New form for the optimal rendezvous equations near a Keplerian orbit

are removable singularities, they may lead to computational instabilities in the solution. Especially bothersome is the fact that computational problems can occur where the true anomaly is near zero. These problems are avoided in the work of solution that does not involve 7(0), but their work is confined to elliptical orbits. The purpose of this Note is to modify the original form by replacing 1(0) by a related integral 7(0), thereby removing all singularities and computational instabilities. The resulting solution, in terms of /(0), is identical for hyperbolic, parabolic, or noncircular elliptic orbits, but the particular case determines the nature of the closed-form evaluation of 7(0). Application of this work to actual problems usually involves the solution of a two-point boundary-value problem and is not considered here. Although we emphasize the case of bounded thrust, the unbounded thrust case can also be investigated through the use of the simpler equations for unpowered flight, which we also present. If the maximum number of impulses is known for an optimal rendezvous in this case, the two-point boundary-value problem is reduced to a problem of parameter optimization on the velocity increments and their locations. We conjecture that the maximum of impulses for this problem is four. If the number of impulses is restricted to two, the problem is solved by methods similar to those of Weiss et al.11'12 For the case of bounded thrust, a method such as that used for the rendezvous problem near circular orbit16 can be applied with starting iteratives obtained from the related unbounded thrust case.