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Closed-form perturbation theory in the Sun-Jupiter restricted three body problem without relegation

Published online by Cambridge University Press:  30 May 2022

Irene Cavallari Open the ORCID record for Irene Cavallari [Opens in a new window]  and
Christos Efthymiopoulos
Irene Cavallari
Affiliation:
Dept. of Mathematics, University of Pisa, Pisa, 56127, Italy email: irene.cavallari@dm.unipi.it
Christos Efthymiopoulos
Affiliation:
Dept. of Mathematics Tullio Levi-Civita, University of Padua, Padua, 35121, Italy email: cefthym@math.unipd.it
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Abstract

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We present a closed-form normalization method suitable for the study of the secular dynamics of small bodies inside the trajectory of Jupiter. The method is based on a convenient use of a book-keeping parameter introduced not only in the Lie series organization but also in the Poisson bracket structure employed in all perturbative steps. In particular, we show how the above scheme leads to a redefinition of the remainder of the normal form at every step of the formal solution of the homological equation. An application is given for the semi-analytical representation of the orbits of main belt asteroids.

Keywords

celestial mechanicsmethods: analyticalsolar system
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. 113 - 119
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of International Astronomical Union

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