Optimal Constant-Thrust Radius Change in Circular Orbit

The problem of minimum-time, constant-thrust orbital transfer between coplanar circular orbits is revisited using a relative motion approach in curvilinear coordinates for the dynamics and an indirect optimization method. This is a continuation of a previous work where the authors studied the orbit rephasing problem. A linearization of state and costate equations leads to approximate analytical relations characterizing the evolution of the system dynamics and the optimal thrust profile as a function of a fundamental nondimensional parameter, chi, which characterizes the maneuver duration. This approach allows one to study the range from very short to multirevolution maneuvers using a unified framework. The optimal solution is seen to undergo a structural change as chi increases, moving from a short-maneuver to a long-maneuver regime and passing through a transition zone. Approximate expressions are obtained that can predict the maneuver duration with reasonable accuracy when sufficiently far from the transition zone. The full nonlinear problem characterized by an additional nondimensional parameter is studied numerically, showing that the effect of nonlinearities can be accommodated by adopting a specific intermediate orbit as a reference. Examples of applications to Earth orbit, interplanetary missions, and orbit control around small bodies are presented.