Abstract
The most general statement of the planar orbital transfer problem defines a trajectory with arbitrarily specified end points located on elliptical (or other conic) orbits with noncoincident apsidal axes. This report presents complete and explicit optimum solutions of the two-impulse orbital transfer problem based on a minimum total velocity increment criterion. By use of hodograph (velocity) parameters, the total velocity increment for transfer is expressed as a function of one independent variable (i.e., one of the transfer orbit hodograph parameters) and the trajectory end-point conditions. In addition to the formulation of an eighth-order (octic) polynomial equation providing interior minima, the absolute total velocity increment minimum is determined by comparing the velocity increments at the end points of the variable parameter range with those obtained from the octic. As a special case, complete analytic solutions and attendant transfer characteristics are presented graphically for transfer between any specified trajectory end points lying on circular orbits.
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