View source for Orbital maneuver

{{Short description|A movement during spaceflight}}
{{Use American English|date=January 2014}}
{{Use American English|date=March 2021}}
{{Use mdy dates|date=March 2021}}
{{Astrodynamics |expanded=Propulsive maneuver}}

In [[spaceflight]], an '''orbital maneuver''' (otherwise known as a '''burn''') is the use of [[spacecraft propulsion|propulsion]] systems to change the [[orbit]] of a [[spacecraft]]. 
For spacecraft far from Earth, an orbital maneuver is called a ''deep-space maneuver (DSM)''.<ref>{{cite web |url=https://science.nasa.gov/learn/basics-of-space-flight/chapter13-1/ |title=Navigation |publisher=NASA}}</ref>

When a spacecraft is not conducting a maneuver, especially in a [[transfer orbit]], it is said to be  ''coasting''.

==General==

===Rocket equation===
{{Main|Tsiolkovsky rocket equation}}
[[File:Tsiolkovsky rocket equation.svg|thumb|Rocket [[mass ratio]]s 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.<ref>{{cite web |url=https://web.mit.edu/16.unified/www/SPRING/propulsion/notes/node103.html |title=The Rocket Equation |publisher=MIT}}</ref> 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]].

=== Delta-v ===
{{Main|Delta-v|delta-v budget}}
The applied change in velocity of each maneuver is referred to as [[delta-v]] (<math>\Delta\mathbf{v}\,</math>).

The delta-v for all the expected maneuvers are estimated for a mission are summarized in a [[delta-v budget]].  With a good approximation of the delta-v budget designers can estimate the propellant required for planned maneuvers.

== Propulsion ==
{{unreferenced |section |date=February 2024}}
===Impulsive maneuvers===
[[File:Impulsive maneuver.svg|thumb|Figure 1: Approximation of a finite thrust maneuver with an impulsive change in velocity]]
An '''impulsive maneuver''' is the mathematical model of a maneuver as an instantaneous change in the spacecraft's [[velocity]] (magnitude and/or direction)<ref>{{cite book |doi=10.1016/B978-0-12-374778-5.00006-4 |chapter=Orbital Maneuvers |title=Orbital Mechanics for Engineering Students |date=2010 |last1=Curtis |first1=Howard D. |pages=319–390 |isbn=978-0-12-374778-5 }}</ref> as illustrated in figure 1. It is the limit case of a burn to generate a particular amount of delta-v, as the burn time tends to zero.

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.

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.

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.

=== Low thrust propulsion ===
Applying a low thrust over a longer period of time is referred to as a '''non-impulsive maneuver'''. 'Non-impulsive' refers to the momentum changing slowly over a long time, as in [[electrically powered spacecraft propulsion]], rather than by a short impulse.<ref>{{Cite web |date=2020-10-22 |title=The Propulsion We're Supplying, It's Electrifying - NASA |url=https://www.nasa.gov/humans-in-space/the-propulsion-were-supplying-its-electrifying/ |access-date=2025-01-03 |language=en-US}}</ref>

Another term is ''finite burn'', where the word "finite" is used to mean "non-zero", or practically, again: over a longer period.

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.

==Assists==

===Oberth effect===
{{Main|Oberth effect}}
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>{{cite report |id=NASA-TT-F-622 |title=Ways to spaceflight |page=200 |first1=Herman |last1=Oberth |date=1970 |first2=R. |last2=Oldenbourg Verlag |publisher=NASA |hdl=2060/19720008133 }}</ref>

The 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.

Since the Oberth maneuver happens in a very limited time (while still at low altitude), to generate a high impulse the engine necessarily needs to achieve high thrust (impulse is by definition the time multiplied by thrust). Thus the Oberth effect is far less useful for low-thrust engines, such as [[ion thruster]]s.

Historically, a lack of understanding of this effect led 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/>

===Gravity assist===
{{Main|Gravity assist}}
[[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]]
In [[astrodynamics]] a  [[gravity assist]] maneuver, gravitational slingshot or swing-by is the use of the relative movement and [[gravity]] of a [[planet]] or other celestial body to alter the trajectory 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.

The "assist" is provided by the motion (orbital [[angular momentum]]) of the gravitating body as it pulls on the spacecraft.<ref>{{cite web |url=http://www2.jpl.nasa.gov/basics/bsf4-1.php | work=Basics of Space Flight |title=Section I. The Environment of Space - Chapter 4. Interplanetary Trajectories |publisher=NASA Jet Propulsion Laboratory |url-status=dead |archive-url=https://web.archive.org/web/20230403173539/https://www2.jpl.nasa.gov/basics/bsf4-1.php |archive-date= Apr 3, 2023 }}</ref> The technique was first proposed as a mid-course maneuver 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.

