Simple Method to Determine Globally Optimal Orbital Transfers

Abstract

This research is intended to describe a simple analytical approach to determine the globally optimal impulsive transfer between two arbitrary Keplerian trajectories, including the case of initial and final elliptic orbits. First, Hohmann and bielliptic transfers are proved to be two possible global optimal transfers between two elliptic orbits without any restriction on the number of impulses. This result is achieved by using ordinary calculus in conjunction with a simple graphical construction. The final choice between these two transfers depends on the apoapse and periapseradiioftheinitialand finalellipses.Inthispaper,asimpleanalyticalprocedureisproposedthatiscapableof determining the optimal choice between a Hohmann and bielliptic transfer for arbitrary initial and final orbits. An approach similar to that used for elliptic orbits leads to results of a global nature for transfers that involve both elliptic orbits and escape trajectories. Nomenclature a = semimajor axis E = trajectory (specific) energy EB = specific energy associated with the generic point B E0 = specified value for the specific energy E e = eccentricity f = true anomaly h = specific angular momentum h = magnitude of the specific angular momentum r = position vector r = radius rA = apoapse radius (for elliptic orbits only) rAB = apoapse radius associated with the generic point B