A Circular Restricted n-body Problem

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.