Abstract
Ballistic capture orbits offer safer Mars injection at longer transfer time. However, the search for such an extremely rare event is a computationally intensive process. Indeed, it requires the propagation of a grid sampling the whole search space. This work proposes a novel ballistic capture search algorithm based on Taylor differential algebra propagation. This algorithm provides a continuous description of the search space compared to classical grid sampling research and focuses on areas where the nonlinearities are the largest. Macroscopic analyses have been carried out to obtain cartography of large sets of solutions. Two criteria, named consistency and quality, are defined to assess this new algorithm and to compare its performances with classical grid sampling of the search space around Mars. Results show that differential algebra mapping works on large search spaces, and automatic domain splitting captures the dynamical variations on the whole domain successfully. The consistency criterion shows that more than 87% of the search space is guaranteed as accurate, with the quality criterion kept over 80%.
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Data availability
The data sets supporting the findings of this study are available on Zenodo with the identifiers https://doi.org/10.5281/zenodo.6103720 and https://doi.org/10.5281/zenodo.5940101.
Notes
Data publicly available at: https://naif.jpl.nasa.gov/pub/naif/generic_kernels/spk/planets/de440s.bsp [retrieved Feb 1, 2022].
Data publicly available at: https://naif.jpl.nasa.gov/pub/naif/generic_kernels/spk/satellites/mars097.bsp [retrieved Feb 1, 2022].
Data publicly available at: https://naif.jpl.nasa.gov/pub/naif/generic_kernels/lsk/naif0012.tls, https://naif.jpl.nasa.gov/pub/naif/generic_kernels/pck/pck00010.tpc, and https://naif.jpl.nasa.gov/pub/naif/generic_kernels/pck/gm_de431.tpc [retrieved Feb 1, 2022]. The gm_de431.tpc PCK kernel is used because the new version consistent with the ephemerides DE440s has not been released yet.
Here B stands for barycenter.
https://extapps.ksc.nasa.gov/Reliability/Documents/Preferred_Practices/2301.pdf [last accessed Feb 1, 2022].
In previous works, this was referred to as stability index (Luo et al. 2014; Luo and Topputo 2015, 2017). However, in Dei Tos et al. (2018), the adjustment from stability to regularity index was proposed to avoid misunderstandings with the periodic orbit stability index. The same nomenclature introduced in Dei Tos et al. (2018) is used in this work.
Library available at: https://github.com/dacelib/dace [last accessed Feb 1, 2022].
The time regressions have been derived from ICs propagated taking into account also the gravitational attractions of Uranus (B), and Neptune (B), later discarded due to their negligible influence.
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Acknowledgements
T.C. would like to thank the Department of Aerospace Science and Technology (DAER) of Politecnico di Milano for the host and the warm welcome, as well as the Toulouse graduate School of Aerospace Engineering (TSAE) for the funding of his stay at Politecnico di Milano. G.M. and F.T. would like to acknowledge the European Research Council (ERC) since part of this work has received funding from the ERC under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 864697).
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Caleb, T., Merisio, G., Lizia, P.D. et al. Stable sets mapping with Taylor differential algebra with application to ballistic capture orbits around Mars. Celest Mech Dyn Astron 134, 39 (2022). https://doi.org/10.1007/s10569-022-10090-8
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DOI: https://doi.org/10.1007/s10569-022-10090-8