Papers by S. Ferraz-mello
Celestial Mechanics and Dynamical Astronomy
The Dynamics of Small Bodies in the Solar System, 1999
We study a modelling of the averaged librations of asteroids in a first order resonance with Jupi... more We study a modelling of the averaged librations of asteroids in a first order resonance with Jupiter based on an asymmetric expansion of the non planar disturbing potential about a libration center with non zero eccentricity. A derivation of an abridged dynamical system that represents the averaged motion of an asteroid in a first order resonance with Jupiter is presented. In this system the perturber lies on an elliptic orbit and the model is more suited for the analysis of the gravitational phenomena in the asteroidal belt than the classical integrable models imposing a circular motion on Jupiter. The libration laws with the proper frequencies that characterize the small amplitude solutions are obtained without any restriction to asteroid eccentricity.
Periodic Orbits, Stability and Resonances, 1970
The purpose of this report is to present some results of the researches carried out, at the Astro... more The purpose of this report is to present some results of the researches carried out, at the Astronomical Observatory of the Technological Institute of Aeronautics, on the problem of construction of absolute orbits in connection with the problem of the motion of the four great satellites of Jupiter.
Extrasolar Planets
... 7 Dynamics of the Extrasolar Planetary Systems Tatiana A. Michtchenko, Sylvio Ferraz-Mello, a... more ... 7 Dynamics of the Extrasolar Planetary Systems Tatiana A. Michtchenko, Sylvio Ferraz-Mello, and Christian Beaugé ... the mutual gravitational interactions may produce an intricate set of complex dynamical effects, hard to explain without the basic concepts of ana-lytical studies. ...
... and J. GETINO-About the ap-plication of action-angle variables to the rotation of deformablec... more ... and J. GETINO-About the ap-plication of action-angle variables to the rotation of deformableceles-tial bodies ... THE CALCULUS OF PERTURBATIONS JD HADJIDEMETRIOU-Symplectic mappings.(Lecture) 255 A. DEPRIT-L'algebre symbolique en mecanique celeste.(Lecture ...
Celestial Mechanics and Dynamical Astronomy, 2010
We present a short account of facts related to the discovery of several multiplanet systems aroun... more We present a short account of facts related to the discovery of several multiplanet systems around nearby stars, and of the systems stability in presence of resonances. The domains of chaotic motion near one planet of PSR 1257+12 are shown.
Proceedings of the International Astronomical Union, 2004
This paper reviews recent results on the dynamics of multiple-planet extra-solar systems, includi... more This paper reviews recent results on the dynamics of multiple-planet extra-solar systems, including main sequence stars and the pulsar PSR B1257+12 and, comparatively, our own Solar System. Taking into account the degree of gravitational interaction of the planets, the known planetary systems may be separated into four main groups: (Ia) Planets in Mean-motion resonance (Ib) Low-eccentricity near-resonant pairs; (II) Non-resonant planets with a significant secular dynamics; and (III) Weakly interacting planet pairs. Different analytical and numerical tools can help to understand the structure of the phase space, to identify stability mechanisms and to categorize different types of motions in the cases of more significant dynamical interaction. The origin of resonant configurations is discussed in the light of the hypothesis of planetary migration.
Research in Astronomy and Astrophysics, 2012
20 years after the discovery of the first planets outside our solar system, the current exoplanet... more 20 years after the discovery of the first planets outside our solar system, the current exoplanetary population includes more than 700 confirmed planets around main sequence stars. Approximately 50% belong to multiple-planet systems in very diverse dynamical configurations, from two-planet hierarchical systems to multiple resonances that could only have been attained as the consequence of a smooth largescale orbital migration. The first part of this paper reviews the main detection techniques employed for the detection and orbital characterization of multiple-planet systems, from the (now) classical radial velocity (RV) method to the use of transit time variations (TTV) for the identification of additional planetary bodies orbiting the same star. In the second part we discuss the dynamical evolution of multi-planet systems due to their mutual gravitational interactions. We analyze possible modes of motion for hierarchical, secular or resonant configurations, and what stability criteria can be defined in each case. In some cases, the dynamics can be well approximated by simple analytical expressions for the Hamiltonian function, while other configurations can only be studied with semi-analytical or numerical tools. In particular, we show how meanmotion resonances can generate complex structures in the phase space where different libration islands and circulation domains are separated by chaotic layers. In all cases we use real exoplanetary systems as working examples.
