Rendezvous revisited: The search for fast-intercept solutions

Orbital interception scenarios typically involve a chaser that is actively maneuvered to encounter an inertial target and may be undertaken for a variety of purposes, including docking spacecraft or colliding with an asteroid for planetary defense studies. Viable intercept trajectories are constrained by the free-fall path of the target and by auxiliary conditions such as the available time or fuel budget. Whereas a constraint on the time to intercept is central to the (extensively studied) Lambert problem, a less common but more visually compelling constraint is that of the available fuel for intercept. This was the basis of a recent study [E. M. Edlund, Am. J. Phys. 89, 559–566 (2021)], which analyzed one of the two families of possible intercept solutions that were identified. The second family, studied in more detail here, describes intercepts at all points in the orbit and has the interesting property that it admits fast-intercept solutions. This work concludes the analysis of this problem; it develops a general condition that describes both families of intercepts, presents representative solutions, and considers the sensitivity of these solutions to errors in the control parameters.