Editing Delta-v (section)

==Delta-''v'' budgets==
{{main article|Delta-v budget}}
{{solar system delta v map.svg}}
When designing a trajectory, delta-''v'' budget is used as a good indicator of how much propellant will be required. Propellant usage is an exponential function of delta-''v'' in accordance with the [[rocket equation]], it will also depend on the exhaust velocity.

It is not possible to determine delta-''v'' requirements from [[conservation of energy]] by considering only the total energy of the vehicle in the initial and final orbits since energy is carried away in the exhaust (see also below). For example, most spacecraft are launched in an orbit with inclination fairly near to the latitude at the launch site, to take advantage of the Earth's rotational surface speed. If it is necessary, for mission-based reasons, to put the spacecraft in an orbit of different [[inclination]], a substantial delta-''v'' is required, though the [[specific kinetic energy|specific kinetic]] and potential energies in the final orbit and the initial orbit are equal.

When rocket thrust is applied in short bursts the other sources of acceleration may be negligible, and the magnitude of the velocity change of one burst may be simply approximated by the delta-''v''. The total delta-''v'' to be applied can then simply be found by addition of each of the delta-''v'''s needed at the discrete burns, even though between bursts the magnitude and direction of the velocity changes due to gravity, e.g. in an [[elliptic orbit]].

For examples of calculating delta-''v'', see [[Hohmann transfer orbit]], [[gravitational slingshot]], and [[Interplanetary Transport Network]]. It is also notable that large thrust can reduce [[gravity drag]].

Delta-''v'' is also required to keep satellites in orbit and is expended in propulsive [[orbital stationkeeping]] maneuvers. Since the propellant load on most satellites cannot be replenished, the amount of propellant initially loaded on a satellite may well determine its useful lifetime.

===Oberth effect===
{{main article|Oberth effect}}
{{see also|Gravitational slingshot#Powered slingshots}}
From power considerations, it turns out that when applying delta-''v'' in the direction of the velocity the [[specific orbital energy]] gained per unit delta-''v'' is equal to the instantaneous speed. This is called the Oberth effect.

For example, a satellite in an elliptical orbit is boosted more efficiently at high speed (that is, small altitude) than at low speed (that is, high altitude).

Another example is that when a vehicle is making a pass of a planet, burning the propellant at closest approach rather than further out gives significantly higher final speed, and this is even more so when the planet is a large one with a deep gravity field, such as Jupiter.

===Porkchop plot===
{{main article|Porkchop plot}}
Due to the relative positions of planets changing over time, different delta-vs are required at different launch dates. A diagram that shows the required delta-''v'' plotted against time is sometimes called a ''porkchop plot''. Such a diagram is useful since it enables calculation of a [[launch window]], since launch should only occur when the mission is within the capabilities of the vehicle to be employed.<ref>{{cite web|url=http://marsprogram.jpl.nasa.gov/spotlight/porkchopAll.html|title=Mars Exploration: Features|website=marsprogram.jpl.nasa.gov}}</ref>

===Around the Solar System{{Anchor |Delta-vs around the Solar System}}===<!-- This section is linked from [[Spacecraft propulsion]] -->
[[Image:Delta-Vs for inner Solar System.svg|upright=1.6|thumb|Delta-''v'' map of the inner Solar System]]
Delta-''v'' needed for various orbital manoeuvers using conventional rockets; red arrows show where optional [[aerobraking]] can be performed in that particular direction, black numbers give delta-''v'' in km/s that apply in either direction.<ref name=marsdeltavs>{{cite web|title=Rockets and Space Transportation |url=http://www.pma.caltech.edu/~chirata/deltav.html |access-date=June 1, 2013|archive-url=https://web.archive.org/web/20070701211813/http://www.pma.caltech.edu/~chirata/deltav.html |archive-date=July 1, 2007 }}</ref><ref>{{cite web|title=Delta-V Calculator|url=http://www.strout.net/info/science/delta-v/intro.html|archive-url=https://web.archive.org/web/20000312041150/http://www.strout.net/info/science/delta-v/intro.html|archive-date=March 12, 2000|url-status=live}} Gives figures of 8.6 from Earth's surface to LEO, 4.1 and 3.8 for LEO to lunar orbit (or L5) and GEO resp., 0.7 for L5 to lunar orbit, and 2.2 for lunar orbit to lunar surface. Figures are said to come from Chapter 2 of [https://science.nas.nasa.gov/Services/Education/SpaceSettlement/75SummerStudy/s.s.doc.html Space Settlements: A Design Study] {{webarchive|url=http://webarchive.loc.gov/all/20011128074814/http://science.nas.nasa.gov/services/education/spacesettlement/75summerstudy/s.s.doc.html |date=2001-11-28 }} on the NASA website .</ref> Lower-delta-''v'' transfers than shown can often be achieved, but involve rare transfer windows or take significantly longer, see: {{section link|Orbital mechanics#Interplanetary Transport Network and fuzzy orbits}}. 
;C3: [[Escape orbit]]
;GEO: [[Geosynchronous orbit]]
;GTO: [[Geostationary transfer orbit]]
;L4/5: Earth–Moon {{L4}}{{L5}} [[Lagrangian point]]
;LEO: [[Low Earth orbit]]
{{clear}}

===LEO reentry===
For example the Soyuz spacecraft makes a de-orbit from the ISS in two steps. First, it needs a delta-''v'' of 2.18 m/s for a safe separation from the space station. Then it needs another 128 m/s for [[Atmospheric entry|reentry]].<ref name="Soyuz returns">{{cite web |last1=Gebhardt |first1=Chris |title=Soyuz MS-17 safely returns three Station crewmembers to Kazakhstan |url=https://www.nasaspaceflight.com/2021/04/soyuz-ms-17-landing/ |website=nasaspaceflight.com |date=17 April 2021 |access-date=10 July 2022}}</ref>