  We consider the Newtonian planar three-body problem, defining a syzygy
(velocity syzygy) as a configuration where the positions (velocities) of the
three bodies become collinear. We demonstrate that if the total energy is
negative, every collision-free solution has an infinite number of velocity
syzygies. Specifically, the velocities of the three bodies become parallel
within every interval of time containing three consecutive syzygies. Using
comparison theory for matrix Riccati equations, we derive new upper and lower
bounds on the moments when syzygies occur.
