Dynamics of Frozen Orbit and Its Critical Case in the Zonal Problem
Publication: Journal of Aerospace Engineering
Volume 35, Issue 1
Abstract
This paper investigates the dynamical behaviors of Earth frozen orbits including the critical inclination orbit in the zonal problem with terms of perturbations up to . From the mean element theory, an analytical expansion of the dynamics model is derived to obtain the frozen conditions. The global existence of Earth frozen orbits is numerically illustrated by exploration of equilibria in the equations of motion based on Lagrangian formulations. Frozen orbits are widely located at the inclination between 0° and 90°, which may be grouped into families: one for the elliptic orbit case, another for the quasicircular orbit case and the other for the critical inclination orbit case. For the elliptic and quasicircular orbit cases, orbits evolve periodically around the frozen ones, and elliptic orbits tend to be more sensitive than quasicircular ones with respect to variation of initial orbital elements. Frozen orbit bifurcations near the critical inclination are shown to illustrate the origins, evolutions, and stability of frozen orbits. For the last critical inclination case, it is observed that eccentricities keep evolving periodically instead of being frozen at the specified ones compared with that in the problem, and then a relationship between the evolution period and terms of zonal perturbations is illustrated.
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Data Availability Statement
All data, models, and code generated or used during the study appear in the paper.
Acknowledgments
The work was supported by the National Key R&D Program of China (No. 2020YFC2201200), the National Natural Science Foundation of China (No. 11772024), and Qian Xuesen Youth Innovation Foundation of China Aerospace Science and Technology Corporation.
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Journal of Aerospace Engineering
Volume 35 • Issue 1 • January 2022
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© 2021 American Society of Civil Engineers.
History
Received: Apr 14, 2021
Accepted: Sep 3, 2021
Published online: Oct 4, 2021
Published in print: Jan 1, 2022
Discussion open until: Mar 4, 2022
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Cited by
- Pei Chen, Xuejian Mao, Jinfei Han, Xiucong Sun, Observability Analysis for Orbit Determination Using Spaceborne Gradiometer, Journal of Aerospace Engineering, 10.1061/JAEEEZ.ASENG-4619, 36, 2, (2023).