title: Angular Momentum and Topological Dependence of Kepler's Third Law in the Broucke-Hadjidemetriou-Hénon Family of Periodic Three-Body Orbits.
abstract: We use 57 recently found topological satellites of Broucke-Hadjidemetriou-Hénon's periodic orbits with values of the topological exponent k ranging from k=3 to k=58 to plot the angular momentum L as a function of the period T, with both L and T rescaled to energy E=-0.5. Upon plotting L(T/k) we find that all our solutions fall on a curve that is virtually indiscernible by the naked eye from the L(T) curve for nonsatellite solutions. The standard deviation of the satellite data from the sixth-order polynomial fit to the progenitor data is σ=0.13. This regularity supports Hénon's 1976 conjecture that the linearly stable Broucke-Hadjidemetriou-Hénon orbits are also perpetually, or Kol'mogorov-Arnol'd-Moser, stable.
authors.affiliation: Faculty of Physics, Belgrade University, Studentski Trg 12, 11000 Belgrade, Serbia.
authors.forename: Marija R
authors.initials: MR
authors.lastname: Janković
authors.affiliation: Institute of Physics, Belgrade University, Pregrevica 118, Zemun, P.O. Box 57, 11080 Belgrade, Serbia.
authors.forename: V
authors.initials: V
authors.lastname: Dmitrašinović