Why do Trojan ASCs (not) Escape?

The orbits of 12 Trojan asteroids, which have Lyapunov times T _L10⁵ years and were previously classified as ASCs(=asteroids in stable chaos), are integrated for 50 Myrs, along with a group of neighbouring initial conditions for each nominal orbit. About 40% of the orbits present strong instabilities in the inclination, which may be attributed primarily to the action of the ₁₆ secular resonance; two escapes are also recorded. Higher-order secular resonances, involving the nodes of the outer planets, are also found to be responsible for chaotic motion. Orbital stability depends critically on the choice of initial conditions and, thus, these objects can be regarded as being on the edge of strong chaos.     

Model orbits of asteroid 3040 Kozai

The orbital evolutions of the asteroid 3040 Kozai and model asteroids with similar orbits have been investigated. Their osculating orbits for an epoch 1991 December 10 were numerically integrated forward within the interval of 20,000 years, using a dynamical model of the solar system consisting of all inner planets, Jupiter, and Saturn.The orbit of the asteroid Kozai is stable. Its motion is affected only by long-period perturbations of planets. With change of the argument of perihelion of the asteroid Kozai, the evolution of the model asteroid orbits changes essentially, too. The model orbits with the argument of perihelion changed by the order of 10% show that asteroids with such orbital parameters may approach the Earth orbit, while asteroids with larger changes may even cross it, at least after 10,000 years. Long-term orbital evolution of asteroids with these orbital parameters is very sensitive on their angular elements.     

Construction of a Nekhoroshev like result for the asteroid belt dynamical system

We investigate the possibility of obtaining a Nekhoroshev like result for the dynamical system describing the motion of an asteroid in the main belt, From the mathematical point of view this is a new result since the problem is degenerate and we want to control also the motion of degenerate actions, We find that there are regions, such as the resonances of low order among the fast angles (mean motion resonances), where a Nekhoroshev like result cannot be proved a priori, Conversely, we are able to confine the motions in the mean motion resonances of logarithmically large order in the perturbation parameters, as well as in the non-resonant region, We discuss also the connection with the existence of invariant tori.     

On the composition of ices incorporated in Ceres

We use the clathrate hydrate trapping theory and gas drag formalism to calculate the composition of ices incorporated in the interior of Ceres. Utilizing a time-dependent solar nebula model, we show that icy solids can drift from beyond 5 au to the present location of the asteroid and be preserved from vaporization. We argue that volatiles were trapped in the outer solar nebula in the form of clathrate hydrates, hydrates and pure condensates prior to having been incorporated in icy solids and subsequently in Ceres. Under the assumption that most of volatiles were not vaporized during the accretion phase and the thermal evolution of Ceres, we determine the per mass abundances with respect to H₂O of CO₂, CO, CH₄, N₂, NH₃, Ar, Xe and Kr in the interior of the asteroid. The Dawn space mission, scheduled to explore Ceres in August 2014, may have the capacity to test some predictions. We also show that an in situ measurement of the D/H ratio in H₂O in Ceres could constrain the distance range in the solar nebula where its icy planetesimals were produced.     

The number density of main-belt asteroids

In this paper we have studied how the number density of asteroids varies as a function of the mean distance from the sun.