Abstract
Loosely captured orbits with circulating and pulsating eccentricity vectors have a variety of attractive mission design properties, including low insertion costs, near-circular and highly eccentric phases, mid- to high inclinations, long-term stability, and spatially distributed close approaches. Such orbits are the known result of averaging third-body perturbations over the spacecraft and system motions. Unfortunately, the doubly averaged model does not match long-term unaveraged motion well at high altitudes. Singly averaged dynamics are accurate for orbits with much higher semimajor axis values, providing a mechanism to predict and characterize high-altitude motion in the unaveraged model. In this work, singly averaged circulating, eccentric orbits are surveyed in the specific context of the dimensioned Earth–Moon system, where high-altitude orbits are expected to have the most useful applications. A global search is performed over non-impacting system resonances, and families of periodic orbits are used as a framework to map the feasible space. The resulting database of periodic orbits is provided as an online supplement. The singly averaged families are shown to provide a reliable bridge between the analytic results of the doubly averaged system and initial guesses that converge to periodic orbits in the unaveraged model. Non-impacting circulating, eccentric orbits are demonstrated to maintain their structure for multiple years in a high-fidelity force model. These circulating, eccentric, lunar orbits may be useful for human-crewed space stations, dedicated science orbits, extended missions, loitering orbits, or transfers between the Lagrange points and low-lunar orbits.
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A database of lunar periodic orbits in singly averaged dynamics has been submitted to this journal as electronic supplementary material and is also available at https://sites.utexas.edu/russell/publications/code/circulating/.
Notes
A previous version of this article was presented as a conference paper at the AIAA SciTech 2020 Forum: see McArdle and Russell (2020).
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Acknowledgements
The authors would like to thank The University of Texas at Austin for its support through the Thrust 2000 Fellowship and the Texas Space Grant Consortium for its support through its graduate fellowship. This material is based upon work supported by NASA under award No. 80NSSC18M0121. The authors would also like to thank the peer-reviewers for their insightful comments.
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This material is based upon work supported by NASA under award No. 80NSSC18M0121.
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Relevant MATLAB code for analyzing circulating eccentric orbits has been submitted to this journal as electronic supplementary material and is also available at https://sites.utexas.edu/russell/publications/code/circulating/.
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McArdle, S., Russell, R.P. Circulating, eccentric periodic orbits at the Moon. Celest Mech Dyn Astr 133, 18 (2021). https://doi.org/10.1007/s10569-021-10013-z
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DOI: https://doi.org/10.1007/s10569-021-10013-z