Molecular escape-speed temperature estimate
= Molecular escape-speed temperature estimate
Equating the molecular root-mean-square speed to the surface <escape velocity> gives $3k_BT/m=2GM/R$, or $T=2mGM/(3k_BR)$. This compares speed scales; the high-speed tail can escape below that <temperature>, and molecular dissociation can invalidate the assumed species at high <temperature>.