Tsiolkovsky Rocket Equation

Rocketry · 1903

Equation: Δv = v_e·ln(m₀/m_f)
Field: Rocketry
Named After: Konstantin Tsiolkovsky
Year: 1903

Symbols

Δv the change in velocity the burn can deliver · v_e exhaust velocity · m₀ mass at ignition, propellant included · m_f dry mass at burnout · the ratio inside the log is the whole game

Significance

A rocket must carry the fuel to push its fuel — so payload shrinks exponentially with the speed you want. Derived by a deaf, self-taught schoolteacher in provincial Russia the year the Wright brothers flew; it is why rockets are staged, why they are 90% propellant on the pad, and why orbit is hard and Mars is harder.