  In a recent paper (arXiv:math-ph/0609076) the authors investigated the basic
global geometry of congruence moduli curves and shape curves of 3-body motions
with vanishing angular momentum. Here the study is extended to the case of
planary 3-body motions in general. In particular, the results on the separation
of the size and the shape variables, as well as the theorem on the unique
parametrization of moduli and shape curves, are established.
