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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 ...
It is related to the thrust, or forward force on the rocket by the equation: [11] = ˙, where ˙ is the propellant mass flow rate, which is the rate of decrease of the vehicle's mass. A rocket must carry all its propellant with it, so the mass of the unburned propellant must be accelerated along with the rocket itself.
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}} .
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).
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 rocket is launched using liquid hydrogen and liquid oxygen cryogenic propellants. Rocket propellant is used as reaction mass ejected from a rocket engine to produce thrust . The energy required can either come from the propellants themselves, as with a chemical rocket , or from an external source, as with ion engines .
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 ...
This is just the rocket equation applied to the sum of the two maneuvers. This is convenient since it means that delta-v can be calculated and simply added and the mass ratio calculated only for the overall vehicle for the entire mission. Thus delta-v is commonly quoted rather than mass ratios which would require multiplication.