Overview

The alteration of a space vehicle's orbit by one or more discrete changes in velocity for the purpose of fulfilling certain mission objectives forms the subject of the present chapter. We first consider ideal impulsive velocity changes which, although physically unrealizable, are, nevertheless, sufficiently good approximations for many purposes if the engine burn time is a small portion of the total mission time. Then, in the last two sections, attention is given to the more realistic problem of powered-flight guidance, i.e., directing the rocket engine thrust vector during the powered maneuver. First, a general-purpose guidance technique is developed, which is applicable to a variety of missions and is based on the velocity-to-be-gained concept. Then, for problems involving more general terminal constraints, some elementary optimal guidance laws are derived.

Many orbital transfer problems involve a minimization criterion to be satisfied. Usually, the objective is to minimize the sum of the required velocity impulses, sometimes referred to as the characteristic velocity. For example, one might require the smallest velocity impulse at a given position in orbit to transfer to a new orbit which will intersect a fixed point. The problem might be expanded to include another velocity change at the target point to place the vehicle in still another orbit. The requirement would then be to choose the transfer orbit which minimizes the sum of the two velocity changes. Of some interest, also, is an original proof of the optimality of the Hohmann transfer a surprisingly difficult result to prove.

Problems...