THE GENERALIZED INVERSE PROBLEM OF ORBIT COMPUTATION
GENERAL ELECTRIC CO PHILADELPHIA PA MISSILE AND SPACE DIV
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The basic problem of celestial mechanics - finding the motion for given initial conditions in a given force field - is inverted by asking for force fields which result in either a specific orbit or which allow to obtain a closed form solution of the equations of motion. The first case leads to a generalized concept of guidance and thrust programs, while the second opens the way to finding new closed form solutions for slightly modified n-body n 2 gravitational fields. The problem discussed in this paper is a generalization in purpose and in method of the classical problem of orbit determination in celestial mechanics. It allows the determination of classes of functions which either furnish optimization opportunities of the guidance problem first case or furnish overall field modifications which allow closed form solutions second case applicable to perturbation calculations as reference orbits with predetermined approximations. Establishing new reference orbits for perturbations and formulating a concise and systematic method of guidance analysis are the two main results presented in the paper.
- Celestial Mechanics