Monitoring Jovian Orbital Resonances of a Spacecraft: Classical and Relativistic Effects

Orbital resonances continue to be one of the most difficult problems in celestial mechanics. They have been studied in connection with the so-called Kirkwood gaps in the asteroid belt for many years. On the other hand, resonant trans-Neptunian objects are also an active area of research in Solar System dynamics, as are the recently discovered resonances in extrasolar planetary systems. A careful monitoring of the trajectories of these objects is hindered by the small size of asteroids or the large distances of the trans-Neptunian bodies. In this paper, we propose a mission concept, called CHRONOS (after the greek god of time), in which a spacecraft could be sent to with the initial condition of resonance with Jupiter in order to study the future evolution of its trajectory. We show that radio monitoring of these trajectories could allow for a better understanding of the initial stages of the evolution of resonant trajectories and the associated relativistic effects.

Resonances and chaos in the asteroid belt

The present paper reviews the evolution of our understanding of the effect of resonances on the distribution of asteroids in the asteroid belt. The history of this problem goes back to the Kirkwood's discovery (1867) of the Kirkwood gaps located at resonances with Jupiter. We started to understand the mechanism of their origin only in last decades. It seems that only gravitational effects are sufficient for the depletion. It is now clear that the overlap of secular resonances inside the orbital resonance is the most effective mechanism leading to large chaos and variation of orbital elements. This results in the final removal of asteroids from the gaps by collisions with the inner planets. Chaos, however, does not always mean fast removal of the body. The question of the so called stable chaos will be discussed together with the offered explanations (the high order resonances and the so called three-body resonances). Recently it was shown that chaotic diffusion can play an important role for the 2/1 resonance where the aforementioned explanation for other gaps fails. Basic facts will be reviewed but we will not go into this problem as the importance of chaotic diffusion in dynamics of asteroids (and comets) will be the subject of invited lecture at this conference given by Morbidelli and Nesvorný.