Constant-rate retro-rocket landing
= Constant-rate retro-rocket landing
With downward <speed> $v$, downward relative exhaust <speed> $v_E>0$ and <mass> $M=M_0-\alpha t$, the ideal vertical equation is $\dot v=g-\alpha v_E/M$. Integration gives $v=v_0+gt+v_E\log(M/M_0)$. Height follows from $\dot h=-v$; its touchdown condition must be imposed together with the final fuel fraction.