Linear cotangential transfers and safe orbits for elliptic orbit rendezvous

This paper presents the theory for linear cotangential transfers and safe orbits for elliptic orbit rendezvous. Expressions for the transfer angle and the required ΔV’s are derived. Singularities in the algorithm can occur if the two orbits intersect. Alternative maneuvers for such singular cases are developed. The linear cotangential transfer algorithm is compared with the nonlinear cotangential transfer and the algorithm is found to be very similar. The development of the linear cotangential transfer leads to a new set of relative orbital elements that are well suited for defining safe trajectories. The characteristics of safe trajectories are discussed and a linear safety checking algorithm is developed. Finally, the combination of the cotangential transfers and safe orbits is used to define safe rendezvous trajectories for elliptical orbit rendezvous.