Order statistics and heavy-tailed distributions for planetary perturbations on Oort cloud comets

¹ University Lille 1, Laboratoire Paul Painlevé, 59655 Villeneuve d'Ascq Cedex, France
² University Lille 1, LAL, 59000 Lille, France e-mail: marc.fouchard@univ-lille1.fr
³ Institut de Mécanique Céleste et Calcul d'Ephémérides, 77 av. Denfert-Rochereau, 75014 Paris, France
⁴ INAF – IASF, via Fosso del Cavaliere 100, 00133 Roma, Italy

Received: 12 July 2009
Accepted: 19 November 2009

Abstract

Aims. This paper tackles important aspects of comet dynamics from a statistical point of view. Existing methodology uses numerical integration to compute planetary perturbations to simulate such dynamics. This operation is highly computational. It is reasonable to investigate a way in which a statistical simulation of the perturbations can be handled more easily.

Methods. The first step to answer such a question is to provide a statistical study of these perturbations in order to determine their main features. The statistical tools used are order statistics and heavy-tailed distributions.

Results. The study carried out indicated a general pattern exhibited by the perturbations around the orbits of the planets. These characteristics were validated through statistical testing and a theoretical study based on the Öpik theory.