Accession Number : AD0680810

Title :   FAMILIES OF PERIODIC ORBITS CONTINUED IN REGULARIZING COORDINATES. THE HECUBA GAP AND THE HILDA GROUP,

Corporate Author : BOEING SCIENTIFIC RESEARCH LABS SEATTLE WASH MATHEMATICS RESEARCH LAB

Personal Author(s) : Deprit,Andre ; Palmore,Julian

Report Date : SEP 1968

Pagination or Media Count : 38

Abstract : The first paper contained in this note documents the numerical method which is the tool used extensively to extract the physical conclusions very concisely reported in the second paper. A predictor-corrector algorithm is proposed for continuing analytically families of periodic orbits beyond collision trajectories in the restricted problem of three bodies. It is based on Hill's equation for normal variations in Thiele's regularizing coordinates. The direct planetary orbits of the first kind and the Hilda family both bifurcate out of the family of retrograde planetary orbits of the first kind by triplication of the same orbit. The branching occurs in the Hecuba gap. The period curve of the Hilda family shows a peak indicative of invariant tori of quasi-periodic motions inside which could be trapped the Hilda group of asteroids. (Author)

Descriptors :   (*CELESTIAL MECHANICS, *ORBITS), (*ASTEROIDS, ORBITS), PERIODIC VARIATIONS, ALGORITHMS, NUMERICAL ANALYSIS, EQUATIONS OF MOTION, COMPUTER PROGRAMMING

Subject Categories : Celestial Mechanics

Distribution Statement : APPROVED FOR PUBLIC RELEASE