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Characterization of the stability for trajectories exterior to Jupiter in the restricted three-body problem via closed-form perturbation theory

Published online by Cambridge University Press:  30 May 2022

Mattia Rossi Open the ORCID record for Mattia Rossi [Opens in a new window]  and
Christos Efthymiopoulos
Mattia Rossi
Affiliation:
Department of Mathematics “Tullio Levi-Civita”, University of Padova, Postal Code 35121, Via Trieste 63, Padova, Italy email: mrossi@math.unipd.it
Christos Efthymiopoulos
Affiliation:
Department of Mathematics “Tullio Levi-Civita”, University of Padova, Postal Code 35121, Via Trieste 63, Padova, Italy email: cefthym@math.unipd.it
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Abstract

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We address the question of identifying the long-term (secular) stability regions in the semi-major axis-eccentricity projected phase space of the Sun-Jupiter planar circular restricted three-body problem in the domains i) below the curve of apsis equal to the planet’s orbital radius (ensuring protection from collisions) and ii) above that curve. This last domain contains several Jupiter’s crossing trajectories. We discuss the structure of the numerical stability map in the (a,e) plane in relation to manifold dynamics. We also present a closed-form perturbation theory for particles with non-crossing highly eccentric trajectories exterior to the planet’s trajectory. Starting with a multipole expansion of the barycentric Hamiltonian, our method carries out a sequence of normalizations by Lie series in closed-form and without relegation. We discuss the applicability of the method as a criterion for estimating the boundary of the domain of regular motion.

Keywords

Asteroidscelestial mechanicsn-body simulations
Type
Research Article
Information
Proceedings of the International Astronomical Union , Volume 15 , Symposium S364: Multi-scale (Time and Mass) Dynamics of Space Objects (Oct 2021) , October 2019 , pp. 232 - 238
Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of International Astronomical Union

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