Angular Momentum and Topological Dependence of Kepler's Third Law in the Broucke-Hadjidemetriou-Henon Family of Periodic Three-Body Orbits

We use 57 recently found topological satellites of Broucke-Hadjidemetriou-Henon'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 s sigma = 0.13. This regularity supports Henon's 1976 conjecture that the linearly stable Broucke-Hadjidemetriou-Henon orbits are also perpetually, or Kol'mogorov-Arnol'd-Moser, stable.