The small-energy three-body systems

We study near-Lagrange collinear configurations in the three-dimensional three-body problem, with arbitrary gravitating masses. A general method, previously developed for Coulombian systems, which provides a unique formalism for treating few-body systems close to the breakup threshold, has been employed to study the motion of three bodies both for bounded and unbounded configurations. The dependence of the triple-escape function on the small total energy E has been evaluated, as well as rovibronic configurations for bounded motion. An approximate characteristic constant is found for symmetrical systems, /, where and are the vertical libration mode and rotational mode angular frequencies, respectively, and is the threshold exponent. For equal-mass systems this constant acquires the value 1.05288.