Engineering Sciences

Rocket Science

1903

Intermediate

Tsiolkovsky Rocket Equation

\Delta v = v_e \ln\frac{m_0}{m_f}

Change in velocity depends on exhaust velocity and the natural log of initial to final mass ratio.

By Konstantin Tsiolkovsky

Engineering Sciences

1903 · Konstantin Tsiolkovsky

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Story PortalWho discovered this?Discover how Konstantin Tsiolkovsky and others shaped this equation.Visual PortalWhat does it look like?See the equation come alive in the Visual Studio.Machine PortalWhere is it used?Explore machines powered by this equation — rocket engines and orbital launchers.Math PortalWhat does it derive from?Trace the mathematical lineage from conservation of momentum.Future PortalWhere is it going?Reusable rockets and interplanetary Δv budgets

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Why it matters: The fundamental equation of rocketry—every space mission depends on it.

Discoverers: Konstantin Tsiolkovsky (1903)

What does it mean?

Change in velocity depends on exhaust velocity and the natural log of initial to final mass ratio.

Why should I care?

The fundamental equation of rocketry—every space mission depends on it.

Equation Compass

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West — History

Konstantin Tsiolkovsky

East — Applications

South — Derivations

Derivation

Variables & Units

Symbol	Name	Unit	Meaning
$Δv$	Delta-v	m/s	Velocity change
$v_e$	Exhaust velocity	m/s	Effective exhaust speed
$m₀$	Initial mass	kg	Wet mass
$m_f$	Final mass	kg	Dry mass

Worked Example

v_e=3000 m/s, mass ratio 10 → Δv ≈ 6907 m/s.

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Sources & further reading

Search Wikipedia Search Wolfram MathWorld Open in Wolfram|Alpha Watch explainers on YouTube

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