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German engineer Hermann Oberth independently derived the equation about 1920 as he studied the feasibility of space travel. 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.
At 30% c, the difference between relativistic mass and rest mass is only about 5%, while at 50% it is 15%, (at 0.75c the difference is over 50%); so above such speeds special relativity is needed to accurately describe motion, while below this range Newtonian physics and the Tsiolkovsky rocket equation usually give sufficient accuracy.
The definition arises naturally from Tsiolkovsky's rocket equation: = where Δv is the desired change in the rocket's velocity; v e is the effective exhaust velocity (see specific impulse) m 0 is the initial mass (rocket plus contents plus propellant)
Thoughts on the use of the rocket principle in the cosmos were expressed by him as early as 1883, and a rigorous theory of rocket propulsion was developed in 1896. Tsiolkovsky derived the formula, which he called the "formula of aviation", now known as Tsiolkovsky rocket equation, establishing the relationship between:
Rocket mass ratios versus final velocity calculated from the rocket equation Main article: Tsiolkovsky rocket equation The ideal rocket equation , or the Tsiolkovsky rocket equation, can be used to study the motion of vehicles that behave like a rocket (where a body accelerates itself by ejecting part of its mass, a propellant , with high speed).
Minimizing the mass of propellant required to achieve a given change in velocity is crucial to building effective rockets. The Tsiolkovsky rocket equation shows that for a rocket with a given empty mass and a given amount of propellant, the total change in velocity it can accomplish is proportional to the effective exhaust velocity.
Delta-v is produced by reaction engines, such as rocket engines, and is proportional to the thrust per unit mass and the burn time. It is used to determine the mass of propellant required for the given maneuver through the Tsiolkovsky rocket equation. For multiple maneuvers, delta-v sums linearly.
The Tsiolkovsky rocket equation, or ideal rocket equation, can be useful for analysis of maneuvers by vehicles using rocket propulsion. [2] A rocket applies acceleration to itself (a thrust) by expelling part of its mass at high speed. The rocket itself moves due to the conservation of momentum.