An automatic tree search algorithm for the Tisserand graph

The Tisserand graph (TG) is a graphical tool commonly employed in the preliminary design of gravity-assisted trajectories. TG two-dimensional map showing essential orbital information regarding Keplerian orbits resulting from close passage by one or more massive bodies, given magnitude hyperbolic excess speed ($v_{\infty}$) and minimum allowed pericenter height for each passage. Contours constant $v_{\infty}$ populate TG. Intersections between contours allow to link consecutive flybys build sequences encounters en route selected destination. When number perturbing bodies large many levels are considered, identification all possible through visual inspection becomes laborious task. Besides, if used as input numerical code trajectory optimization, an automated examination desirable. This contribution describes automatic technique explore find encounter paths. based on tree search method, intersections found using regula-falsi scheme. method validated comparisons with solutions available open literature. Examples application interplanetary mission scenarios, including coupling optimizer.