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  • A new generating principle for two-fixed-center orbits : conic solutions

    Paper ID



    • S.P. Altman
    • J.S. Pistiner


    Space system Organization, General Electric Missile and Space Division






    The newly-developed state-space theory of astro- dynamics has been applied with outstanding success to the analysis of the complete conic family of two-fixed- center orbits. This paper presents new forms of solution and solution results for elliptic, periodic hyperbolic, and aperiodic hyperbolic orbits of the two- fixed-center problem, together with an algorithm for generating the orbital state loci in velocity vector space. It is shown that the two invariants of orbital motion (orbital energy E and the momenta-based invariants) can be decomposed into mutually exclusive components due to each force center alone. Consequently, the two-fixed-center orbital solutions are generated by a nonlinear algorithm using the orbital velocity hodographs (due to each force center) as generators. Extension of the generating principle to the general solution of two-fixed-center orbits is discussed, with the objective of ultimately obtaining a new transformation based on state-space formulation for the restricted three-body problem.