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

TL;DR

This paper investigates the statistical properties of planetary perturbations on Oort cloud comets using order statistics and heavy-tail distributions, aiming to simplify the modeling of comet dynamics.

Contribution

It introduces a statistical approach to analyze planetary perturbations, providing insights that could reduce reliance on computationally intensive numerical simulations.

Findings

Perturbations exhibit a general pattern around major planets.

Heavy-tail distributions effectively model the perturbation data.

Statistical validation supports the theoretical analysis.

Abstract

This paper tackles important aspects of comets dynamics from a statistical point of view. Existing methodology uses numerical integration for computing planetary perturbations for simulating such dynamics. This operation is highly computational. It is reasonable to wonder whenever statistical simulation of the perturbations can be much more easy to handle. The first step for answering such a question is to provide a statistical study of these perturbations in order to catch their main features. The statistical tools used are order statistics and heavy tail distributions. The study carried out indicated a general pattern exhibited by the perturbations around the orbits of the important planet. These characteristics were validated through statistical testing and a theoretical study based on Opik theory.