An analysis of two-impulse orbital transfer

Abstract

Analytical investigations of two-impulse transfers between inclined elliptical orbits, using vector analysis and other mathematical techniques, have yielded pertinent, heretofore unknown facts about an orbital transfer function. A geometric analysis helped to show not only that the minimum velocity increment solution between two points on elliptical orbits could be along a hyperbola, but also that there could be two relative minima in this impulse function. Particular examples of both of these phenomena are given. An eighth-order polynomial expression, the real roots of which may refer to extrema in the impulse function, is then determined. Since it can be shown that some of these roots are extraneous, not corresponding to impulse minima, two test functions are next determined which define regions in which all extrema must lie. These regions identify those roots that do correspond to extrema in the impulse function and those that are extraneous. These new analytical findings have been incorporated into an earlier computer contour mapping program that locates the optimum transfer between elliptical orbits.