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| In [[spaceflight]], an '''orbital maneuver''' is the use of [[spacecraft propulsion|propulsion]] systems to change the [[orbit]] of a [[spacecraft]].
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| For spacecraft far from Earth (for example those in orbits around the Sun) an orbital maneuver is called a ''deep-space maneuver (DSM)''.{{citation needed (lead)|date=September 2011}} | |
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| The rest of the flight, especially in a [[transfer orbit]], is called '''coasting'''.
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| ==General==
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| ===Rocket equation===
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| {{main|Tsiolkovsky rocket equation}}
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| [[File:Rocket mass ratio versus delta-v.svg|thumb|right|Rocket [[mass ratio]]s versus final velocity calculated from the rocket equation]]
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| The '''Tsiolkovsky rocket equation''', or '''ideal rocket equation''' is an equation that is useful for considering vehicles that follow the basic principle of a [[rocket]]: where a device that can apply acceleration to itself (a [[thrust]]) by expelling part of its mass with high speed and moving due to the conservation of [[momentum]]. Specifically, it is a mathematical equation that relates the [[delta v#Astrodynamics|delta-v]] (the maximum change of speed 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]].)
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| For any such maneuver (or journey involving a number of such maneuvers):
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| :<math>\Delta v = v_\text{e} \ln \frac {m_0} {m_1}</math>
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| where:
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| :<math>m_0</math> is the initial total mass, including propellant,
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| :<math>m_1</math> is the final total mass,
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| :<math>v_\text{e}</math> is the [[effective exhaust velocity]] (<math>v_\text{e} = I_\text{sp} \cdot g_0</math> where <math>I_\text{sp}</math> is the [[specific impulse]] expressed as a time period and <math>g_0</math> is the gravitational constant),
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| :<math>\Delta v\ </math> is delta-v - the maximum change of speed of the vehicle (with no external forces acting).
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| ===Delta-v===
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| {{main|Delta-v}}
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| The applied change in speed of each maneuver is referred to as [[delta-v]] (<math>\Delta\mathbf{v}\,</math>).
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| ===Delta-v budget===
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| {{main|delta-v budget}}
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| The total delta-v for all and each maneuver is estimated for a mission is called a [[delta-v budget]]. With a good approximation of the delta-v budget designers can estimate the fuel to payload requirements of the spacecraft using the [[Tsiolkovsky rocket equation|rocket equation]].
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| ===Impulsive maneuvers===
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| [[File:Impulsive maneuver.svg|thumb|Figure 1: Approximation of a finite thrust maneuver with an impulsive change in velocity]]
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| An "impulsive maneuver" is the mathematical model of a maneuver as an instantaneous change in the spacecraft's [[velocity]] (magnitude and/or direction) as illustrated in figure 1.
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| In the physical world no truly instantaneous change in velocity is possible as this would require an "infinite force" applied during an "infinitely short time" but as a mathematical model it in most cases describes the effect of a maneuver on the orbit very well.
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| The off-set of the velocity vector after the end of real burn from the velocity vector at the same time resulting from the theoretical impulsive maneuver is only caused by the difference in gravitational force along the two paths (red and black in figure 1) which in general is small.
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| In the planning phase of space missions designers will first approximate their intended orbital changes using impulsive maneuvers that greatly reduces the complexity of finding the correct orbital transitions.
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| ===Applying a low thrust over a longer period of time===
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| Applying a low thrust over a longer period of time is referred to as a '''non-impulsive maneuver''' (where 'non-impulsive' refers to the maneuver not being of a short time period rather than not involving ''[[impulse (physics)|impulse]]''- change in momentum, which clearly must take place).{{Citation needed|date=December 2011}}
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| Another term is ''finite burn'', where the word "finite" is used to mean "non-zero", or practically, again: over a longer period.
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| For a few space missions, such as those including a [[space rendezvous]], high fidelity models of the trajectories are required to meet the mission goals. Calculating a "finite" burn requires a detailed model of the [[spacecraft]] and its thrusters. The most important of details include: [[mass]], [[center of mass]], [[moment of inertia]], thruster positions, thrust vectors, thrust curves, [[specific impulse]], thrust [[centroid]] offsets, and fuel consumption.
