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Database of Planar and Three-Dimensional Periodic Orbits and Families Near the Moon

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Abstract

The renewed interest in Lunar exploration prompts a need to better understand the dynamics of spacecraft in the vicinity of the Moon. Here, a detailed survey is conducted via a broad grid search to find, characterize, and archive symmetric periodic orbits. The resulting database contains over 13 million planar and three-dimensional solutions in the Earth–Moon circular restricted three-body problem, grouped into 33,980 family and sub-family clusters. The work is a direct follow-on to previous periodic orbit grid searches, with a focus on the Earth–Moon mass ratio, the addition of x–z symmetric orbits, and family clustering. Each periodic orbit successfully identified is evaluated for stability properties, perilune distance, number and center of revolutions, and other defining properties. DBSCAN, an unsupervised learning clustering algorithm, is used to isolate family curves in phase space and group orbits into family or sub-family clusters. The clustered orbits are then sorted to form smooth, ordered curves in phase space, allowing for arbitrary data resolution and improved labeling of the discrete grid solutions. A custom cluster confidence measure is introduced and applied. Over 80% of 3D data and over 62% of planar data are clustered with high confidence for all solutions regardless of number of revolutions, with better results at lower revolutions. Approximately 4.25% of 3D solutions and less than 0.5% of planar solutions are classified as outliers. The resulting database is an extension of several recent Lunar periodic orbit studies, and can be considered a modern update to Broucke’s seminal database of planar cislunar periodic orbits. This new public database is a tool for future mission design and has potential use in a variety of catalogue maintenance space situational awareness applications. The database, along with code and an interactive GUI to help parse it, is open source and available online.

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Notes

  1. See footnote in the Database Section for the DOI and archival link to access.

  2. The database and accompanying software is open-source and archived here: https://doi.org/10.5281/zenodo.6411980. The following link will always point to the most recent version: https://doi.org/10.5281/zenodo.6411979.

  3. Approved for public release; distribution is unlimited. Public Affairs release approval # RV-45787 AFRL-2021-2876

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Acknowledgements

The authors thank both anonymous reviewers for their insightful comments that greatly improved the quality of this paper. This work was funded in part by the Air Force Research Laboratory award number FA9451-18-2-0105 under a subcontract through the University of Arizona. The authors acknowledge the Texas Advanced Computing Center (TACC) at The University of Texas at Austin for providing high performance computing resources that contributed to the research results reported within this paper. http://www.tacc.utexas.edu

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    Carter J. Franz & Ryan P. Russell

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Franz, C.J., Russell, R.P. Database of Planar and Three-Dimensional Periodic Orbits and Families Near the Moon. J Astronaut Sci 69, 1573–1612 (2022). https://doi.org/10.1007/s40295-022-00361-9

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