 Stellar collision cross-section

For two approximately spherical stars approaching with speed $v_{\infty }$, contact at separation $R_1+R_2$ has gravitationally focused cross section $\pi (R_1+R_2{)}^2[1+2G(m_1+m_2)/((R_1+R_2)v_{\infty }^2)]$. This measures direct stellar encounters, not the probability of a collective encounter between their host galaxies.