Abstract
The dynamics of two families of minor inner solar system bodies that suffer frequent close encounters with the planets is analyzed. These families are: Jupiter family comets (JF comets) and Near Earth Asteroids (NEAs).
The motion of these objects has been considered to be chaotic in a short time scale,and the close encounters are supposed to be the cause of the fast chaos. For a better understanding of the chaotic behavior we have computed Lyapunov Characteristic Exponents (LCEs) for all the observed members of both populations. LCEs are a quantitative measure of the exponential divergence of initially close orbits. We have observed that most members of the two families show a concentration of Lyapunov times (inverse of LCE) around 50–100yr. The concentration is more pronounced for JF comets than for NEAs, among which a lesser spread is observed for those that actually cross the Earth's orbit (mean perihelion distance q < 1.05 AU). It is also observed that a general correspondence exists between Lyapunov times and the time between consecutive encounters.
A simple model is introduced to describe the basic characteristics of the dynamical evolution. This model considers an impulsive approach, where the particles evolve unperturbedly between encounters and suffer ‘kicks’ in semimajor axis at the encounters. It also reproduces successfully the short Lyapunov times observed in the numerical integrations and is able to estimate the dynamical lifetimes of comets during a stay in the Jupiter family in correspondence with previous estimates.
It has been demonstrated with the model that the encounters with the largest effect on the exponential growth of the distance between initially nearby orbits are neither the infrequent deep encounters, nor the frequent and far ones; instead, the intermediate approaches have the most relevant contribution to the error growth. Such encounters are at a distance a few times the radius of the Hill's sphere of the planet (e.g. 3).
An even simpler model allows us to get analytical estimates of the Lyapunov times in good agreement with the values coming from the model above and the numerical integrations.
The predictability of the medium‐term evolution and the hazard posed to the Earth by those objects are analysed in the Discussion section.
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Tancredi, G. Chaotic dynamics of planet‐encountering bodies. Celestial Mechanics and Dynamical Astronomy 70, 181–200 (1998). https://doi.org/10.1023/A:1008331422678
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DOI: https://doi.org/10.1023/A:1008331422678