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| ===Assists===
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| ====Oberth effect====
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| {{main|Oberth effect}}
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| In [[astronautics]], the '''Oberth effect''' is where the use of a [[rocket engine]] when travelling at high speed generates much more useful energy than one at low speed. Oberth effect occurs because the [[propellant]] has more usable energy (due to its kinetic energy on top of its chemical potential energy) and it turns out that the vehicle is able to employ this kinetic energy to generate more mechanical power. It is named after [[Hermann Oberth]], the [[Austria-Hungary|Austro-Hungarian]]-born, [[Germany|German]] [[physicist]] and a founder of modern [[rocket]]ry, who apparently first described the effect.<ref name=ways>[http://hdl.handle.net/2060/19720008133 NASA-TT-F-622: Ways to spaceflight p 200 - Herman Oberth]</ref>
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| Oberth effect is used in a '''powered flyby''' or '''Oberth maneuver''' where the application of an impulse, typically from the use of a rocket engine, close to a gravitational body (where the [[gravity potential]] is low, and the speed is high) can give much more change in [[kinetic energy]] and final speed (i.e. higher [[specific energy]]) than the same impulse applied further from the body for the same initial orbit. For the Oberth effect to be most effective, the vehicle must be able to generate as much impulse as possible at the lowest possible altitude; thus the Oberth effect is often far less useful for low-thrust reaction engines such as [[ion drive]]s, which have a low propellant flow rate.
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| Oberth effect also can be used to understand the behaviour of multi-stage rockets; the upper stage can generate much more usable kinetic energy than might be expected from simply considering the chemical energy of the propellants it carries.
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| Historically, a lack of understanding of this effect led early investigators to conclude that interplanetary travel would require completely impractical amounts of propellant, as without it, enormous amounts of energy are needed.<ref name=ways/>
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| ====Gravitational assist====
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| {{main|Gravity assist}}
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| [[Image:Voyager Path.svg|thumb|The trajectories that enabled NASA's twin Voyager spacecraft to tour the four gas giant planets and achieve velocity to escape our solar system]]
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| In [[orbital mechanics]] and [[aerospace engineering]], a '''gravitational slingshot''', '''gravity assist maneuver''', or '''swing-by''' is the use of the relative movement and [[gravity]] of a [[planet]] or other celestial body to alter the [[Course (navigation)|path]] and [[speed]] of a [[spacecraft]], typically in order to save [[propellant]], [[time]], and expense. Gravity assistance can be used to [[accelerate]], [[deceleration|decelerate]] and/or re-direct the path of a spacecraft.
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| The "assist" is provided by the motion (orbital [[angular momentum]]) of the gravitating body as it pulls on the spacecraft.<ref>http://www2.jpl.nasa.gov/basics/bsf4-1.php Basics of Space Flight, Sec. 1 Ch. 4, NASA Jet Propulsion Laboratory</ref> The technique was first proposed as a mid-course manoeuvre in 1961, and used by interplanetary probes from ''[[Mariner 10]]'' onwards, including the two ''[[Voyager program|Voyager]]'' probes' notable fly-bys of Jupiter and Saturn.
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| ==Transfer orbits==
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| [[Orbit insertion]] is a general term for a maneuver that is more than a small correction. It may be used for a maneuver to change a [[transfer orbit]] or an ascent orbit into a stable one, but also to change a stable orbit into a descent: ''descent orbit insertion''. Also the term '''orbit injection''' is used, especially for changing a stable orbit into a transfer orbit, e.g. [[trans-lunar injection]] (TLI), [[trans-Mars injection]] (TMI) and [[trans-Earth injection]] (TEI).
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| ===Hohmann transfer===
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| [[Image:Hohmann transfer orbit.svg|thumb|Hohmann Transfer Orbit]]
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| {{main|Hohmann transfer orbit}}
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| In [[orbital mechanics]], the '''Hohmann transfer orbit''' is an elliptical orbit used to transfer between two [[circular orbit]]s of different altitudes, in the same [[Plane (geometry)|plane]].
