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 speed and move due to the conservation of momentum. The equation relates the delta-v (the maximum change of speed 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 number of such maneuvers):
where:
- is the initial total mass, including propellant,
- is the final total mass,
- is the effective exhaust velocity ( where is the specific impulse expressed as a time period and is Standard Gravity),
- is delta-v - the maximum change of speed of the vehicle (with no external forces acting),
- refers to the natural logarithm function.
Units used for mass or velocity do not matter as long as they are consistent.
The equation is named after Konstantin Tsiolkovsky who independently derived it and published it in his 1903 work.
Read more about Tsiolkovsky Rocket Equation: History, Derivation, Applicability, Examples, Stages, Common Misconceptions
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