DataSheet1_Double Tisserand graphs for low-energy lunar transfer design.pdf

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.

蒂瑟兰图是星际轨迹和月球旅行设计中的广泛应用工具。它们基于雅可比常数为圆限制三体问题（CR3BP）的运动积分；因此，经典的蒂瑟兰图不包括除飞越体之外的其他天体的摄动。地球-月球系统中的低能转移利用了地球、月球和太阳的联合引力，通过利用第三体摄动以减少转移速度变化Δv达到月球。因此，本文提出了一种新型的双重蒂瑟兰图，其中地球-月球和太阳-地球CR3BP的水平线叠加，将复杂的四体动力学描绘在单一图表中。沿此类水平线的路径对应于利用月球或太阳或两者的动力学效应的轨迹。我们展示了如何有效地利用此类图表进行弱稳定性边界转移、月球共振转移、月球飞越、弱月球捕获或任何这些组合的初步设计。