Studying the Equilibrium Points of the Modified Circular Restricted Three-Body Problem: the Case of Sun-Haumea System

TL;DR

This paper investigates a modified planar CRTBP incorporating perturbations like oblateness, radiation, elongation, and disk effects, applied specifically to the Sun-Haumea system, revealing shifts in equilibrium points and their stability conditions.

Contribution

It develops a new mathematical model of the modified CRTBP with perturbations and applies it to the Sun-Haumea system, analyzing equilibrium points and their stability.

Findings

Five equilibrium points identified, with three collinear and two non-collinear.

Perturbations cause shifts in equilibrium point positions compared to classical CRTBP.

Non-collinear points are stable in the Sun-Haumea system.

Abstract

We intend to study a modified version of the planar Circular Restricted Three-Body Problem (CRTBP) by incorporating several perturbing parameters. We consider the bigger primary as an oblate spheroid and emitting radiation while the small primary has an elongated body. We also consider the perturbation from a disk-like structure encompassing this three-body system. First, we develop a mathematical model of this modified CRTBP. We have found there exist five equilibrium points in this modified CRTBP model, where three of them are collinear and the other two are non-collinear. Second, we apply our modified CRTBP model to the Sun-Haumea system by considering several values of each perturbing parameter. Through our numerical investigation, we have discovered that the incorporation of perturbing parameters has resulted in a shift in the equilibrium point positions of the Sun-Haumea system compared to their positions in the classical CRTBP. The stability of equilibrium points is investigated. We have shown that the collinear equilibrium points are unstable and the stability of non-collinear equilibrium points depends on the mass parameter $\mu$ of the system. Unlike the classical case, non-collinear equilibrium points have both a maximum and minimum limit of $\mu$ for achieving stability. We remark that the stability range of $\mu$ in non-collinear equilibrium points depends on the perturbing parameters. In context of the Sun-Haumea system, we have found that the non-collinear equilibrium points are stable.