Analytical solution of the plane, averaged, restricted, three-body problem in the case of circulation of the pericenter of the orbit of the particle

Details Analytical solution of the plane, averaged, restricted, three-body problem in the case of circulation of the pericenter of the orbit of the particle Analytical solution of the plane, averaged, restricted, three-body problem in the case of circulation of the pericenter of the orbit of the particle

Aug 1980

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1980azh....57..824v&link_type=abstract

(Astronomicheskii Zhurnal, vol. 57, July-Aug. 1980, p. 824-832.) Soviet Astronomy, vol. 24, July-Aug. 1980, p. 474-478. Transla

Astronomy and Astrophysics

Astronomy

Equations Of Motion, Orbital Elements, Orbital Mechanics, Three Body Problem, Eccentricity, Euler-Lagrange Equation

Scientific paper

The problem under consideration in the present paper is integrable in quadratures. A qualitative analysis of the integrals of motion showed that if the orbital eccentricity of the perturbing body is small and the initial conditions satisfy certain requirements, then the pericenter of the particle's orbit will undergo revolving motion. Besides a secular term, the equation for the pericenter will contain periodic terms, while the eccentricity will also be subject to periodic perturbations. For all the periodic terms the overall period will be the time required for one complete revolution of the pericenter. A method allowing the reversal of quadratures in the case when the described type of motion occurs is proposed. Explicit analytical equations are found which give the orbital elements as functions of time with the accuracy of the square of the orbital eccentricity of the perturbing body.

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