Illustration of the Primer Vector in Time-Fixed Orbit Transfer

In optimal (minimum-fuel) impulsive orbit transfer, few results are known for the "time-fixed" case (prescribed transfer time) in comparison with the known "time-open" solutions, such as the Hohmann transfer. Time-fixed results have been reported in Refs. 3 and 4.

In this Note a technique for obtaining optimal time-fixed impulsive solutions, applied to orbital rendezvous in Ref. 4, is illustrated by applying it to a very simple system. The technique is based on satisfying a set of necessary conditions (NC) derived by Lawden and described in terms of the primer vector, the vector of adjoint variables associated with the vehicle velocity vector. A simple illustrative example allows an uncomplicated presentation of the technique and yields optimal solution that are verifiable by physical reasoning. In addition it is shown that for this example the NC are also sufficient.