The Coriolis asymmetry in the classical restricted 3-body problem and the Jacobian integral

Details The Coriolis asymmetry in the classical restricted 3-body problem and the Jacobian integral The Coriolis asymmetry in the classical restricted 3-body problem and the Jacobian integral

Jan 1980

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1980aj.....85...81i&link_type=abstract

Astronomical Journal, vol. 85, Jan. 1980, p. 81-85. Research supported by the Natural Sciences and Engineering Research Council

Statistics

Applications

4

Classical Mechanics, Coriolis Effect, Jacobi Integral, Orbital Mechanics, Three Body Problem, Circular Orbits, Equations Of Motion, Radii

Scientific paper

Certain aspects of the restricted three-body problem are reexamined and several new results are derived. A more complete analytical derivation of the formulae used in an earlier paper (Innanen, 1979) is supplied, together with a generalization to include inclined orbits. The important results are summarized in equations (23), (24) and (30) and in Fig. 4. It is shown, in the limit, that the condition of zero relative acceleration between the particle bound to one of the finite masses supplies a stronger restriction on the Jacobi integral than does the zero velocity criterion, for direct orbits. Stable retrograde orbits populate the entire space of the zero velocity "Fig. 8" envelopes of the 3-body problem (Fig. 5). The behavior of the galaxy IC 10 (Cohen, 1979; Huchtmeir, 1979) may be explained if there is a ring or disk of H I in retrograde motion about the main body of that galaxy. The plane of that ring (disk) defines the galactic orbit plane of IC 10, as in the case of the Sculptor galaxy (Innanen and Papp, 1979). The equation of motion for small oscillations of the particle perpendicular to its orbit plane is briefly mentioned, as are several other possible applications.

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