Astronomy and Astrophysics – Astronomy
Scientific paper
Mar 1984
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1984baicz..35..104s&link_type=abstract
Astronomical Institutes of Czechoslovakia, Bulletin (ISSN 0004-6248), vol. 35, March 1984, p. 104-111.
Astronomy and Astrophysics
Astronomy
Celestial Mechanics, Orbital Elements, Three Body Problem, Degrees Of Freedom, Eccentric Orbits, Elliptical Orbits, Hamiltonian Functions
Scientific paper
The double-averaged planar three-body problem is brought to one degree of freedom. For the restricted case, the double-average Hamiltonian is independent of mean anomalies and, therefore, represents an integral of motion. This integral gives the complicated implicit relation between eccentricity e and the distance d of pericenters. The evolution of the orbit is best expressed in the x, y plane for which e, d are polar coordinates. The explicit calculations are carried out up to the fourth degree in eccentricities while the ratio sigma of the semi-major axes is taken into account in all degrees, asuming sigma less than one but not necessarily much less than one. The trajectories in the x, y plane are then ellipses. The center of each ellipse depends on energy. The ellipse degenerating into one point represents the libration point whose x coordinate may be interpreted as the forced eccentricity. The dependence of the parameters on sigma is investigated.
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