Constrained Multiple-Revolution Lambert's Problem

Abstract

A fixed-time, multiple-revolution Lambert’s problem is solved under given constraints. For Nmax revolutions, there exist 2Nmax 1 mathematical solutions to Lambert’s problem. Unfortunately, not all of these solutions are feasible. Practical solutions require that the perigee radius be greater than a minimum value (to avoid Earthimpacting trajectories) and the apogee radius be lower than a maximum value (to avoid expensive changes in eccentricity). In particular, short-path and long-path solutions require different considerations to discriminate betweentheunfeasiblesolutions.Asolutionprocedureforthesemimajor-axisrangeisproposedthattakesthese two constraints into account. Based on the semimajor-axis range, the solutions with a feasible number of revolutions can beeasilyselected.Thecaseofzerorevolutionsisalsodiscussed,asthetrajectorymaybefeasibleevenifnotcomplying withthebounds.Numericalexamplesshowthatthenumberoffeasiblesolutionsgreatlydecreaseswhenconsidering the constraints.