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Tsiolkovsky 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 speed 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 number of such maneuvers):
:$\Delta v = v_\text \ln \frac$
where:
:$m_0$ is the initial total mass, including propellant. The mass measurements can be made in any unit form (kg, lb, tonnes, etc). This is because the ratios will still be the same.
:$m_1$ is the final total mass without propellant, also known as dry mass.
:$v_\text$ is the effective exhaust velocity,
:$\Delta v\$ is delta-v - the maximum change of velocity of the vehicle (with no external forces acting), and
:$\ln$ refers to the natural logarithm function.
(The equation can also be written using the specific impulse instead of the effective exhaust velocity by applying the formula $v_\text = I_\text \cdot g_0$ where $I_\text$ is the specific impulse expressed as a time period and $g_0$ is standard gravity ≈9.8 m/s^2.)
The equation is named after Russian scientist Konstantin Tsiolkovsky who independently derived it and published it in his 1903 work.〔К. Э. Циолковский, Исследование мировых пространств реактивными приборами, 1903. It is available online (here ) in a RARed PDF〕 The equation had been derived earlier by the British mathematician William Moore in 1813.〔
==History==
This equation was independently derived by Konstantin Tsiolkovsky towards the end of the 19th century and is sometimes known under his name, but more often simply referred to as 'the rocket equation' (or sometimes the 'ideal rocket equation').
While the derivation of the rocket equation is a straightforward calculus exercise, Tsiolkovsky is honored as being the first to apply it to the question of whether rockets could achieve speeds necessary for space travel.

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