Chaotic dynamics of planet‐encountering bodies |
| |
| Authors: | G Tancredi |
| |
| Institution: | (1) Dpto. Astronomía Fac. Ciencias, Iguá 4225 esq. Mataojo, 11400 Montevideo, Uruguay (e-mail |
| |
| 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.
This revised version was published online in July 2006 with corrections to the Cover Date. |
| |
| Keywords: | chaos dynamics comets NEAs Lyapunov exponent |
| 本文献已被 SpringerLink 等数据库收录！ |
|
