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

Abstract

International audienceIn 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 non zero 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 even though the planet acts as a perturbator. In the last few years, the discoveries of asteroids in this type of motion made the term " quasi-satellite " more and more present in the literature. However, some authors rather use the term " retrograde satellite " when referring to this kind of motion in the studies of the restricted problem in the rotating frame. In this paper we intend to clarify the terminology to use, in order to bridge the gap between the perturbative co-orbital point of view and the more general approach in the rotating frame. Through a numerical exploration of the co-orbital phase space, we describe the quasi-satellite domain and highlight that it is not reachable by low eccentricities by averaging process. We will show that the quasi-satellite domain is effectively included in the domain of the retrograde satellites and neatly defined in terms of frequencies. Eventually, we highlight a remarkable high eccentric quasi-satellite orbit corresponding to a frozen ellipse in the heliocentric frame. We extend this result to the eccentric case (planet on an eccentric motion) and show that two families of frozen ellipses originate from this remarkable orbit

On quasi-satellite periodic motion in asteroid and planetary dynamics

“…The maximum amplitude of libration, θ max , which corresponds to the orbit of the last invariant tori of the island region, increases as the orbits become more distant from the Planet. This has been shown also by Pousse et al (2017) with the use of an average model. However, due to the absence of chaos in the averaged model, the maximum amplitude of libration is overestimated.…”

“…In the last twenty years, much attention has been given to QS asteroid motion. Evidence for the existence of stable QS-type motion around giant planets of our Solar system has been found after having considered analytical or semi-analytical perturbative methods (Mikkola and Innanen, 1997;Namouni, 1999;Nesvorný et al, 2002;Mikkola et al, 2006;Sidorenko et al, 2014;Pousse et al, 2017) or numerical integrations (Wiegert et al, 2000;Christou, 2000a,b). A lot of studies have also focused on particular observed asteroids and Centaurs e.g.…”

On the coplanar eccentric non-restricted co-orbital dynamics

“…However, if we consider the inclined and/or eccentric cases, the phase space is significantly more complex. New co-orbital configurations appear, such as quasi-satellites (Namouni 1999;Mikkola et al 2006;Sidorenko et al 2014;Pousse et al 2017) in the eccentric case and retrograde co-orbitals (Morais and Namouni 2013) in the inclined one. For no-null eccentricities and/or inclination, secular dynamics kicks in, increasing the number of dimension to consider in order to correctly describe the dynamics.…”

Asteroid 2017 FZ2 et al.: signs of recent mass-shedding from YORP?

“…Although the first quasi-satellite (of Jupiter) may have been identified (and lost) in 1973 (Chebotarev 1974), 10 the first bona fide quasi-satellite (of Venus in this case), 2002 VE 68 , was documented by Mikkola et al (2004). A modern theory of quasi-satellites has been developed in the papers by Mikkola et al (2006), Sidorenko et al (2014) and Pousse, Robutel & Vienne (2017). A recent review of confirmed quasi-satellites has been presented by de la Fuente Marcos & de la Fuente Marcos (2016e).…”