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The Tsiolkovsky rocket equation or ideal rocket equation is an equation used to calculate the impulse imparted by a rocket which other object ejecting mass, such as a hose. The equation is

$ \Delta v = v_\text{e} \ln \frac {m_i} {m_f} $

where ∆v is the change in velocity, ve is the velocity of the ejected material, mi is the initial mass and mf is the final mass. In a gravitational field, this becomes

$ \Delta v = v_\text{e} \ln \frac {m_i} {m_f} - gt $