Abstract
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, ω′/ζκ, where ω′ and ω are the vertical libration mode and rotational mode angular frequencies, respectively, and κ is the threshold exponent. For equal-mass systems this constant acquires the value 1.05288.
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