Spacecraft intercept using minimum control energy and wait time

A new approach to the minimum energy impulse intercept problem for spacecraft in orbit is explored. The types of orbits investigated in this paper are not restricted to a particular one. The constrained optimization technique is formulated with the universal variable, which is used to describe orbit information with sufficient accuracy for general types of orbits. Two optimization problems are posed. First, a problem for minimum velocity change and time of flight for intercept are investigated with the constraint on the final position of two satellites. Next, the so-called wait time is also added as an additional parameter to be determined. Although a closed-form solution is not obtained, the Newton iteration technique is successfully applicable. Finally, by numerically comparing the proposed solution to the Hohmann transfer, the suggested approach is demonstrated to be a feasible technique applicable to a broad class of orbit transfer problems.