THE GLOBAL FLOW OF THE MANEV PROBLEM

The Manev problem (a two-body problem given by a potential of the form A/r + B/r(2), where r is the distance between particles and A,B are p ositive constants) comprises several important physical models, having its roots in research done by Isaac Newton. We provide its analytic s olution, then completely describe its global flow using McGehee coordi nates and topological methods, and offer the physical interpretation o f all solutions. We prove that if the energy constant is negative, the orbits are, generically, precessional ellipses, except for a zero-mea sure set of initial data, for which they are ellipses. For zero energy , the orbits are precessional parabolas, and for positive energy they are precessional hyperbolas. In all these cases, the set of initial da ta leading to collisions has positive measure. (C) 1996 American Insti tute of Physics.