DELTA-V

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 ($Delta\; mathbf\{v\},$) or scalar ($Delta\{v\},$). In both cases it is equal to the acceleration (vector or scalar) integrated over time:
:$Delta\; mathbf\{v\}\; =\; mathbf\{v\}\_1\; -\; mathbf\{v\}\_0\; =\; int^\{t\_1\}\_\{t\_0\}\; mathbf\; \{a\}\; ,\; dt$ (vector version)
:$Delta\{v\}\; =\; \{v\}\_1\; -\; \{v\}\_0\; =\; int^\{t\_1\}\_\{t\_0\}\; \{a\}\; ,\; dt$ (scalar version)
where:

★ $mathbf\{v\_0\},$ or $\{v\_0\},$ is initial velocity vector or scalar at time $t\_0,$,

★ $mathbf\{v\_1\},$ or $\{v\_1\},$ is target velocity vector or scalar at time $t\_1,$.

Contents

Astrodynamics

Energy

Delta-vs around the Solar System

Abbreviations used

See also

References

Astrodynamics

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 change of delta-v is the magnitude of the acceleration ''caused by the engines'', i.e., the thrust per kilogram total current mass. The actual acceleration vector is found by adding the gravity vector and the vectors representing any other forces acting on the object to the vector representing the thrust per kilogram. Without gravity or other external forces, delta-v, in the case of thrust in the direction of the velocity, is simply the change in speed.
The total delta-v needed is a good starting point for early design decisions since consideration of the added complexities are deferred to later times in the design process.
When designing a trajectory, delta-v is used as an indicator of how much fuel will be required. Actual fuel usage depends much more than linearly on delta-v according to the rocket equation.
It is not possible to determine delta-v requirements by considering only the total energy in the initial and final orbits (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 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 dramatically increases, 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). High thrust is anyway needed at launch, and the higher it is, the less gravity drag there is; 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. Since most satellites cannot be refueled, the fuel may well determine the useful lifetime of a satellite.

Energy

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. 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. Thus for example the energy of a satellite in an elliptic orbit is boosted more efficiently at high speed (i.e., small altitude) than at low speed (i.e., high altitude). (Whether this is the most suitable choice depends on other objectives regarding the orbit too.)
See also .

Delta-vs around the Solar System

Abbreviations used

C3	Escape orbit
GEO	Geosynchronous orbit
GTO	Geostationary transfer orbit
L5	Earth-Moon fifth Lagrangian point
LEO	Low Earth orbit

See also

★ Delta-v budget

★ Gravity drag

★ Orbital maneuver

★ Orbital stationkeeping

★ Spacecraft propulsion

★ Specific impulse

★ Tsiolkovsky rocket equation

References

1. table of cislunar/mars delta-vs
2. cislunar delta-vs