Hill stability cannot be easily established in the classical 3-body problem with point masses, as sufficient energy for escape of one of the bodies can always be extracted from the gravitational potential energy. For the finite density, so-called Full 3-body problem the lower limits on the gravitational potential energy ensure that Hill stability can exist. For the equal mass Full 3-body problem this can be easily established, with the result that for any equal mass, finite density 3-body problem in or near a contact equilibrium, none of the components of the system can escape in the ensuing motion.
%0 Journal Article
%1 scheeres2014stability
%A Scheeres, D J
%D 2014
%J Proceedings of the International Astronomical Union
%K 3-body_problem hills_mechanism orbital_motion
%N S310
%P 134-137
%R 10.1017/S1743921314008047
%T Hill Stability in the Full 3-Body Problem
%U https://www.cambridge.org/core/product/identifier/S1743921314008047/type/journal_article
%V 9
%X Hill stability cannot be easily established in the classical 3-body problem with point masses, as sufficient energy for escape of one of the bodies can always be extracted from the gravitational potential energy. For the finite density, so-called Full 3-body problem the lower limits on the gravitational potential energy ensure that Hill stability can exist. For the equal mass Full 3-body problem this can be easily established, with the result that for any equal mass, finite density 3-body problem in or near a contact equilibrium, none of the components of the system can escape in the ensuing motion.
@article{scheeres2014stability,
abstract = {Hill stability cannot be easily established in the classical 3-body problem with point masses, as sufficient energy for escape of one of the bodies can always be extracted from the gravitational potential energy. For the finite density, so-called Full 3-body problem the lower limits on the gravitational potential energy ensure that Hill stability can exist. For the equal mass Full 3-body problem this can be easily established, with the result that for any equal mass, finite density 3-body problem in or near a contact equilibrium, none of the components of the system can escape in the ensuing motion.},
added-at = {2024-05-08T21:51:08.000+0200},
author = {Scheeres, D J},
biburl = {https://www.bibsonomy.org/bibtex/22b4fab4f102d077e3c951d2091e8eff3/tabularii},
doi = {10.1017/S1743921314008047},
interhash = {576658688a9610d2b6b5c27ac7e98289},
intrahash = {2b4fab4f102d077e3c951d2091e8eff3},
journal = {Proceedings of the International Astronomical Union},
keywords = {3-body_problem hills_mechanism orbital_motion},
number = {S310},
pages = {134-137},
timestamp = {2024-05-10T15:49:56.000+0200},
title = {Hill Stability in the Full 3-Body Problem},
url = {https://www.cambridge.org/core/product/identifier/S1743921314008047/type/journal_article},
volume = 9,
year = 2014
}