### The 3-body problem in Shape Space (2)

Let's compare the Newtonian decription with the one on

**S**,
for now in Newtonian time.

The dynamics starts near a 2-body collision, which in Newtonian
terms corresponds to one of the particles being very far from the
others. The distant particle moves towards the others, the moment
of inertia is decreasing and the dilatational momentum is
negative, but increasing in time. The representative point
emerges from the potential well in

**S**, as the third
body gets closer to the Keplerian pair (red curve).

When the representative point on

**S** has climbed out of the
potential well, the pair is destroyed and a three-body dynamics
dominates for a short (Newtonian) time. During this phase the
dilatational momentum reaches 0, and the logarithmic Shape time
encounters a coordinate singularity.

The arrow of time is reversed here, and the yellow curve starts. A
new Keplerian pair is formed, in this case between the same two
particles as before, meaning that the yellow curve sinks into the
same potential well the red curve came out of. The isolated
particle flies away and the Keplerian pair become increasingly
isolated, with a dynamics that becomes increasingly more
energy-preserving.

As the moment of inertia keeps growing indefinitely, the
representative point in

**S** falls ever more deeply into its
potential well.