Spacecraft Rendezvous in Closed Keplerian Orbits Using Constant Radial Thrust Acceleration

An analytical solution for spacecraft rendezvous within closed Keplerian orbits is presented using continuous radial thrust. The two spacecraft are assumed to be initially placed within the same closed orbit with arbitrary phase angle separation. The target spacecraft is assumed to always remain in the same initial orbit. The chaser vehicle, however, uses a judiciously designed maneuver sequence comprising constant-acceleration radial thrust phases interspersed with coast phases. Importantly, the proposed maneuver design is analytically characterized by one or two (depending on whether the parking orbit is circular or elliptical, respectively) nonlinear algebraic equations that determine the time intervals for the different phases. The set of initial conditions from which rendezvous is feasible is also characterized. Additionally, orbit rotation (that is, changing the orbit argument of periapsis in plane) is also demonstrated for the elliptical parking orbit case. Finally, the remarkable emergence of the golden and silver ratios, as well as their connections to Kepler's triangle, is demonstrated for a specific sequence of thrust and coast arcs.