Tsiolkovsky's rocket equation

The Tsiolkovsky rocket equation, or ideal rocket equation, describes the motion of vehicles that follow the basic principle of a rocket: a device that can apply acceleration to itself (a thrust) by expelling part of its mass with high velocity and thereby move due to the conservation of momentum. The equation relates the delta-v (the maximum change of velocity of the rocket if no other external forces act) with the effective exhaust velocity and the initial and final mass of a rocket (or other reaction engine).

For any such maneuver (or journey involving a sequence of such maneuvers):

where:

(The equation can also be written using the specific impulse instead of the effective exhaust velocity by applying the formula ${\displaystyle v_{\text{e}}=I_{\text{sp}}\cdot g_{0}}$ where ${\displaystyle I_{\text{sp}}}$ is the specific impulse expressed as a time period and ${\displaystyle g_{0}}$ is standard gravity ≈ 9.8 m/s².)

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