Hovering rocket mass flow
= Hovering rocket mass flow
{title2=$\alpha(t)=gM_0e^{-gt/u}/u$}
For constant gravity and downward <rocket exhaust speed> $u$, hovering requires <rocket thrust> $u\alpha=Mg$ with $\alpha=-\dot M$. Hence $M=M_0e^{-gt/u}$ and the required <mass flow rate> decays exponentially. A nonzero <rocket dry mass> ends the hover at finite time, even though this mass equation tends to zero only asymptotically.