A Circular Restricted n-body Problem

TL;DR

The paper introduces the Circular Restricted n-Body Problem (CRNBP), an efficient model for analyzing complex dynamics in multi-body systems, especially useful for preliminary trajectory design in outer planetary systems.

Contribution

It extends the bicircular restricted four-body problem to n bodies, simplifying trajectory analysis by reducing computational complexity and demonstrating its structural stability and practical utility.

Findings

CRNBP reproduces complex dynamical behaviors of ephemerides n-body problems.

It requires only six differential equations, making it computationally efficient.

Illustrative examples show its effectiveness in trajectory design.

Abstract

This paper introduces the Circular Restricted n-Body Problem (CRNBP), an extension of the bicircular restricted four-body problem (BCR4BP) designed to describe the dynamics of an n-body system. In the CRNBP, each massive body in the system is constrained to follow a Keplerian motion, similar to the BCR4BP's artificial constraint. The CRNBP is an efficient alternative for trajectory design in multiple-body systems, particularly for outer planetary systems, as it requires integrating only six first-order ordinary differential equations compared to the 6N equations in an ephemerides model. By reproducing complex dynamical behaviors observed in ephemerides n-body problems, we demonstrate the structural stability of the CRNBP. Additionally, we propose a straightforward approach to relate the CRNBP with ephemerides, enabling the exploration of trajectory design possibilities before committing to a dedicated ephemerides analysis. This allows for the identification of general dynamical behaviors and provides valuable insights into the dynamics of multiple body systems. Finally, illustrative examples highlight the richness of trajectories and potential advantages of using the CRNBP for designing complex trajectories in outer planetary systems. The CRNBP proves to be a valuable tool for preliminary trajectory design, facilitating the identification of low-energy trajectories and providing a foundation for further exploration in future dedicated studies.