In general physics, delta-v is simply the change in velocity.

Depending on the situation delta-v can be referred to as a spatial vector ($\backslash Delta\; \backslash mathbf\{v\}\backslash ,$) or scalar ($\backslash Delta\{v\}\backslash ,$). In both cases it is equal to the acceleration (vector or scalar) integrated over time:

$\backslash Delta\; \backslash mathbf\{v\}\; =\; \backslash mathbf\{v\}\_1\; -\; \backslash mathbf\{v\}\_0\; =\; \backslash int^\{t\_1\}\_\{t\_0\}\; \backslash mathbf\; \{a\}\; \backslash ,\; dt$ (vector version)

$\backslash Delta\{v\}\; =\; \{v\}\_1\; -\; \{v\}\_0\; =\; \backslash int^\{t\_1\}\_\{t\_0\}\; \{a\}\; \backslash ,\; dt$ (scalar version)

where:

• $\backslash mathbf\{v\_0\}\backslash ,$ or $\{v\_0\}\backslash ,$ is initial velocity vector or scalar at time $t\_0\backslash ,$,
• $\backslash mathbf\{v\_1\}\backslash ,$ or $\{v\_1\}\backslash ,$ is target velocity vector or scalar at time $t\_1\backslash ,$.

Astrodynamics

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In astrodynamics delta-v is a scalar measure for the amount of "effort" needed to carry out an orbital maneuver, i.e., to change from one orbit to another. A delta-v is typically provided by the thrust of a rocket engine. The time-rate of delta-v is the magnitude of the acceleration, i.e., the thrust per kilogram total current mass, produced by the engines. The actual acceleration vector is found by adding the gravity vector to the vector representing the thrust per kilogram.

Without gravity or other external forces, delta-v is, in the case of thrust in the direction of the velocity, simply the change in speed. However, in a gravitational field, orbits involve changes in speed without requiring any delta-v, while gravity can cause the change of speed to be less or more than the delta-v of a vehicle.

When applying delta-v in the direction of the velocity and against gravity the specific orbital energy gained per unit delta-v is equal to the instantaneous speed. For a burst of thrust during which both the acceleration produced by the thrust and the gravity are constant, the specific orbital energy gained per unit delta-v is the mean value of the speed before and the speed after the burst.

It is not possible to determine delta-v requirements by considering only the total energy in the initial and final orbits. 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 kinetic and potential energies in the final orbit and the launch orbit are equal.

When rocket thrust is applied in short bursts the other sources of acceleration may be negligible, and the speed 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-vs 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.

The rocket equation shows that the required amount of propellant can dramatically increase, and that the possible payload can dramatically decrease, with increasing delta-v. Therefore in modern spacecraft propulsion systems considerable study is put into reducing the total delta-v needed for a given spaceflight, as well as designing spacecraft that are capable of producing a large delta-v.

For examples of the first, see Hohmann transfer orbit, gravitational slingshot, and Interplanetary Superhighway; also, a large thrust reduces gravity drag.

For the second some possibilities are:

• staging
• large specific impulse
• since a large thrust can not be combined with a very large specific impulse, applying different kinds of engine in different parts of the spaceflight (the ones with large thrust for the launch from Earth). The reason to use high thrust at launch is that the loss to gravity can be minimized; once in space, high specific impulse saves fuel.
• reducing the "dry mass" (mass without propellant) while keeping the capability of carrying much propellant, by using light, yet strong, materials; when other factors are the same, it is an advantage if the propellant has a high density, because the same mass requires smaller tanks.

Delta-v is also required to keep satellites in orbit and is expended in orbital stationkeeping maneuvers.

Delta-vs around the Solar System

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Acronyms used

• Low Earth orbit (LEO)
• Medium Earth Orbit (MEO or ICO)
• Geosynchronous Orbit (GEO)
• Geostationary Orbit (GSO)
• Geostationary Transfer Orbit (GTO)
• Lunar Transfer Orbit (LTO)

Games

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Delta-V is a high speed, sci-fi flying game published by Bethesda Softworks in 1994.

See also

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• Delta-v budget
• Gravity drag
• Orbital maneuver
• Orbital stationkeeping
• Spacecraft propulsion
• Specific impulse
• Tsiolkovsky rocket equation

References

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Astrodynamics | Celestial mechanics | Spacecraft propulsion

Delta v | Delta-v | Delta-v