Alexandre Pousse

2020. "On the co-orbital motion in three-body problem: the existence of quasi-periodic horseshoe-shaped orbits"

L. Niederman, A. Pousse, and P. Robutel, Commun. Math. Phys., 377, 551-612. 

https://doi.org/10.1007/s00220-020-03690-8

Janus and Epimetheus are two moons of Saturn with very peculiar motions. As they orbit around Saturn on quasi-coplanar and quasi-circular trajectories whose radii are only 50 km apart (less than their respective diameters), every four (terrestrial) years the bodies approach each other and their mutual gravitational influence lead to a swapping of the orbits: the outer moon becomes the inner one and vice-versa. This behavior generates [...] arXiv:1806.07262

 2017. "On the co-orbital motion in the planar restricted three-body problem: the quasi-satellite motion revisited" 

A. Pousse, P. Robutel, and A. Vienne, Celest. Mech. Dyn. Astron., 128 (4): 383-407. 

https://doi.org/10.1007/s10569-016-9749-1

In the framework of the planar and circular restricted three-body problem, we consider an asteroid that orbits the Sun in quasi-satellite motion with a planet. A quasi-satellite trajectory is a heliocentric orbit in co-orbital resonance with the planet, characterized by a nonzero eccentricity and a resonant angle that librates around zero. Likewise, in the rotating frame with the planet, it describes the same trajectory as the one of a retrograde satellite [...] arXiv:1603.06543 

2018. "Janus et Epimethee: un ballet perpetuel autour de Saturne? De l’observation astronomique à la theorie KAM"

A. Pousse, L. Niederman, and  P. Robutel, Images des Mathematiques, CNRS.

http://images.math.cnrs.fr/Janus-et-Epimethee-un-ballet-perpetuel-autour-de-Saturne

(In French) Popular science article associated with the work "On the co-orbital motion in the three-body problem: existence of quasi-periodic horseshoe-shaped orbits" from the same authors. Janus and Epimetheus are two moons of Saturn which exhibit a really peculiar dynamics. As they orbit on circular trajectories whose radii are only 50 km apart (less than their respective diameters), every four (terrestrial) years the bodies are getting closer and their mutual gravitational influence leads to a swapping of the orbits: the outer moon becoming the inner one and vice-versa. In this article, we describe how, from this specific astronomical problem to the KAM theory, we came to prove the existence of perpetually stable trajectories associated with the Janus and Epimetheus orbits. arXiv:1807.10220

2014. "The family of Quasi-satellite periodic orbits in the circular co-planar RTBP". 

A. Pousse, P. Robutel, and A. Vienne, Proceedings of the International Astronomical Union, 9(S310), 172-173. 

https://doi.org/10.1017/S1743921314008175, arXiv:1412.3540

2016. "Les quasi-satellites et autres configurations remarquables en resonance co-orbitale"

A. Pousse, Ecole doctorale Astronomie et astrophysique d’Ile-de-France

https://www.theses.fr/2016PSLEO006 

(In French) This work of thesis focuses on the study of the coorbital resonance. 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 L4 and L5, as well as to the Eulerian’s configurations L1, L2 and L3. A major example in the solar system is given by the "Trojan" asteroids harboured by Jupiter in the neighborhood of L4 and L5. 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 have 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". This reveals an ambiguity on the definition of these trajectories. For these reasons, the first part of this thesis consisted in clarifying the definition of these orbits by revisiting the planar-circular case (planet on circular motion) in the framework of the averaged problem. In the second part of this thesis, we developed an analytic method to explore the quasi-satellite domain in the averaged problem. We realized this exploration in the planar-circular case and proposed an extension to the planar-eccentric and spatial-circular cases. The recent discoveries around the exo-planets motivated some works on the co-orbital resonance in the planetary Three-Body Problem. In this context, Giuppone et al. (2010) highlighted (numerically) the quasi-satellite as well as new families of remarkable configurations: the "anti-Lagrange". Then the third part of this thesis presents an analytical method for the planetary problem that allows to reveal the anti-Lagrange orbits as well as a sketch of study of quasi-satellite trajectories.