arXiv subjects

Philippe Robutel

Publications and source records attributed to Philippe Robutel.

24 records · Page 2Linked to original sources

arXiv2014

Spin-orbit resonances and rotation of coorbital bodies in quasi-circular orbits

The rotation of asymmetric bodies in eccentric Keplerian orbits can be chaotic when there is some overlap of spin-orbit resonances. Here we show that the rotation of two coorbital bodies (two planets orbiting a star or two satellites of a planet) can also be chaotic even for quasi-circular orbits around the central body. When dissipation is present, the rotation period of a body on a nearly circular orbit is believed to always end synchronous with the orbital period. Here we demonstrate that for coorbital bodies in quasi-circular orbits, stable non-synchronous rotation is possible for a wide range of mass ratios and body shapes. We further show that the rotation becomes chaotic when the natural rotational libration frequency, due to the axial asymmetry, is of the same order of magnitude as the orbital libration frequency.

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arXiv2013

Spin-orbit coupling and chaotic rotation for coorbital bodies in quasi-circular orbits

Coorbital bodies are observed around the Sun sharing their orbits with the planets, but also in some pairs of satellites around Saturn. The existence of coorbital planets around other stars has also been proposed. For close-in planets and satellites, the rotation slowly evolves due to dissipative tidal effects until some kind of equilibrium is reached. When the orbits are nearly circular, the rotation period is believed to always end synchronous with the orbital period. Here we demonstrate that for coorbital bodies in quasi-circular orbits, stable non-synchronous rotation is possible for a wide range of mass ratios and body shapes. We show the existence of an entirely new family of spin-orbit resonances at the frequencies $n\pm kν/2$, where $n$ is the orbital mean motion, $ν$ the orbital libration frequency, and $k$ an integer. In addition, when the natural rotational libration frequency due to the axial asymmetry, $σ$, has the same magnitude as $ν$, the rotation becomes chaotic. Saturn coorbital satellites are synchronous since $ν\llσ$, but coorbital exoplanets may present non-synchronous or chaotic rotation. Our results prove that the spin dynamics of a body cannot be dissociated from its orbital environment. We further anticipate that a similar mechanism may affect the rotation of bodies in any mean-motion resonance.

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arXiv2013

On the co-orbital motion of two planets in quasi-circular orbits

We develop an analytical Hamiltonian formalism adapted to the study of the motion of two planets in co-orbital resonance. The Hamiltonian, averaged over one of the planetary mean longitude, is expanded in power series of eccentricities and inclinations. The model, which is valid in the entire co-orbital region, possesses an integrable approximation modeling the planar and quasi-circular motions. First, focusing on the fixed points of this approximation, we highlight relations linking the eigenvectors of the associated linearized differential system and the existence of certain remarkable orbits like the elliptic Eulerian Lagrangian configurations, the Anti-Lagrange (Giuppone et al., 2010) orbits and some second sort orbits discovered by Poincaré. Then, the variational equation is studied in the vicinity of any quasi-circular periodic solution. The fundamental frequencies of the trajectory are deduced and possible occurrence of low order resonances are discussed. Finally, with the help of the construction of a Birkhoff normal form, we prove that the elliptic Lagrangian equilateral configurations and the Anti-Lagrange orbits bifurcate from the same fixed point L4.

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arXiv2012

Influence of the coorbital resonance on the rotation of the Trojan satellites of Saturn

The Cassini spacecraft collects high resolution images of the saturnian satellites and reveals the surface of these new worlds. The shape and rotation of the satellites can be determined from the Cassini Imaging Science Subsystem data, employing limb coordinates and stereogrammetric control points. This is the case for Epimetheus (Tiscareno et al. 2009) that opens elaboration of new rotational models (Tiscareno et al. 2009; Noyelles 2010; Robutel et al. 2011). Especially, Epimetheus is characterized by its horseshoe shape orbit and the presence of the swap is essential to introduce explicitly into rotational models. During its journey in the saturnian system, Cassini spacecraft accumulates the observational data of the other satellites and it will be possible to determine the rotational parameters of several of them. To prepare these future observations, we built rotational models of the coorbital (also called Trojan) satellites Telesto, Calypso, Helene, and Polydeuces, in addition to Janus and Epimetheus. Indeed, Telesto and Calypso orbit around the L_4 and L_5 Lagrange points of Saturn-Tethys while Helene and Polydeuces are coorbital of Dione. The goal of this study is to understand how the departure from the Keplerian motion induced by the perturbations of the coorbital body, influences the rotation of these satellites. To this aim, we introduce explicitly the perturbation in the rotational equations by using the formalism developed by Erdi (1977) to represent the coorbital motions, and so we describe the rotational motion of the coorbitals, Janus and Epimetheus included, in compact form.

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arXiv2010

Analytical description of physical librations of Saturnian coorbital satellites Janus and Epimetheus

Janus and Epimetheus are famously known for their distinctive horseshoe-shaped orbits resulting from a 1:1 orbital resonance. Every four years these two satellites swap their orbits by a few tens of kilometers as a result of their close encounter. Recently Tiscareno et al. (2009) have proposed a model of rotation based on images from the Cassini orbiter. These authors inferred the amplitude of rotational librational motion in longitude at the orbital period by fitting a shape model to the recent Cassini ISS images. By a quasiperiodic approximation of the orbital motion, we describe how the orbital swap impacts the rotation of the satellites. To that purpose, we have developed a formalism based on quasi-periodic series with long and short-period librations. In this framework, the amplitude of the libration at the orbital period is found proportional to a term accounting for the orbital swap. We checked the analytical quasi-periodic development by performing a numerical simulation and find both results in good agreement. To complete this study, the results regarding the short-period librations are studied with the help of an adiabatic-like approach.

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arXiv2009

The resonant structure of Jupiter's trojan asteroids-II. What happens for different configurations of the planetary system

In a previous paper, we have found that the resonance structure of the present Jupiter Trojan swarms could be split up into four different families of resonances. Here, in a first step, we generalize these families in order to describe the resonances occurring in Trojan swarms embedded in a generic planetary system. The location of these families changes under a modification of the fundamental frequencies of the planets and we show how the resonant structure would evolve during a planetary migration. We present a general method, based on the knowledge of the fundamental frequencies of the planets and on those that can be reached by the Trojans, which makes it possible to predict and localize the main events arising in the swarms during migration. In particular, we show how the size and stability of the Trojan swarms are affected by the modification of the frequencies of the planets. Finally, we use this method to study the global dynamics of the Jovian Trojan swarms when Saturn migrates outwards. Besides the two resonances found by Morbidelli et al (2005) which could have led to the capture of the current population just after the crossing of the 2:1 orbital resonance, we also point out several sequences of chaotic events that can influence the Trojan population.

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