On The Effect of Giant Planets on the Scattering of Parent Bodies of Iron Meteorite from the Terrestrial Planet Region into the Asteroid Belt: A Concept Study

In their model for the origin of the parent bodies of iron meteorites, Bottke et al proposed differentiated planetesimals that were formed in the region of 1-2 AU during the first 1.5 Myr, as the parent bodies, and suggested that these objects and their fragments were scattered into the asteroid belt as a result of interactions with planetary embryos. Although viable, this model does not include the effect of a giant planet that might have existed or been growing in the outer regions. We present the results of a concept study where we have examined the effect of a planetary body in the orbit of Jupiter on the early scattering of planetesimals from terrestrial region into the asteroid belt. We integrated the orbits of a large battery of planetesimals in a disk of planetary embryos, and studied their evolutions for different values of the mass of the planet. Results indicate that when the mass of the planet is smaller than 10 Earth-masses, its effects on the interactions among planetesimals and planetary embryos is negligible. However, when the planet mass is between 10 and 50 Earth-masses, simulations point to a transitional regime with ~50 Earth-mass being the value for which the perturbing effect of the planet can no longer be ignored. Simulations also show that further increase of the mass of the planet strongly reduces the efficiency of the scattering of planetesimals from the terrestrial planet region into the asteroid belt. We present the results of our simulations and discuss their possible implications for the time of giant planet formation.Comment: 20 pages, 7 figures, accepted for publication in Ap

The evolution of the orbit distance in the double averaged restricted 3-body problem with crossing singularities

We study the long term evolution of the distance between two Keplerian confocal trajectories in the framework of the averaged restricted 3-body problem. The bodies may represent the Sun, a solar system planet and an asteroid. The secular evolution of the orbital elements of the asteroid is computed by averaging the equations of motion over the mean anomalies of the asteroid and the planet. When an orbit crossing with the planet occurs the averaged equations become singular. However, it is possible to define piecewise differentiable solutions by extending the averaged vector field beyond the singularity from both sides of the orbit crossing set. In this paper we improve the previous results, concerning in particular the singularity extraction technique, and show that the extended vector fields are Lipschitz-continuous. Moreover, we consider the distance between the Keplerian trajectories of the small body and of the planet. Apart from exceptional cases, we can select a sign for this distance so that it becomes an analytic map of the orbital elements near to crossing configurations. We prove that the evolution of the 'signed' distance along the averaged vector field is more regular than that of the elements in a neighborhood of crossing times. A comparison between averaged and non-averaged evolutions and an application of these results are shown using orbits of near-Earth asteroids.Comment: 29 pages, 8 figure

Terrestrial Planet Formation Constrained by Mars and the Structure of the Asteroid Belt

Reproducing the large Earth/Mars mass ratio requires a strong mass depletion in solids within the protoplanetary disk between 1 and 3 AU. The Grand Tack model invokes a specific migration history of the giant planets to remove most of the mass initially beyond 1 AU and to dynamically excite the asteroid belt. However, one could also invoke a steep density gradient created by inward drift and pile-up of small particles induced by gas-drag, as has been proposed to explain the formation of close-in super Earths. Here we show that the asteroid belt's orbital excitation provides a crucial constraint against this scenario for the Solar System. We performed a series of simulations of terrestrial planet formation and asteroid belt evolution starting from disks of planetesimals and planetary embryos with various radial density gradients and including Jupiter and Saturn on nearly circular and coplanar orbits. Disks with shallow density gradients reproduce the dynamical excitation of the asteroid belt by gravitational self-stirring but form Mars analogs significantly more massive than the real planet. In contrast, a disk with a surface density gradient proportional to $r^{-5.5}$ reproduces the Earth/Mars mass ratio but leaves the asteroid belt in a dynamical state that is far colder than the real belt. We conclude that no disk profile can simultaneously explain the structure of the terrestrial planets and asteroid belt. The asteroid belt must have been depleted and dynamically excited by a different mechanism such as, for instance, in the Grand Tack scenario.Comment: Accepted for publication in MNRA

Studies of asteroids, comets, and Jupiter's outer satellites

Observational, theoretical, and computational research was performed, mainly on asteroids. Two principal areas of research, centering on astrometry and photometry, are interrelated in their aim to study the overall structure of the asteroid belt and the physical and orbital properties of individual asteroids. Two highlights are: detection of CN emission from Chiron; and realization that 1990 MB is the first known Trojan type asteroid of a planet other than Jupiter. A new method of asteroid orbital error analysis, based on Bayesian theory, was developed