COMPUTATION OF AN OPTIMAL MANIFOLD TO ASSIST IN THE CHOICE OF A TARGET AND ITS ATTAINMENT WITH THE LEAST EXPENDITURE

A method of choosing from among a long list of targets which move alon g known paths, those which can be attained with minimum losses with re spect to the functional, is proposed. It involves interpolating the pa rameter values needed to construct optimal paths as solutions of the C auchy problem. These parameter values are proved to be continuously de pendent on the terminal coordinates in a small neighbourhood of the st arting point. Asymptotic formulae are given for the initial approximat ions. The choice of the nearest asteroids as targets for the fastest f light of a spacecraft with a solar sail is discussed. (C) 1998 Elsevie r Science Ltd. All rights reserved.