Double Tisserand graphs for low-energy lunar transfer design

Abstract

Tisserand graphs are a widespread tool for interplanetary trajectory and Moon tour design. They are based on the Jacobi constant being an integral of motion in the Circular Restricted Three Body Problem (CR3BP); as such, the classical Tisserand graph does not include the perturbation of bodies other than the flyby bodies. Low-energy transfers in the Earth-Moon system make use of the combined Earth, Moon, and Sun gravities, exploiting the third body perturbations to reach the Moon with a reduced transfer Δv. The paper, therefore, proposes a novel double Tisserand graph, where the level lines of both the Earth-Moon and the Sun-Earth CR3BPs are superimposed, portraying the complex 4-body dynamics into a single plot. Paths along such level lines correspond to trajectories utilizing the dynamical effect of the Moon or the Sun or a combination of both. We show how such a graph can be efficiently used for preliminary design of Weak Stability Boundary transfers, lunar resonance transfers, lunar flybys, weak lunar captures or any combination of them.