THE DYNAMICAL MEMORY OF JUPITER FAMILY COMETS

Short period comets with period less than 20 years are grouped as the Jupiter family (JF) of comets, since the planet controls their dynamical evolution through frequent close encounters. The motion of these objects is known to be chaotic in a shea time scale, making the prediction of their long-term future or past hopeless. But for how long we could reliably follow the dynamics of these objects when we know the starting conditions with a certain precision? In other words, what are their dynamical memories? Lyapunov Characteristic Exponents (LCE) are a quantitative measure of the exponential divergence of initially close orbits. By computing LCEs for all the already observed JF comets, we analyze the questions stated above and study the characteristics of the phase space where the motion of these objects takes place. Most members of the family shows a concentration of Lyapunov times (inverse of LCE) around 50-100 yrs, that indicates a possible common value and a connected region of chaos. The chaoticity is due to frequent close encounters and the extreme dependence of the their outputs to the approaching conditions to the planet. Since the median time between two consecutive close encounters are in the same range of values, we confirm the simple intuitive idea that JF comets cannot be reliably tracked after a pair of close encounter. The short dynamical memories of the observed JF members are a quantitative support to the hypothesis that long-term integrations of these objects can be used to dynamically simulate the evolution of the whole family.