The conditions to be satisfied by a rocket trajectory joining two specified terminals in space, if it is to be stationary relative to the fuel expenditure, are calculated. The rocket is supposed to be moving in a general gravitational field and to be subject to aerodynamic forces which are known functions of ita velocity. The general theory is illustrated by application to tho problem of the optimum programming of fuel expenditure to achieve a given height with a rocket ascending vertically from the earth's surface, subject to uniform gravity and air resistartee proportional to the square of its velocity.