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Equation stating that the change in velocity (delta-v) of a single stage rocket is equal to the exhaust velocity times the natural log of the ratio of final to initial mass, named after Russian scientist Konstantin Tsiolkovsky.

The Tsiolkovsky Rocket Equation states that the change in velocity (delta-v) of a single stage rocket is equal to the exhaust velocity times the natural log of the ratio of final to initial mass. It is named after Russian scientist Konstantin Tsiolkovsky.

$$\Delta v = v_{ex} log\left( \frac{m_0}{m_f} \right)$$

where $$m_0$$ and $$m_f$$ are the initial and final masses and $$v_e$$ is the exhaust velocity.

The equation should be applied to a single stage at a time, because it assumes that all of the change in mass ($$m_0 - m_f$$) is reaction mass, leaving at the exhaust velocity $$v_e$$.