Tabaré Gallardo

The dynamics of the HD 12661 extrasolar planetary system

The main goal of this work is to analyze the possible dynamical mechanisms that dominate the motion of the HD 12661 extrasolar planetary system. By an analytical approach using the expansion of the disturbing function given by Ellis and Murray, we solve the equation of motion working in a Hamiltonian formulation with the corresponding canonical variables and by means of appropriate canonical transformations. Comparing these results with a direct numerical integration, we can conclude that the system is dominated by a pure secular evolution that is very well reproduced with a disturbing function including at least sixth-order terms in the eccentricities. Because of the uncertainties in the orbital elements of the planets, we also contemplate the occurrence of mean motion resonances in the system and analyze possible contribution from these resonant terms to the total motion.

The relativistic factor in the orbital dynamics of point masses

There is a growing population of relativistically relevant minor bodies in the Solar System and a growing population of massive extrasolar planets with orbits very close to the central star where relativistic effects should have some signature. Our purpose is to review how general relativity affects the orbital dynamics of the planetary systems and to define a suitable relativistic correction for Solar System orbital studies when only point masses are considered. Using relativistic formulae for the N body problem suited for a planetary system given in the literature we present a series of numerical orbital integrations designed to test the relevance of the effects due to the general theory of relativity in the case of our Solar System. Comparison between different algorithms for accounting for the relativistic corrections are performed. Relativistic effects generated by the Sun or by the central star are the most relevant ones and produce evident modifications in the secular dynamics of the inner Solar System. The Kozai mechanism, for example, is modified due to the relativistic effects on the argument of the perihelion. Relativistic effects generated by planets instead are of very low relevance but detectable in numerical simulations.

Planetary and satellite three body mean motion resonances

Abstract We propose a semianalytical method to compute the strengths on each of the three massive bodies participating in a three body mean motion resonance (3BR). Applying this method we explore the dependence of the strength on the masses, the orbital parameters and the order of the resonance and we compare with previous studies. We confirm that for low eccentricity low inclination orbits zero order resonances are the strongest ones; but for excited orbits higher order 3BRs become also dynamically relevant. By means of numerical integrations and the construction of dynamical maps we check some of the predictions of the method. We numerically explore the possibility of a planetary system to be trapped in a 3BR due to a migrating scenario. Our results suggest that capture in a chain of two body resonances is more probable than a capture in a pure 3BR. When a system is locked in a 3BR and one of the planets is forced to migrate the other two can react migrating in different directions. We exemplify studying the case of the Galilean satellites where we show the relevance of the different resonances acting on the three innermost satellites.

The Scattered Disk Population and the Oort Cloud

The trans-Neptunian belt has been subject to a strong depletion that has reduced its primordial population by a factor of one hundred over the solar systems age. One by-product of such a depletion process is the existence of a scattered disk population in transit from the belt to other places, such as the Jupiter zone, the Oort cloud or interstellar space. We have integrated the orbits of the scattered disk objects (SDOs) so far discovered by 2500 Myr to study their dynamical time scales and the probability of falling in each of the end states mentioned above, paying special attention to their contribution to the Oort cloud. We found that their dynamical half-time is close to 2.5 Gyr and that about one third of the SDOs end up in the Oort cloud.

Dynamical evolution and end states of active and inactive Centaurs

Abstract We numerically study the dynamical evolution of observed samples of active and inactive Centaurs and clones that reach the Jupiter-Saturn region. Our aim is to compare the evolution between active and inactive Centaurs, their end states and their transfer to Jupiter family comets and Halley-type comets. We find that the median lifetime of inactive Centaurs is about twice longer than that for active Centaurs, suggesting that activity is related to the residence time in the region. This view is strengthened by the observation that high-inclination and retrograde Centaurs (Tisserand parameters with respect to Jupiter T J 2 ) which have the longest median dynamical lifetime ( = 1.37 × 10 6 yr) are all inactive. We also find that the perihelion distances of some active, comet-like Centaurs have experienced drastic drops of a few au in the recent past ( ∼ 10 2 − 10 3 yr), while such drops are not found among inactive Centaurs. Inactive Centaurs with T J ≲ 2.5 usually evolve to Halley-type comets, whereas inactive Centaurs with T J ≳ 2.5 and active Centaurs (that also have T J ≳ 2.5 ) evolve almost always to Jupiter family comets and very seldom to Halley type comets. Inactive Centaurs are also more prone to end up as sungrazers, and both inactive and active Centaurs transit through different mean motion resonances (generally with Jupiter) during their evolution.

Resonances in the asteroid and trans–Neptunian belts: A brief review

Abstract Mean motion resonances play a fundamental role in the dynamics of the small bodies of the Solar System. The last decades of the 20th century gave us a detailed description of the dynamics as well as the process of capture of small bodies in coplanar or small inclination resonant orbits. More recently, semianalytical or numerical methods allowed us to explore the behavior of resonant motions for arbitrary inclination orbits. The emerging dynamics is very rich, including large orbital changes due to secular effects inside mean motion resonances. The process of capture in highly inclined or retrograde resonant orbits was addressed showing that the capture in retrograde resonances is more efficient than in direct ones. A new terminology appeared in order to characterize the properties of the resonances. Numerical explorations in the transneptunian region showed the relevance and the particular dynamics of the exterior resonances with Neptune which can account for some of the known high perihelion orbits in the scattered disk. Moreover, several asteroids evolving in resonance with planets other than Jupiter or Neptune were found and a large number of asteroids in three-body resonances were identified.

Strength, stability and three dimensional structure of mean motion resonances in the solar system

Abstract In the framework of the circular restricted three body problem we show that the numerically computed strength SR(e, i, ω) is a good indicator of the strength and width of the mean-motion resonances in the full space (e, i, ω). We present a survey of strengths in the space (e, i) for typical interior and exterior resonances. The resonance strength is highly dependent on (e, i, ω) except for exterior resonances of the type 1:k for which the dependence with (i, ω) is softer. Such resonances are thus strong even for retrograde orbits. All other resonances are weaker at very-high eccentricities for ω ∼ 90° or 270° and 60° ≲ i ≲ 120°. We explore the resonance structure in the space (a, i) by means of dynamical maps and we find structures similar to those of space (a, e).

Co–orbital resonance with a migrating proto–giant planet

Abstract In this work we pose the possibility that, at an early stage, the migration of a proto–giant planet caused by the presence of a gaseous circumstellar disk could explain the continuous feeding of small bodies into its orbit. Particularly, we study the probability of capture and permanence in co–orbital resonance of these small bodies, as planets of diverse masses migrate by interaction with the gaseous disk, and the drag induced by this disk dissipates energy from these small objects, making capture more likely. Also, we study the relevance of the circumplanetary disk, a structure formed closely around the planet where the gas density is enhanced, in the process of capture. It is of great interest for us to study the capture of small bodies in 1:1 resonance because it could account for the origin of the Trojan population, which has been proposed (Kortenkamp and Joseph, 2011) as a mechanism of quasi-satellites and irregular satellites capture.

How to take into account the relativistic effects in dynamical studies of comets

Comet-like orbits with low perihelion distances tend to be affected by relativistic effects. In this work we discuss the origin of the relativistic corrections, how they affect the orbital evolution and how to implement these corrections in a numerical integrator. We also propose a model that mimics the principal relativistic effects and, contrary to the original ”exact” formula, has low computational cost. Our model is appropriated for numerical simulations but not for precise ephemeris computations.