Proceedings of the International Astronomical Union
Preface; Organizing committee; Conference participants; Part I. Exoplanet Detection; Part II. Phy... more Preface; Organizing committee; Conference participants; Part I. Exoplanet Detection; Part II. Physics of Atmospheres and Close-in Planets; Part III. Planet Formation; Part IV. Protoplanetary Disks and Migration; Part V. Dynamics of Multiple Exoplanet Systems; Author index; Object index.
Celestial Mechanics and Dynamical Astronomy
Study of stationary solutions of the problem of the motion of an artificial satellite averaged ne... more Study of stationary solutions of the problem of the motion of an artificial satellite averaged near a first-order resonance with the rotation of the Earth. Determination of the law of structure giving the position of the libration centers and the libration periods for 12-hr satellites.
Proceedings of the International Astronomical Union
Periodic Orbits and Variational Methods.- On the variational approach to the periodic n-body prob... more Periodic Orbits and Variational Methods.- On the variational approach to the periodic n-body problem.- On families of periodic solutions of the restricted three-body problem.- Hip-hop solutions of the 2N-body problem.- Double choreographical solutions for n-body type problems.- From the circular to the spatial elliptic restricted three-body problem.- Stability of axial orbits in galactic potentials.- Perturbation Theory and Regularization.- KAM tori for N-body problems: a brief history.- Analysis of the chaotic behaviour of orbits diffusing along the Arnold web.- The scattering map in the planar restricted three body problem.- On final evolutions in the restricted planar parabolic three-body problem.- Quaternions and the perturbed Kepler problem.- Dynamics of Solar and Extrasolar Systems.- The 3:2 spin-orbit resonant motion of Mercury.- Symmetric and asymmetric librations in extrasolar planetary systems: a global view.- The influence of mutual perturbations on the eccentricity excit...
t the opening of the "Third Meeting on Celestial Mechanics - CELMEC III", strong sensat... more t the opening of the "Third Meeting on Celestial Mechanics - CELMEC III", strong sensations hit our minds. The conference (18-22 June 2001) was being held in Villa Mondragone, a beautiful complex of buildings and gardens located within the township of Monte Porzio Catone, on the hills surrounding Rome. A former papal residence, the building has been recently restored by the University of Rome "Tor Vergata" to host academic activities and events
The Dynamics of Small Bodies in the Solar System, 1999
The determination of the maximum Lyapunov exponents in the 2/1 and 3/2 Jovian resonances (Ferraz-... more The determination of the maximum Lyapunov exponents in the 2/1 and 3/2 Jovian resonances (Ferraz-Mello 1994) suggested that the chaotic diffusion in the 2/1 resonance may be much faster than in the 3/2. As this fact could explain why the primordial population of the 2/1 resonance was removed (forming the Hecuba gap) and the 3/2-population was kept (Hilda group), we have decided to evaluate the diffusion speed for a large number of initial conditions using the frequency map analysis of Laskar (1988) (see also: Laskar 1996), adapted for the particular problem of Jovian resonances (Nesvorý and Ferraz-Mello 1997a). The ‘diffusion maps’ were also computed for the 4/3 Jovian resonance as it is, due to its similarity to the 3/2 resonance, a potential candidate for stable motion.
Modern Celestial Mechanics: From Theory to Applications, 2002
Explicit construction of the solutions of the Hamiltonian system given by H = H 0 (J) − εA(J) cos... more Explicit construction of the solutions of the Hamiltonian system given by H = H 0 (J) − εA(J) cos θ (ideal resonance problem), two orders of approximation beyond the well-known pendulum approximation. The given solutions are valid for libration amplitudes of order O(4 √ ε). The procedure used is extended to allow the construction of the solutions of Hamiltonians with perturbations involving two degrees of freedom; the post-pendulum solution of an example of this kind is constructed.
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Papers by S. Ferraz-mello