  Geometric reduction of the Newtonian planar three-body problem is
investigated in the framework of equivariant Riemannian geometry, which reduces
the study of trajectories of three-body motions to the study of their moduli
curves, that is, curves which record the change of size and shape, in the
moduli space of oriented mass-triangles. The latter space is a Riemannian cone
over the shape 2-sphere, and the shape curve is the image curve on this sphere.
It is shown that the time parametrized moduli curve is in general determined by
the relative geometry of the shape curve and the shape potential function. This
also entails the reconstruction of time, namely the geometric shape curve
determines the time parametrization of the moduli curve, hence also the
three-body motion itself, modulo a fixed rotation of the plane. The first
version of this work is an (unpublished) paper from 2012, and the present
version is an editorial revision of this.
