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A rocket's required mass ratio as a function of effective exhaust velocity ratio. The classical rocket equation, or ideal rocket equation is a mathematical equation that describes the motion of vehicles that follow the basic principle of a rocket: a device that can apply acceleration to itself using thrust by expelling part of its mass with high velocity and can thereby move due to the ...
This equation can be rewritten in the following equivalent form: = / The fraction on the left-hand side of this equation is the rocket's mass ratio by definition. This equation indicates that a Δv of n {\displaystyle n} times the exhaust velocity requires a mass ratio of e n {\displaystyle e^{n}} .
Relativistic rocket means any spacecraft that travels close enough to light speed for relativistic effects to become significant. The meaning of "significant" is a matter of context, but often a threshold velocity of 30% to 50% of the speed of light (0.3c to 0.5c) is used.
The specific impulse of a rocket can be defined in terms of thrust per unit mass flow of propellant. This is an equally valid (and in some ways somewhat simpler) way of defining the effectiveness of a rocket propellant. For a rocket, the specific impulse defined in this way is simply the effective exhaust velocity relative to the rocket, v e ...
Rocket mass ratios versus final velocity calculated from the rocket equation. 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 Tsiolkovsky rocket equation shows that the delta-v of a rocket (stage) is proportional to the logarithm of the fuelled-to-empty mass ratio of the vehicle, and to the specific impulse of the rocket engine. A key goal in designing space-mission trajectories is to minimize the required delta-v to reduce the size and expense of the rocket that ...
When applied to a rocket as a whole, a low mass fraction is desirable, since it indicates a greater capability for the rocket to deliver payload to orbit for a given amount of fuel. Conversely, when applied to a single stage, where the propellant mass fraction calculation doesn't include the payload, a higher propellant mass fraction ...
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).