==Transfer orbits==
[[Orbit insertion]] maneuvers leave a spacecraft in a destination orbit. In contrast, orbit injection maneuvers occur when a spacecraft enters a transfer orbit, e.g. [[trans-lunar injection]] (TLI), [[trans-Mars injection]] (TMI) and [[trans-Earth injection]] (TEI). These are generally larger than small trajectory correction maneuvers. Insertion, injection and sometimes initiation are used to describe entry into a ''descent orbit'', e.g. the [[Powered Descent Initiation]] maneuver used for Apollo lunar landings.

===Hohmann transfer===
[[Image:Hohmann transfer orbit.svg|thumb|Hohmann Transfer Orbit]]
{{Main|Hohmann transfer orbit}}
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]].

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, ''[[iarchive:nasa_techdoc_19980230631|The Attainability of Heavenly Bodies]]'' (Washington: NASA Technical Translation F-44, 1960).</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}}

===Bi-elliptic transfer===
[[File:Bi-elliptic transfer.svg|thumb|Bi-elliptic transfer from blue to red circular orbit]]
{{Main|Bi-elliptic transfer}}
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.

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}}

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 = https://books.google.com/books?id=PJLlWzMBKjkC}}</ref>

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>

===Low energy transfer===
{{Main|low energy transfer}}
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|author-link= 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|author-link=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=[https://archive.org/details/flymetomoonusing00belb/page/176 176]|isbn=978-0-691-12822-1|url=https://archive.org/details/flymetomoonusing00belb/page/176|url-access=registration}}</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.

Low energy transfer are also known as [[Weak Stability Boundary|weak stability boundary]] trajectories, or ballistic capture trajectories.

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]].

===Orbital inclination change===
{{Main|orbital inclination change}}
'''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).

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.

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 spacecraft into a higher orbit, change the orbit plane at the higher apogee, and then lower the spacecraft 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 |access-date=2012-03-22 |archive-url=https://web.archive.org/web/20120204054322/http://www.braeunig.us/space/orbmech.htm#maneuver |archive-date=2012-02-04 |url-status=dead }}</ref>

===Constant-thrust trajectory===
Constant-thrust and [[Space travel using constant acceleration|constant-acceleration]] trajectories involve the spacecraft firing its engine in a prolonged constant burn. In the limiting case where the vehicle acceleration is high compared to the local gravitational acceleration, the spacecraft points straight toward the target (accounting for target motion), and remains accelerating constantly under high thrust until it reaches its target. In this high-thrust case, the trajectory approaches a straight line.  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.

In the constant-thrust trajectory,<ref>W. E. Moeckel, [https://archive.org/details/nasa_techdoc_19980223074 Trajectories with Constant Tangential Thrust in Central Gravitational Fields], ''Technical Report R-63'', NASA Lewis Research Center, 1960 (accessed 26 March 2014)</ref> the vehicle's acceleration increases during thrusting period, since the fuel use means the vehicle mass decreases.  If, instead of constant thrust, the vehicle has constant acceleration, the engine thrust must decrease during the trajectory.

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.

More practically, this type of maneuver is used in low thrust maneuvers, for example with [[ion engines]], [[Hall-effect thruster]]s, and others.  These types of engines have very high specific impulse (fuel efficiency) but currently are only available with fairly low absolute thrust.

==Rendezvous and docking==

===Orbit phasing===
{{Main|Orbit phasing}}
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]].

===Space rendezvous and docking===
{{Main|Space rendezvous}}
[[Image:Gemini 7 in orbit - GPN-2006-000035.jpg|thumb|upright|[[Gemini 7]] photographed from [[Gemini 6]] in December 1965]]
A '''space rendezvous''' is a sequence of orbital maneuvers 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 is commonly followed by [[Spacecraft Docking and Berthing Mechanisms|docking or berthing]], procedures which bring the spacecraft into physical contact and create a link between them.

==See also==
{{Portal|Spaceflight}}
* [[Clohessy-Wiltshire equations]] for co-orbit analysis
* [[Collision avoidance (spacecraft)]]
* [[Flyby (spaceflight)]]
* [[Spacecraft propulsion]]
* [[Orbital spaceflight]]

==References==
{{Reflist}}

==External links==
*[http://www.cambridge.org/catalogue/catalogue.asp?isbn=9780521089869 Handbook Automated Rendezvous and Docking of Spacecraft] by [[Wigbert Fehse]]

{{Orbits}}
{{Authority control}}

{{DEFAULTSORT:Orbital Maneuver}}
[[Category:Astrodynamics]]
[[Category:Orbital maneuvers| ]]