Closed-form solution of an idealized, optimal, highly eccentric hyperbolic rendezvous problem

Closed-form solutions of optimal impulsive rendezvous problems are difficult to obtain, even using linearized equations. An idealized model of a highly eccentric hyperbolic impulsive rendezvous problem is constructed by considering the limit as the eccentricity tends to infinity. In this manner, a closed-form solution of an idealized hyperbolic rendezvous problem can be obtained. This idealized solution establishes an arbitrarily good approximation to a solution of the problem of optimal impulsive rendezvous of a spacecraft near a satellite in hyperbolic orbit of sufficiently high eccentricity.