Fuel-optimal transfers between elliptic orbits are computed individually: given two orbits, find the two-impulse maneuver that minimizes total velocity change. Each problem instance yields an optimal solution. Each solution appears to be its own result, unrelated to solutions for nearby orbital geometries.
The solutions are connected (arXiv:2603.11538). Numerical continuation reveals that seemingly unrelated optima belong to continuous solution families — curves in parameter space along which the optimal transfer varies smoothly. As the orbital geometry changes (eccentricity, inclination, relative phasing), the optimal solution moves along a branch. Different branches emerge, merge, and exchange optimality.
The global map of the solution landscape shows how the set of locally optimal transfers is organized. For a given pair of orbits, there may be multiple local optima on different branches. As parameters vary, branches can cross — the global optimum jumps from one family to another. Near these crossings, alternative transfers from the non-optimal branch provide near-optimal options that may be preferred for operational reasons (shorter transfer time, lower sensitivity to errors).
The practical value is in the near-optimal alternatives. The global optimum is a single point. The family structure reveals the neighborhood of that point — the set of good-enough transfers that trade small amounts of fuel for other desirable properties. Mission design benefits from knowing the landscape, not just the peak.
Isolated optima were always connected. The computation that found them individually was not wrong — it was incomplete.