  Mission designers must study many dynamical models to plan a low-cost
spacecraft trajectory that satisfies mission constraints. They routinely use
Poincar\'e maps to search for a suitable path through the interconnected web of
periodic orbits and invariant manifolds found in multi-body gravitational
systems. This paper is concerned with the extraction and interactive visual
exploration of this structural landscape to assist spacecraft trajectory
planning. We propose algorithmic solutions that address the specific challenges
posed by the characterization of the topology in astrodynamics problems and
allow for an effective visual analysis of the resulting information. This
visualization framework is applied to the circular restricted three-body
problem (CR3BP), where it reveals novel periodic orbits with their relevant
invariant manifolds in a suitable format for interactive transfer selection.
Representative design problems illustrate how spacecraft path planners can
leverage our topology visualization to fully exploit the natural dynamics
pathways for energy-efficient trajectory designs.
