This then yields Δ Δ V = v e ln ⁡ ⁡ m 0 m f or equivalently m f = m 0 e − − Δ Δ V / v e or m 0 = m f e Δ Δ V / v e or m 0 − − m f = m f ( e Δ Δ V / v e − − 1 ) where m 0 is the initial total mass including propellant, m f the final mass, and v e the velocity of the rocket exhaust with respect to the rocket (the specific impulse, or, if measured in time, that multiplied by gravity -on-Earth acceleration). If v e is NOT constant, we might not have rocket equations that are as simple as the above forms. Many rocket dynamics researches were based on the Tsiolkovsky's constant v e hypothesis.