Numerical investigation of the manifold I_{ qp } in the SunJupiter case of the restricted threebody problem
Abstract
Message and Taylor (1978) have given values of the mean eccentricities and commensurabilities which correspond to bifurcation orbits of families of symmetric periodic orbits with families of asymmetric periodic orbits in the limit as the mass ratio tends to zero. These bifurcations have been given in a way that they seem to be isolated and unrelated from the whole structure of the periodic orbits of the system. In this paper a numerical investigation of the horizontal stability of the family I and its branches reveals the above bifurcations orbits in the SunJupiter case of the restricted threebody problem and associates these orbits with the whole structure of the system, giving extensive information on them.
 Publication:

Astrophysics and Space Science
 Pub Date:
 May 1979
 DOI:
 10.1007/BF00645471
 Bibcode:
 1979Ap&SS..62..299K
 Keywords:

 Dynamic Stability;
 Jupiter (Planet);
 Manifolds (Mathematics);
 Solar Orbits;
 Three Body Problem;
 Asymmetry;
 Eccentricity;
 Graphs (Charts);
 Astronomy