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Satellites’ orbital stability through normal forms

Published online by Cambridge University Press:  30 May 2022

Irene De Blasi Open the ORCID record for Irene De Blasi [Opens in a new window] ,
Alessandra Celletti  and
Christos Efthymiopoulos
Irene De Blasi
Affiliation:
Department of Mathematics, University of Turin and Politecnico of Turin, Turin, Italy email: irene.deblasi@unito.it
Alessandra Celletti
Affiliation:
Department of Mathematics, University of Roma Tor Vergata, Rome, Italy email: celletti@mat.uniroma2.it
Christos Efthymiopoulos
Affiliation:
Department of Mathematics, University of Padova, Padua, Italy email: cefthym@math.unipd.it
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Abstract

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A powerful tool to investigate the stability of the orbits of natural and artificial bodies is represented by perturbation theory, which allows one to provide normal form estimates for nearly-integrable problems in Celestial Mechanics. In particular, we consider the orbital stability of point-mass satellites moving around the Earth. On the basis of the J 2 model, we investigate the stability of the semimajor axis. Using a secular Hamiltonian model including also lunisolar perturbations, the so-called geolunisolar model, we study the stability of the other orbital elements, namely the eccentricity and the inclination. We finally discuss the applicability of Nekhoroshev’s theorem on the exponential stability of the action variables. To this end, we investigate the non-degeneracy properties of the J 2 and geolunisolar models. We obtain that the J 2 model satisfies a “three-jet” non-degeneracy condition, while the geolunisolar model is quasi-convex non-degenerate.

Keywords

Celestial mechanicsNormal formsSatellite dynamics
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. 146 - 151
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

References

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