Comparison of analytical and numerical calculations of the first class periodic orbits

Details Comparison of analytical and numerical calculations of the first class periodic orbits Comparison of analytical and numerical calculations of the first class periodic orbits

Sep 1986

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1986cemec..39..267h&link_type=abstract

Celestial Mechanics (ISSN 0008-8714), vol. 39, no. 3, 1986, p. 267-281.

Physics

5

Celestial Mechanics, Orbit Calculation, Three Body Problem, Approximation, Equations Of Motion, Particle Motion, Poincare Problem, Radial Velocity

Scientific paper

A general method of constructing the analytical continuation of periodic orbits is applied to the direct Poincare first-class periodic orbits in the planar circular restricted three-body problem. The expressions for the initial conditions and the radial velocity curve are given in explicit form to the linear approximation in the relative mass mu of the second body. Analytical results are found to agree well with numerically determined orbits for large values of mu. The analytical approximation is found to be sufficiently accurate even for a mass ratio within the range of interest for binary stars.

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