On the advantages of exploiting the hierarchical structure of astrodynamical models

In this paper an algorithm is developed that combines the capabilities and advantages of several different astrodynamical models of increasing complexity. Splitting these models in a strict hierarchical order yields a clearer grasp on what is available. With the effort of developing a comprehensive model overhead, the equations for the spacecraft motion in simpler models can be readily obtained as particular cases. The proposed algorithm embeds the circular and elliptic restricted three-body problems, the four-body bicircular and concentric models, an averaged n-body model, and, at the top hierarchic ladder, the full ephemeris SPICE-based restricted n-body problem. The equations of motion are reduced to the assignment of 13 time-varying coefficients, which multiply the states and the gravitational potential to reproduce the proper vector field. This approach yields an efficient and quick way to check solutions for different dynamics and parameters. We show that in bottom-up applications, a gradual increase of model complexity benefits accuracy, the chances of success and the convergence rate of a continuation algorithm. Case studies are simple periodic orbits and low-energy transfers.