Seminario di Fisica Matematica: “Around quasi-satellites and remarkable configurations in the co-orbital resonance”

Mercoledì 28 Giugno 2017, ore 11:30 - Aula 2BC30 - Alexandre Pousse


Mercoledì 28 Giugno 2017 alle ore 11:30 in Aula 2BC30, Alexandre Pousse (Dipartimento di Matematica e Applicazioni “R. Caccioppoli” - Università di Napoli) terrà un seminario dal titolo “Around quasi-satellites and remarkable configurations in the co-orbital resonance”.

My talk will focus on the study of the co-orbital resonance in the three-body problem.
This domain of particular trajectories, where an asteroid and a planet gravitate around the Sun with the same period possesses a very rich dynamics connected to the famous Lagrange?s equilateral configurations $L_4$ and $L_5$, as well as to the Eulerian?s configurations $L_1$, $L_2$ and $L_3$. A major example in the solar system is given by the Trojan asteroids harboured by Jupiter in the neighbourhood of $L_4$ and $L_5$. A second astonishing configuration is given by the system Saturn-Janus-Epimetheus; this peculiar dynamics is known as “horseshoe”.
Recently, a new type of dynamics has been highlighted in the context of co-orbital resonance: the quasi-satellites. They correspond to remarkable configurations: in the rotating frame with the planet, the trajectory of the asteroid seems the one of a retrograde satellite. Some asteroids harboured by Venus, Jupiter and the Earth has been observed in this kind of configuration.
The quasi-satellite dynamics possesses great interest not only because it connects the different domains of the co-orbital resonance (see works of Namouni, 1999), but also because it seems to bridge the gap between satellization and heliocentric trajectories. However, despite the term quasi-satellite has become dominant in the celestial mechanics community, some authors rather use the term “retrograde satellite” which reveals an ambiguity on the definition of these trajectories.
In the first part of my talk, I will present a numerical study that clarify the definition of these orbits by revisiting the planar-circular case (planet on circular motion) and describe the idea of an analytic method adapted to explore the quasi-satellite domain.
All the previous results involve the averaged problem, an approximation of the Three-Body Problem. KAM type results on co-orbital motions are possible: in the last part of my talk, I will sketch in which frame we intend to give a rigorous proof (and up to our knowledge, the first one) of existence of the “horseshoe” dynamics over infinite times.
This last part is a joint work with Laurent Niederman (Observatoire de Paris, Universite? Paris XI “Orsay”) and Philippe Robutel (Observatoire de Paris).

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