The planar isosceles problem for Maneff's gravitational law




Diacu, Florin N.

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Maneff's gravitational law explains with a very good approximation the perihelion advance of the inner planets as well as the orbit of the Moon. Here we study the invariant set of planar isosceles solutions of the 3-body problem for Maneff's model. We show that every solution leads to a collision singularity and consequently has no periodic orbits. Using McGehee's technique we blow-up the triple collision singularity and regularize binary-collision solutions. The flow on the collision manifold is shown to be non-gradient-like and the set of collision/ejection solutions is described. The center manifold and the block-regularization problems are analysed. The network of homoclinic and heteroclinic orbits is further discussed. Finally we study an anisotropic model having the property that the flow on the collision manifold changes dramatically when the mass parameter is varied, giving rise to a subcritical pitchfork bifurcation of the equilibria.