Nearly cancelling recoil momenta in payload ejection

For downward pre-ejection speed $v_0$, total mass $M_0$, payload mass $m_p$, and downward payload speed $v_p$ in the original inertial frame, the remaining body's upward speed is $(m_p{v}_p-M_0{v}_0)/(M_0-m_p)$. When the numerator nearly cancels, distinguishing total initial mass from final body mass is essential.