Near Periodic solution of the Elliptic RTBP for the Jupiter Sun system

TL;DR

This paper finds a near-periodic, stable spacecraft trajectory in the elliptic restricted three-body problem for Jupiter and Sun, with initial conditions ensuring return within a few meters after one orbit, supported by numerical evidence.

Contribution

It provides initial conditions for a near-periodic and stable spacecraft orbit in the elliptic RTBP for Jupiter-Sun, with detailed numerical validation.

Findings

Trajectory returns within 4 meters after one period

Solution demonstrated to be stable numerically

Ephemeris of spacecraft motion provided from 2017 to 2028

Abstract

Let us consider the elliptic restricted three body problem (Elliptic RTBP) for the Jupiter Sun system with eccentricity $e=0.048$ and $\mu=0.000953339$. Let us denote by $T$ the period of their orbits. In this paper we provide initial conditions for the position and velocity for a spacecraft such that after one period $T$ the spacecraft comes back to the same place, with the same velocity, within an error of 4 meters for the position and 0.2 meters per second for the velocity. Taking this solution as periodic, we present numerical evidence showing that this solution is stable. In order to compare this periodic solution with the motion of celestial bodies in our solar system, we end this paper by providing an ephemeris of the spacecraft motion from February 17, 2017 to December 28, 2028.