Formulation of the Circular Restricted N-Body Problem (CRNBP) in the Jovian system

Simplified models such as the Circular Restricted 3-Body Problem (CR3BP) are widely used to obtain an understanding of periodic and quasi-periodic orbits without the need for a higher-fidelity model. However, such models only account for the gravitational perturbations caused by one additional body on the trajectory of a spacecraft, when real-world systems may be affected by a greater number of significantly massive celestial bodies. Third-body perturbation models used to analytically incorporate additional gravitational effects on a spacecraft do not include the effect of the perturbing body on the other massive bodies in the system. In the Circular Restricted N-Body Problem (CRNBP), an unlimited number of bodies and their effects on both the spacecraft and each other can be effectively modeled. To exhibit these outcomes, trajectories in the Jupiter-Europa CR3BP are compared to trajectories with identical initial conditions in the CRNBP to include the gravitational effects of Io, Ganymede, and Callisto on the satellite in addition to accounting for the gravitational effect of these moons on each other. This demonstration is then expanded to include not only the Galilean moons but also the inner Jovian moons based on their low eccentricities and inclinations. The effect of the initial position of each body, represented by the phasing angle relative to the position of Europa, demonstrates the importance and applicability of the CRNBP as significant perturbations are demonstrated. Several families of orbits are tested and compared to the traditional CR3BP for model validation. The results of propagated orbits in the CRNBP highlight the importance of understanding gravitational perturbations beyond a three-body system, yielding insight which has the potential to aid in the selection of more stable trajectories.