Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-26T09:07:38.716Z Has data issue: false hasContentIssue false
  • English
  • Français

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: [email protected]
Christos Efthymiopoulos
Affiliation:
Department of Mathematics “Tullio Levi-Civita”, University of Padova, Postal Code 35121, Via Trieste 63, Padova, Italy email: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

References

Deprit, André, Palacián, Jesúus & Deprit, Etienne 2001, Cel. Mech. and Dyn. Astron., 79, 157–182 CrossRefGoogle Scholar
Guzzo, Massimiliano & Lega, Elena 2018, Physica D: Nonlin. Phen., 373, 38–58 CrossRefGoogle Scholar
Lara, Martin, San-Juan, Juan F. & López-Ochoa, Luis M. 2013, Mathem. Problems in Engin.CrossRefGoogle Scholar
Laskar, Jacques & Petit, AC 2017, A&A, 605, A72 Google Scholar
Lega, Elena, Guzzo, Massimiliano & Froeschlé, Claude 2016, Chaos Detec. and Predict., 35–54 CrossRefGoogle Scholar
Libert, Anne-Sophie & Sansottera, Marco 2013, Cel. Mech. and Dyn. Astron., 117, 149–168 CrossRefGoogle Scholar
Métris, G & Exertier, Pierre 1995, A&A, 294, 278–286 Google Scholar
Palacián, Jesús 2002, Journal of Diff. Equat., 180, 471–519 CrossRefGoogle Scholar
Ramos, Ximena Soledad, Correa-Otto, Jorge Alfredo & Beauge, Cristian 2015, Cel. Mech. and Dyn. Astron., 123, 453–479 CrossRefGoogle Scholar
Sansottera, Marco & Ceccaroni, Marta 2017, Cel. Mech. and Dyn. Astron., 127, 1–18 CrossRefGoogle Scholar
Todorović, Nataša, Wu, Di & Rosengren, Aaron J 2020, Science advances, 6, eabd1313CrossRefGoogle Scholar