Abstract
We consider the Hill four-body problem where three oblate, massive bodies form a relative equilibrium triangular configuration, and the 4th, infinitesimal body orbits in a neighborhood of the smallest of the three massive bodies. We regularize collisions between the infinitesimal body and the smallest massive body, via McGehee coordinate transformation. We describe the corresponding collision manifold and show that it undergoes a bifurcation when the oblateness coefficient of the smallest massive body passes through the zero value.
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Acknowledgements
We are grateful to Jaime Burgos-García for useful discussions.
Funding
E.B. and M.G. were partially supported by NSF grant DMS-1814543. W-T.L. was partially supported by NSF grant DMS-1814543 and DMS-2138090 .
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This article is part of the topical collection on Variational and perturbative methods in Celestial Mechanics. Guest Editors: Angel Jorba, Susanna Terracini, Gabriella Pinzari and Alessandra Celletti.
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Belbruno, E., Gidea, M. & Lam, WT. Regularization of the Hill four-body problem with oblate bodies. Celest Mech Dyn Astron 135, 6 (2023). https://doi.org/10.1007/s10569-023-10122-x
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DOI: https://doi.org/10.1007/s10569-023-10122-x