OPTIMAL OPEN LOW-COST TWO-IMPULSE TRANSFERS IN A PLANE

The problem of finding a planar open optimal two-impulse transfer orbit between two known Keplerian orbits is found in terms of a set of necessary conditions for minimizing the total characteristic velocity of the transfer arcs and a test to pick the minimizing orbit from the extremals. The problem is open in the sense that the difference between the final and initial true anomaly is unbounded. Using a transformation of the variables presented in previous work, necessary conditions for an optimal transfer are determined, followed by a proof that an optimal transfer exists, concluding with some sufficiency arguments. Application of the work to non-circular elliptical boundary orbits reveals a set of boundary conditions that result in "low-cost" optimal transfers having velocity increments that are tangent to the boundary orbits at their apogees. These boundary conditions consist of only three types. A simple closed-form solution is provided for each type. More general boundary conditions that result in more complicated optimal solutions are to be discussed in a work that follows.