Abstract
Necessary conditions for minimum characteristic velocity are applied to the problem of optimal impulsive transfer between arbitrary coplanar elliptical orbits. Additionally some existence and sufficient conditions for optimal transfer are presented. Equations for calculating optimal bi-parabolic transfers and optimal two-impulse transfers between orbits reduce to the problem of solving three nonlinear equations in three unknowns. Minimizing impulses are found to be applied tangentially if and only if the initial elliptical orbits have directionally aligned apses. In these cases minimizing impulses can be found in closed form.Four fundamental theorems are presented to unify these closed-form solutions. All of these closed-form minimizing transfers are either generalized Hohmann or bi-parabolic. Bi-elliptic transfers are never optimal but can approach arbitrarily close to a bi-parabolic transfer. An example is presented for perigees aligned in the same direction and another for aligned perigees in opposition.
Published Version
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