Negative-energy gravitational collision ($t_{\mathrm{coll}}=\pi \sqrt{a^3/[8G(m_1+m_2)]}$)

Two point masses released from rest at separation $a$ have negative mechanical energy $-G{m}_1{m}_2/a$ but collide in time $\pi \sqrt{a^3/[8G(m_1+m_2)]}$. Their separation approaches zero along a regular trajectory before collision. The energy sign alone therefore does not supply a positive lower separation bound.