A possible long-lived asteroid population at the equilateral Lagrangian points of Saturn

The Lagrangian equilateral points of a planetary orbit are points of equilibrium that trail at 60°, ahead (L4) or behind (L5), the trajectory of a planet. Jupiter is the only major planet in our Solar system harbouring a known population of asteroids at those locations. Here we report the existence of orbits close to the Lagrangian points of Saturn, stable at time-scales comparable to the age of the Solar system. By scaling with respect to the Trojan population we have estimated the number of objects that would populate the regions, which gives a significant figure. Moreover, mutual physical collisions over the age of the Solar system would be very rare, so the evaporation rate of this swarm arising from mutual interactions would be very low. A population of asteroids not self-collisionally evolved after their formation stage would be the first to be observed in our planetary system. Our present estimations are based on the assumption that the capture efficiency at Saturn's equilateral points is comparable with the one corresponding to Jupiter, thus our figures may be taken as upper limits. In any case, observational constraints on their number would provide fundamental clues to our understanding of the history of the outer Solar system. If they existed, the surface properties and size distribution of those objects would represent unusually valuable fossil records of our early planetary system.Facultad de Ciencias Astronómicas y Geofísica

On the accretion of Uranus and Neptune

In this paper, we discuss some problems concerning the formation of Uranus and Neptune. We find that the adoption of reduced Hill spheres as the region of close interaction between planetesimals introduces an enhancement of the gravitational cross-sections in previous numerical simulations. We also discuss a way to make possible the formation of Uranus and Neptune on time-scales shorter than the age of the Solar system.Facultad de Ciencias Astronómicas y Geofísica

An alternative stable solution for the Kepler-419 system, obtained with the use of a genetic algorithm

Context. The mid-Transit times of an exoplanet may be nonperiodic. The variations in the timing of the transits with respect to a single period, that is, the transit timing variations (TTVs), can sometimes be attributed to perturbations by other exoplanets present in the system, which may or may not transit the star. Aims. Our aim is to compute the mass and the six orbital elements of an nontransiting exoplanet, given only the central times of transit of the transiting body. We also aim to recover the mass of the star and the mass and orbital elements of the transiting exoplanet, suitably modified in order to decrease the deviation between the observed and the computed transit times by as much as possible. Methods. We have applied our method, based on a genetic algorithm, to the Kepler-419 system. Results. We were able to compute all 14 free parameters of the system, which, when integrated in time, give transits within the observational errors. We also studied the dynamics and the long-Term orbital evolution of the Kepler-419 planetary system as defined by the orbital elements computed by us, in order to determine its stability.Instituto de Astrofísica de La Plat

An alternative stable solution for the Kepler-419 system, obtained with the use of a genetic algorithm

Context. The mid-Transit times of an exoplanet may be nonperiodic. The variations in the timing of the transits with respect to a single period, that is, the transit timing variations (TTVs), can sometimes be attributed to perturbations by other exoplanets present in the system, which may or may not transit the star. Aims. Our aim is to compute the mass and the six orbital elements of an nontransiting exoplanet, given only the central times of transit of the transiting body. We also aim to recover the mass of the star and the mass and orbital elements of the transiting exoplanet, suitably modified in order to decrease the deviation between the observed and the computed transit times by as much as possible. Methods. We have applied our method, based on a genetic algorithm, to the Kepler-419 system. Results. We were able to compute all 14 free parameters of the system, which, when integrated in time, give transits within the observational errors. We also studied the dynamics and the long-Term orbital evolution of the Kepler-419 planetary system as defined by the orbital elements computed by us, in order to determine its stability.Instituto de Astrofísica de La Plat

Apse-alignment in narrow-eccentric ringlets and its implications for the ϵ-ring of Uranus and the ring system of (10199) Chariklo

The discovery of ring systems around objects of the outer Solar System provides a strong motivation to apply theoretical models in order to better estimate their physical and orbital parameters, which can constrain scenarios for their origin. We review the criterion for maintaining apse-alignment across a ring and the balance between the energy input rate provided by a close by satellite and the internal dissipation rate occurring through ring particle collisions that is required to maintain ring eccentricity, as derived from the equations of motion governing the Lagrangian-displacements of the ring-particle orbits. We use the case of the ϵ -ring of Uranus, to calibrate our theoretical discussion and illustrate the basic dynamics governing these types of ring. In the case of the ring system of (10199) Chariklo, where the evidence that the rings are eccentric is not conclusive, we apply the theory of apse-alignment to derive information about the most plausible combination of values of the surface density and eccentricity-gradient, as well as the masses and locations of their postulated but -presently undetected- shepherd-satellites. When the balance conditions that we predict are applied to the ring system of (10199) Chariklo, we are able to estimate the minimum mass of a shepherd satellite required to prevent eccentricity decay, as a function of its orbital location, for two different models of dissipation. We conclude that the satellite mass required to maintain the m  = 1 eccentric mode in the ring, would be similar or smaller than that needed to confine the rings radially. Our estimation of the most plausible combinations of eccentricity gradient and surface density consistent with apse-alignment are based on a standard model for the radial form of the surface density distribution, which approximately agrees with the optical depth profile derived by the stellar occultations. We find a diverse range of solutions, with combinations of eccentricity gradient and surface mass density that tend to minimize required enhanced collisional effects, having adopted estimated values of the form factor of the second degree harmonic of the gravitational potential.Facultad de Ciencias Astronómicas y Geofísica

A possible long-lived asteroid population at the equilateral Lagrangian points of Saturn

The Lagrangian equilateral points of a planetary orbit are points of equilibrium that trail at 60°, ahead (L4) or behind (L5), the trajectory of a planet. Jupiter is the only major planet in our Solar system harbouring a known population of asteroids at those locations. Here we report the existence of orbits close to the Lagrangian points of Saturn, stable at time-scales comparable to the age of the Solar system. By scaling with respect to the Trojan population we have estimated the number of objects that would populate the regions, which gives a significant figure. Moreover, mutual physical collisions over the age of the Solar system would be very rare, so the evaporation rate of this swarm arising from mutual interactions would be very low. A population of asteroids not self-collisionally evolved after their formation stage would be the first to be observed in our planetary system. Our present estimations are based on the assumption that the capture efficiency at Saturn's equilateral points is comparable with the one corresponding to Jupiter, thus our figures may be taken as upper limits. In any case, observational constraints on their number would provide fundamental clues to our understanding of the history of the outer Solar system. If they existed, the surface properties and size distribution of those objects would represent unusually valuable fossil records of our early planetary system.Facultad de Ciencias Astronómicas y Geofísica

On the accretion of Uranus and Neptune

In this paper, we discuss some problems concerning the formation of Uranus and Neptune. We find that the adoption of reduced Hill spheres as the region of close interaction between planetesimals introduces an enhancement of the gravitational cross-sections in previous numerical simulations. We also discuss a way to make possible the formation of Uranus and Neptune on time-scales shorter than the age of the Solar system.Facultad de Ciencias Astronómicas y Geofísica