Closed-Form solution of the ℓ-Optimal bi-Impulsive coplanar orbital transfer problem

Article presents a closed-form solution of the optimal biimpulsive transfer between coplanar initial and terminal orbits for satellites exerting thrust by using three orthogonal thrusters aligned with the local-vertical local-horizontal frame. Coplanar maneuvers usually consume less propellant than more general transfers wherein the orbital planes are modified. An implicit assumption in most of the aforementioned works is that the propellant consumption is measured by the Euclidean norm of the velocity change vectors. Therefore, for satellites using orthogonal thrusters the optimization approach should be modified. With this consideration in mind, this work formulates the cost function for a general coplanar transfer between two noncollinear position vectors with prescribed terminal velocities, and analytically determines the set of points that satisfy the necessary conditions for minima.