Accession Number:

AD0661389

Title:

NATURAL ORBITS OF THE FIRST KIND IN THE RESTRICTED PROBLEM,

Descriptive Note:

Corporate Author:

BOEING SCIENTIFIC RESEARCH LABS SEATTLE WASH MATHEMATICS RESEARCH LAB

Personal Author(s):

Report Date:

1967-09-01

Pagination or Media Count:

67.0

Abstract:

Lindstedts method is applied to expand analytically the natural families of periodic orbits of the first kind in the restricted problem of three bodies. The mass ratio is kept as a literal variable the series proceed in the powers of Hills ratio of periods. They cover all four cases at once, namely the direct or retrograde orbits for either inferior planets or for satellites. When the mass ratio is given a numerical value, the expansions contain less terms and thus can be carried up to degree 17 within a 32K core of an IBM 7094. For the system Sun-Jupiter, the initial conditions provided by the series have been corrected to yield the beginnings of all four natural families, and the characteristic exponents have been computed. Comparison between the values computed out of the series and their improvement by numerical integrations and successive variational corrections show that, within an accuracy of one part in ten thousand, the series represent moderately well even the orbit of J VIII the retrograde planetary orbits are fairly well covered up to 90 of the distance from Sun-Jupiter, whereas the direct planetary orbits are covered only up to 60 of that distance. Author

Subject Categories:

  • Celestial Mechanics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE