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==Theory== The [[Tsiolkovsky rocket equation]] shows, using the law of [[conservation of momentum]], that for a [[rocket engine]] propulsion method to change the momentum of a spacecraft, it must change the momentum of something else in the opposite direction. In other words, the rocket must exhaust mass opposite the spacecraft's acceleration direction, with such exhausted mass called [[propellant]] or [[reaction mass]].<ref>{{Cite book |last=Turner |first=Martin J. L. |title=Rocket and spacecraft propulsion: principles, practice and new developments |date=2009 |publisher=Praxis Publ |isbn=978-3-540-69202-7 |edition=3rd |series=Springer-Praxis books in astronautical engineering |location=Chichester, UK}}</ref>{{Rp|location=Sec 1.2.1}}<ref name="ReactiveFlyingMachines">{{Cite web |last=Tsiolkovsky |first=K. |title=Reactive Flying Machines |url=http://epizodsspace.airbase.ru/bibl/inostr-yazyki/tsiolkovskii/tsiolkovskii-nhedy-t2-1954.pdf}}</ref> For this to happen, both reaction mass and energy are needed. The impulse provided by launching a particle of reaction mass with mass ''m'' at velocity ''v'' is ''mv''. But this particle has kinetic energy ''mv''Β²/2, which must come from somewhere. In a conventional [[solid rocket|solid]], [[liquid-propellant rocket|liquid]], or [[hybrid rocket]], fuel is burned, providing the energy, and the reaction products are allowed to flow out of the [[Rocket engine nozzle|engine nozzle]], providing the reaction mass. In an [[ion thruster]], electricity is used to accelerate ions behind the spacecraft. Here other sources must provide the electrical energy (e.g. a [[Photovoltaic module|solar panel]] or a [[nuclear reactor]]), whereas the ions provide the reaction mass.<ref name="beginners_guide" /> The rate of change of [[velocity]] is called [[acceleration]] and the rate of change of [[momentum]] is called [[force]].<ref>{{Cite web |title=Momentum |url=https://pages.uoregon.edu/jschombe/glossary/momentum.html |access-date=2024-04-19 |website=pages.uoregon.edu}}</ref> To reach a given velocity, one can apply a small acceleration over a long period of time, or a large acceleration over a short time; similarly, one can achieve a given impulse with a large force over a short time or a small force over a long time. This means that for maneuvering in space, a propulsion method that produces tiny accelerations for a long time can often produce the same impulse as another which produces large accelerations for a short time.<ref name=":2">{{Cite web |title=Impulsive Maneuvers β Orbital Mechanics & Astrodynamics |url=https://orbital-mechanics.space/orbital-maneuvers/impulsive-maneuvers.html |access-date=2024-05-18 |website=orbital-mechanics.space}}</ref> However, when launching from a planet, tiny accelerations cannot overcome the planet's gravitational pull and so cannot be used.<ref>{{cite web|publisher=National Air and Space Museum| url=https://howthingsfly.si.edu/ask-an-explainer/how-much-force-rocket-launch | date=January 14, 2014 |access-date=September 7, 2024| title=Ask an Explainer: How much force is in a rocket launch?}}</ref> Some designs however, operate [[#Without internal reaction mass|without internal reaction mass]] by taking advantage of magnetic fields or light pressure to change the spacecraft's momentum. === Efficiency === When discussing the efficiency of a propulsion system, designers often focus on the effective use of the reaction mass, which must be carried along with the rocket and is irretrievably consumed when used.<ref name=embry>{{cite web| publisher=Embry Riddle Aeronautical University|url=https://eaglepubs.erau.edu/introductiontoaerospaceflightvehicles/chapter/rocket-engines/ | title=Introduction to Aerospace Flight Vehicles|date=January 2023 |access-date=September 7, 2024|quote=The shape and length of the combustion chamber and exit nozzle are essential design parameters for a rocket engine. The combustion chamber must be long enough for complete propellant combustion before the hot gases enter the nozzle, ensuring efficient combustion and maximizing thrust production. |last1=Leishman |first1=J. Gordon }}</ref> Spacecraft performance can be quantified in ''amount of change in momentum per unit of propellant consumed,'' also called [[specific impulse]]. This is a measure of the amount of [[Impulse (physics)|impulse]] that can be obtained from a fixed amount of reaction mass. The higher the specific impulse, the better the efficiency. [[Ion thruster|Ion propulsion engines]] have high specific impulse (~3000 s) and low thrust<ref>{{Cite web |title=Xenon Ion Propulsion System (XIPS) Thrusters |url=https://www2.l3t.com/edd/pdfs/datasheets/EP_Thrusters-XIPS_PPU%20Overview%20datasheet.pdf |archive-url=https://web.archive.org/web/20180417143504/http://www2.l3t.com/edd/pdfs/datasheets/EP_Thrusters-XIPS_PPU%20Overview%20datasheet.pdf |archive-date=17 April 2018 |access-date=16 March 2019 |website=L3 Technologies}}</ref> whereas chemical rockets like [[Monopropellant rocket|monopropellant]] or [[bipropellant]] rocket engines have a low specific impulse (~300 s) but high thrust.<ref>{{Cite web |title=Chemical Bipropellant thruster family |url=http://www.space-propulsion.com/brochures/bipropellant-thrusters/bipropellant-thrusters.pdf |access-date=16 March 2019 |website=Ariane Group}}</ref> The impulse per unit weight-on-Earth (typically designated by <math>I_\text{sp}</math>) has units of seconds.<ref name=":2" /> Because the weight on Earth of the reaction mass is often unimportant when discussing vehicles in space, specific impulse can also be discussed in terms of impulse per unit mass, with the same units as velocity (e.g., meters per second).<ref>{{Cite web |title=Specific Impulse |url=https://www.grc.nasa.gov/www/k-12/airplane/specimp.html |access-date=May 18, 2024 |website=[[NASA]]}}</ref> This measure is equivalent to the [[effective exhaust velocity]] of the engine, and is typically designated <math>v_{e}</math>.<ref>{{Cite web |title=Chapter 3: Gravity & Mechanics β NASA Science |url=https://science.nasa.gov/learn/basics-of-space-flight/chapter3-2/ |access-date=2024-04-19 |website=science.nasa.gov |date=20 July 2023 |language=en-US}}</ref> Either the change in momentum per unit of propellant used by a spacecraft, or the velocity of the propellant exiting the spacecraft, can be used to measure its "specific impulse." The two values differ by a factor of the [[standard gravity|standard acceleration due to gravity, ''g''<sub>n</sub>]], 9.80665 m/sΒ² (<math>I_\text{sp} g_\mathrm{n} = v_{e}</math>).<ref name=":4">{{Cite web |title=III.4.2.1: Rockets and Launch Vehicles |url=https://www.faa.gov/sites/faa.gov/files/about/office_org/headquarters_offices/avs/III.4.2.1_Rockets_and_Launch_Vehicles.pdf |access-date=May 18, 2024 |website=www.faa.gov}}</ref> In contrast to chemical rockets, electrodynamic rockets use electric or magnetic fields to accelerate a charged propellant. The benefit of this method is that it can achieve exhaust velocities, and therefore <math>I_\text{sp}</math>, more than 10 times greater than those of a chemical engine, producing steady thrust with far less fuel. With a conventional chemical propulsion system, 2% of a rocket's total mass might make it to the destination, with the other 98% having been consumed as fuel. With an electric propulsion system, 70% of what's aboard in low Earth orbit can make it to a deep-space destination.<ref>{{Cite web|last=Boyle|first=Alan|date=2017-06-29|title=MSNW's plasma thruster just might fire up Congress at hearing on space propulsion|url=https://www.geekwire.com/2017/msnws-plasma-thruster-just-might-fire-congress-hearing-space-propulsion/|access-date=2021-08-15|website=GeekWire|language=en-US}}</ref> However, there is a trade-off. Chemical rockets transform propellants into most of the energy needed to propel them, but their electromagnetic equivalents must carry or produce the power required to create and accelerate propellants. Because there are currently practical limits on the amount of power available on a spacecraft, these engines are not suitable for launch vehicles or when a spacecraft needs a quick, large impulse, such as when it brakes to enter a capture orbit. Even so, because electrodynamic rockets offer very high <math>I_\text{sp}</math>, mission planners are increasingly willing to sacrifice power and thrust (and the extra time it will take to get a spacecraft where it needs to go) in order to save large amounts of propellant mass.<ref name=" :4" />
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