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  • Accuracy Requirements for interplanetary ballistic trajectories

    Paper ID



    • T A Magness
    • J B McGuire
    • O K Smith


    Space Technology Laboratories






    Accuracy Requirements for Interplanetary Ballistic Trajectories. This paper examines guidance requirements for a variety of interplanetary trajectories. Emphasis is on Earth-Mars and Earth-Venus shots, but the methods used apply, in general, to transfer ellipses from one satellite to another in a central gravitational Held. Previous investigations have concentrated on minimum energy trajectories, which involve large ballistic error coefficients. The present analysis shows that error coefficients depend critically upon the choice of nominal trajectory and may be improved by factors of ten and more over minimum energy values. An approximate analytical model involving the following assumptions is utilized in the calculations: (1) The “n-body problem” may be approximated by a sequence of two-body problems. (2) The earth and the target planet rotate about a fixed sun in circular orbits. (3) The orbits of the eai’th and the target planet are coplanar. The method used for deriving guidance requirements is first to study elliptical trajectories connecting two moving points of infinitesimal mass travelling in circular satellite orbits about the sun. These trajectories are then perturbed by errors in initial (or burnout) conditions, and the misses due to these perturbations are calculated by examining the first derivative of the distance of closest approach with respect to burnout parameters. A trajectory for which one or more of these derivatives, or miss coefficients, vanishes is called a “guidance minimum” trajectory. On such a trajectory, the permissible errors in burnout parameters are many times greater than for most other trajectories. The chief aim of the paper has been to estimate the orders of magnitude of the various miss coefficients and to establish the existence of guidance minimum trajectories. The analysis techniques used are not exact for an n-body problem, and the limitations thus imposed on the results are discussed. Genauigkeitserfoi'dernisse fiir interplanetarische ballistische Bahnen. Die vor- liegende Arbeit untersucht Lenkungserfordernisse fiir eine Vielheit interplanetari- scher Bahnen. Das Hauptgewicht wird auf Fahrten von der Erde zum Mars und von der Erde zur Venus gelegt, doch sind die angewandten Methoden im allgemeinen auch für Übergangsellipsen von einem Satelliten zum anderen in einem zentralen Gravitationsfeld brauchbar. Friihere Untersuchungen konzentrierten sich auf Bahnen minimalen Energieverbrauches, wobei grofie ballistische Fehlerkoeffizienten auftreten. Die vorliegende Analyse zeigt, daB Fehlerkoeffizienten kritisch von der Wahl der Bahn abhangen und gegen die Minimalenergie-Bahnen um Faktoren von 10 und mehr verbessert werden konnen.