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Encounter in the keplerian field: Analytical treatment

V. A. Brumberg, T. V. Ivanova

Celestial Mechanics and Dynamical Astronomy, 49(2) (1990)

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In extending the results of Henon and Petit (1986) an algorithm is suggested for constructing the series representing the general encounter-type solution of the spatial eccentric Hill's problem. The series are arranged in powers of the eccentricity E of Hill's problem and two integration constants e and k characterizing eccentricity and inclination of the relative motion. A particular non-periodic solution of Henon and Petit corresponding to E = e = k = 0 is taken as an intermediary. The perturbations to this solution are constructed similar to the lunar theory of Hill and Brown.