: Nauka [in Russian].
9. Fortescue P. W., Stark J. P., Swinerd G. G. (2011). Spacecraft systems engineering. 4th Edition. Wiley and Sons, Inc. ISBN:9780470750124.
https://doi.org/10.1002/9781119971009
10. Hoots F. R., Roehrich R. L. (1980). Models for Propagation of NORAD Element Sets. Spacetrack Report № 3. U.S. Air Force: Aerospace Defense Command.
https://doi.org/10.21236/ADA093554
URL: https://www.celestrak.com/NORAD/documentation/spacetrk.pdf (Last accessed: 17.01.2022).
11. Kozai Y. (1959). The motion of a close earth satellite. Astron. J., 64, 367-377.
https://doi.org/10.1086/107957
doi.org/10.1086/107957.
12. Markov Y. G., Mikhailov M. V., Perepelkin V. V., Pochukaev V. N., Rozhkov S. N., Semenov A. S. (2016). Analysis of the effect of various disturbing factors on high-precision forecasts of spacecraft orbits. Cosmic Res., 54, 155-163.
https://doi.org/10.1134/S0010952515060015
DOI: 10.1134/S0010952515060015.
https://doi.org/10.1134/S0010952515060015
13. Pirozhenko A. V., Maslova A. I., Khramov D. A., Volosheniuk O. L., Mischenko A. V. (2020). Development of a new form of equations of disturbed motion of a satellite in nearly circular orbits. Eastern-European J. Enterprise Technol., 4 (5/106), 70-77.
https://doi.org/10.15587/1729-4061.2020.207671
doi.org/10.15587/1729-4061.2020.207671
14. 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.
https://doi.org/10.15407/knit2019.02.003
doi.org/10.15407/knit2019.02.003
15. San-Juan J. F., Pérez I., San-Martín M., Vergara E. P. (2017). Hybrid SGP4 orbit propagator. Acta Astronautica, 137, 254-260.
https://doi.org/10.1016/j.actaastro.2017.04.015
doi.org/10.1016/j.actaastro.2017.04.015.
16. Spiridonova S., Kirschner M., Hugentobler U. (2014). Precise mean orbital elements determination for LEO monitoring and maintenance.
URL: https://elib.dlr.de/103814/1/Spiridonova_ISSFD_2014_upd.pdf (Last accessed: 17.01.2022).
17. Vallado D. A. (2013). Fundamentals of astrodynamics and applications. 4th edition. Microcosm Press. ISBN: 978-11881883180.