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Orbital perturbation coupling of primary oblateness and solar radiation pressure

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Abstract

Solar radiation pressure can have a substantial long-term effect on the orbits of high area-to-mass ratio spacecraft, such as solar sails. We present a study of the coupling between radiation pressure and the gravitational perturbation due to polar flattening. Removing the short-period terms via perturbation theory yields a time-dependent two-degree-of-freedom Hamiltonian, depending on one physical and one dynamical parameter. While the reduced model is non-integrable in general, assuming coplanar orbits (i.e., both Spacecraft and Sun on the equator) results in an integrable invariant manifold. We discuss the qualitative features of the coplanar dynamics, and find three regions of the parameters space characterized by different regimes of the reduced flow. For each regime, we identify the fixed points and their character. The fixed points represent frozen orbits, configurations for which the long-term perturbations cancel out to the order of the theory. They are advantageous from the point of view of station kee**, allowing the orbit to be maintained with minimal propellant consumption. We complement existing studies of the coplanar dynamics with a more rigorous treatment, deriving the generating function of the canonical transformation that underpins the use of averaged equations. Furthermore, we obtain an analytical expression for the bifurcation lines that separate the regions with different qualitative flow.

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No datasets, other than the numerical results presented in the figures, have been generated as part of this research. The information provided in this manuscript is sufficient to reproduce those results.

Notes

  1. nssdc.gsfc.nasa.gov/nmc/spacecraft/1958-002B; last accessed December 25, 2023.

  2. https://space.jpl.nasa.gov/msl/QuickLooks/echoQL; last accessed December 25, 2023.

  3. Some authors use the supplementary angle of \(\theta \).

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Acknowledgements

The authors acknowledge Khalifa University of Science and Technology’s internal grant CIRA-2021-65 (8474000413). ML also acknowledges partial support from the Spanish State Research Agency and the European Regional Development Fund (Projects PID2020-112576GB-C22 and PID2021-123219OB-I00, AEI/ERDF, EU). EF has been partially supported by Spanish MINECO’s funds PID2020-112576GB-C21 and PID2021-1239 68NB-I00. RF received support from MINECO “Severo Ochoa Programme for Centres of Excellence in R &D” (CEX2018-000797-S).

Funding

The financial support for the execution of the research here presented was provided by the following grants: Khalifa University of Science and Technology’s CIRA-2021-65 / 8474000413 (recipient: E. Fantino), Spanish National funds PID2020-112576GB-C22 (recipient: M. Lara), PID2021-123219OB-I00 (recipient: M. Lara), PID2020-112576GB-C21 (recipient: E. Fantino), PID2021-123968NB-I00 (recipient: E. Fantino) and CEX2018-000797-S (recipient: R. Flores).

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  1. Scientific Computation and Technical Innovation Center, University of La Rioja, 26006, Logroño, Spain

    Martin Lara

  2. Aerospace Engineering Department, Khalifa University of Science and Technology, P.O. Box 127788, Abu Dhabi, United Arab Emirates

    Martin Lara, Elena Fantino & Roberto Flores

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The study conception and design were performed by M. Lara who wrote the first draft of the manuscript. All authors collaborated on improving subsequent versions of the paper, and read and approved the final manuscript.

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Correspondence to Elena Fantino.

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A preliminary version of this research was presented at the Third International Nonlinear Dynamics Conference— NODYCON 2023 held in Rome, Italy, 18–22 June 2023 [52].

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Lara, M., Fantino, E. & Flores, R. Orbital perturbation coupling of primary oblateness and solar radiation pressure. Nonlinear Dyn (2024). https://doi.org/10.1007/s11071-024-09757-8

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