2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/107512A syzygy in the three-body problem is a collinear instant. We prove that with the exception of Lagrange's solution every solution to the zero angular momentum Newtonian three-body problem suffers syzygies. The proof works for all mass ratios.12 pages. 1 figureDynamical SystemsClassical Analysis and ODEs34C25, 37J20, 70E55The only syzygy-free solution is Lagrange'stext