Orbits of the three-body problem with large potential

Consider the planar three-body problem with masses positive $m_1,m_2,m_3$ position vector $q(t)=(q_1(t),q_2(t),q_3(t))\in {\mathbb{R}}^6$. Let $$U(q)=\frac{m_1{m}_2}{r_{12}}+\frac{m_1{m}_3}{r_{13}}+\frac{m_2{m}_3}{r_{23}}$$ where $r_{ij}=\mathrm{\mid }{q}_i-q_j\mathrm{\mid }$. Assume that the angular momentum is nonzero so that triple collision is impossible and fix any negative energy… Then given any constant $K>0$ there are solutions with $U(q(t))\ge K$ for all $t\in \mathbb{R}$. These solutions will have a single close approach to triple collision. The configuration will always be a tight binary with $m_1,m_2$ close and the distance from the binary to $m_3$ diverging as $t\to \pm \mathrm{\infty }$.