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| The orbital maneuver to perform the Hohmann transfer uses two engine impulses which move a [[spacecraft]] onto and off the transfer orbit. This maneuver was named after [[Walter Hohmann]], the [[Germany|German]] scientist who published a description of it in his 1925 book ''Die Erreichbarkeit der Himmelskörper'' (''The Accessibility of Celestial Bodies'').<ref>Walter Hohmann, ''The Attainability of Heavenly Bodies'' (Washington: NASA Technical Translation F-44, 1960) [http://www.archive.org/details/nasa_techdoc_19980230631 Internet Archive].</ref> Hohmann was influenced in part by the German science fiction author [[Kurd Laßwitz]] and his 1897 book ''[[Two Planets]]''.{{Citation needed|date=November 2011}}
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| ===Bi-elliptic transfer===
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| {{main|Bi-elliptic transfer}}
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| In [[astronautics]] and [[aerospace engineering]], the '''bi-elliptic transfer''' is an orbital maneuver that moves a [[spacecraft]] from one [[orbit]] to another and may, in certain situations, require less [[delta-v]] than a [[Hohmann transfer orbit|Hohmann transfer]] maneuver.
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| The bi-elliptic transfer consists of two half [[elliptic orbit]]s. From the initial orbit, a delta-v is applied boosting the spacecraft into the first transfer orbit with an [[apoapsis]] at some point <math>r_b</math> away from the [[central body]]. At this point, a second delta-v is applied sending the spacecraft into the second elliptical orbit with [[periapsis]] at the radius of the final desired orbit, where a third delta-v is performed, injecting the spacecraft into the desired orbit.{{Citation needed|date=December 2011}}
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| While they require one more engine burn than a Hohmann transfer and generally requires a greater travel time, some bi-elliptic transfers require a lower amount of total delta-v than a Hohmann transfer when the ratio of final to initial [[semi-major axis]] is 11.94 or greater, depending on the intermediate semi-major axis chosen.<ref>{{Cite book | last = Vallado | first = David Anthony | title = Fundamentals of Astrodynamics and Applications | page = 317 | publisher = Springer | year = 2001 | isbn = 0-7923-6903-3 | url = http://books.google.com/books?id=PJLlWzMBKjkC&printsec}}</ref>
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| The idea of the bi-elliptical transfer trajectory was first published by [[Ary Sternfeld]] in 1934.<ref>Sternfeld A., Sur les trajectoires permettant d'approcher d'un corps attractif central à partir d'une orbite keplérienne donnée. - Comptes rendus de l'Académie des sciences (Paris), vol. 198, pp. 711 - 713.</ref>
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| ===Low energy transfer===
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| {{main|low energy transfer}}
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| A '''low energy transfer''', or low energy [[trajectory]], is a route in space which allows spacecraft to change [[orbit]]s using very little fuel.<ref name=Capture>{{cite book|last=Belbruno|first=Edward|authorlink= Edward Belbruno |title=Capture Dynamics and Chaotic Motions in Celestial Mechanics: With Applications to the Construction of Low Energy Transfers|publisher=[[Princeton University Press]]|year=2004|pages=224|isbn=978-0-691-09480-9|url=http://press.princeton.edu/titles/7687.html}}</ref><ref name=FlyMe>{{cite book|last=Belbruno|first=Edward|authorlink= Edward Belbruno |title= Fly Me to the Moon: An Insider's Guide to the New Science of Space Travel |publisher=[[Princeton University Press]]|year=2007|pages=176|isbn= 978-0-691-12822-1|url=http://press.princeton.edu/titles/8375.html}}</ref> These routes work in the [[Earth]]-[[Moon]] system and also in other systems, such as traveling between the [[satellites of Jupiter]]. The drawback of such trajectories is that they take much longer to complete than higher energy (more fuel) transfers such as [[Hohmann transfer orbit]]s.
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| Low energy transfer are also known as weak stability boundary trajectories, or ballistic capture trajectories.
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| Low energy transfers follow special pathways in space, sometimes referred to as the [[Interplanetary Transport Network]]. Following these pathways allows for long distances to be traversed for little expenditure of [[delta-v]].
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| ===Orbital inclination change===
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| {{main|orbital inclination change}}
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| '''Orbital inclination change''' is an orbital maneuver aimed at changing the [[inclination]] of an orbiting body's [[orbit]]. This maneuver is also known as an orbital plane change as the plane of the orbit is tipped. This maneuver requires a change in the orbital velocity vector ([[delta v]]) at the [[orbital nodes]] (i.e. the point where the initial and desired orbits intersect, the line of orbital nodes is defined by the intersection of the two orbital planes).
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| In general, inclination changes can require a great deal of delta-v to perform, and most mission planners try to avoid them whenever possible to conserve fuel. This is typically achieved by launching a spacecraft directly into the desired inclination, or as close to it as possible so as to minimize any inclination change required over the duration of the spacecraft life.
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| Maximum efficiency of inclination change is achieved at [[apoapsis]], (or [[apogee]]), where orbital velocity <math>v\,</math> is the lowest. In some cases, it may require less total delta v to raise the satellite into a higher orbit, change the orbit plane at the higher apogee, and then lower the satellite to its original altitude.<ref name=Braeunig>{{cite web |url=http://www.braeunig.us/space/orbmech.htm#maneuver |title=Basics of Space Flight: Orbital Mechanics |last=Braeunig |first=Robert A}}</ref>
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| ===Brachistochrone trajectory===
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| A Brachistochrone trajectory is the fastest possible transit time between two points or bodies in space. It involves the spacecraft pointing straight towards the target position (accounting for the motion of the target), and then firing its engine in a prolonged constant burn. The spacecraft remains accelerating constantly under high thrust until it reaches its target. If it is required that the spacecraft rendezvous with the target, rather than performing a flyby, then the spacecraft must flip its orientation halfway through the journey, and decelerate the rest of the way.
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| This trajectory requires that the spacecraft maintain a high acceleration for long durations. For interplanetary transfers, days, weeks or months of constant thrusting may be required. As a result, there are no currently available spacecraft propulsion systems capable of using this trajectory. It has been suggested that some forms of nuclear (fission or fusion based) or antimatter powered rockets would be capable of this trajectory.
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| ==Rendezvous and docking==
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| ===Orbit phasing===
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| {{main|Orbit phasing}}
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| In [[astrodynamics]] '''orbit phasing''' is the adjustment of the time-position of spacecraft along its [[orbit]], usually described as adjusting the orbiting spacecraft's [[true anomaly]].
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| ===Space rendezvous and docking===
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| {{main|Space rendezvous}}
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| [[Image:Gemini 7 in orbit - GPN-2006-000035.jpg|right|thumb|Gemini 7 photographed from Gemini 6 in 1965]]
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| A '''space rendezvous''' is an orbital maneuver during which two [[spacecraft]], one of which is often a [[space station]], arrive at the same [[orbit]] and approach to a very close distance (e.g. within visual contact). Rendezvous requires a precise match of the [[orbital speed|orbital velocities]] of the two spacecraft, allowing them to remain at a constant distance through [[orbital station-keeping]]. Rendezvous may or may not be followed by [[Spacecraft Docking and Berthing Mechanisms|docking or berthing]], procedures which bring the spacecraft into physical contact and create a link between them.
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| ==See also==
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| {{Portal|Spaceflight}}
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| * [[Collision avoidance (spacecraft)]]
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| * [[In-space propulsion technologies]]
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| ==References==
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| {{reflist}}
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| ==External links==
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| *[http://www.cambridge.org/catalogue/catalogue.asp?isbn=9780521089869 Handbook Automated Rendezvous and Docking of Spacecraft] by [[Wigbert Fehse]]
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| {{Orbits}}
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| {{Use American English|date=January 2014}}
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| {{DEFAULTSORT:Orbital Maneuver}}
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| [[Category:Astrodynamics]]
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| [[Category:Orbital maneuvers]]
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