In astrodynamics, the term delta-v, literally "change in velocity" (see symbol delta), has a specific meaning: it is a scalar which takes units of speed that measures the amount of "effort" needed to carry out an orbital maneuver, i. Orbital mechanics or astrodynamics is the application of Celestial mechanics to the practical problems concerning the motion of Rockets and other Spacecraft Delta (uppercase Δ, lowercase δ; Δέλτα Thelta is the fourth letter of the Greek alphabet. Speed is the rate of motion, or equivalently the rate of change in position often expressed as Distance d traveled per unit of In Spaceflight, an orbital maneuver is the use of propulsion systems to change the Orbit of a Spacecraft. e. , to change from one trajectory to another. Trajectory is the path a moving object follows through space The object might be a Projectile or a Satellite, for example

Where

T is the instantaneous thrust

m is the instantaneous mass

In the absence of external forces, and when thrust is applied in a constant direction this simplifies to:

which is simply the magnitude of the change in velocity. Thrust is a reaction force described quantitatively by Newton 's Second and Third Laws. Mass is a fundamental concept in Physics, roughly corresponding to the Intuitive idea of how much Matter there is in an object In Physics, a force is whatever can cause an object with Mass to Accelerate. For the special astrodynamical meaning see Delta-v. In general physics delta-v is simply the change in Velocity.

Delta-v's used for trajectories

When designing a trajectory, delta-v is used as an indicator of how much propellant will be required. Propellant usage is an exponential function of delta-v in accordance with the rocket equation. Tsiolkovsky's rocket equation, or ideal rocket equation is named after Konstantin Tsiolkovsky, who independently derived it and published in his 1903 work considers

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 the propellant carries energy away in the exhaust (see also below); as well as propellant being used up in a burn. In Physics, the law of conservation of energy states that the total amount of Energy in an isolated system remains constant and cannot be created although it may 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 and potential energies in the final orbit and the initial orbit are equal. Inclination in general is the Angle between a Reference plane and another plane or axis of direction Specific kinetic energy is Kinetic energy per unit mass ( J /kg

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-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. In Astrodynamics or Celestial mechanics an elliptic orbit is a Kepler orbit with the eccentricity greater than 0 and less than 1

For examples of calculating Delta-v, see Hohmann transfer orbit, gravitational slingshot, and Interplanetary Superhighway. In Astronautics and Aerospace engineering, the Hohmann transfer orbit is an Orbital maneuver using two engine impulses which under standard assumptions In Orbital mechanics and Aerospace engineering, a gravitational slingshot, gravity assist or swing-by is the use of the relative movement and The Interplanetary Transport Network (ITN is a collection of Gravitationally determined pathways through the Solar system that require very little Energy It is also notable that large thrust can reduce gravity drag. In Astrodynamics and Rocketry, gravity drag (or gravity losses) is the difference between the Delta-v expended and the actual change in speed

Delta-v is also required to keep satellites in orbit and is expended in propulsive orbital stationkeeping maneuvers. In Astrodynamics orbital station-keeping is a term used to describe a particular set of Orbital maneuvers used to keep a spacecraft in assigned Orbit 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

It turns out that from power considerations 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. In Astrodynamics the specific Orbital energy \epsilon\\! (or vis-viva energy) of an Orbiting body traveling through Space 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. For example, the energy of 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). This is called the Oberth effect. The Oberth effect is a feature of Astronautics where using a Rocket engine close to a gravitational body gives a higher final speed than the same burn executed further

See also powered slingshotshttp://en.wikipedia.org../../../../articles/g/r/a/Gravitational_slingshot.html#Powered_slingshots. In Orbital mechanics and Aerospace engineering, a gravitational slingshot, gravity assist or swing-by is the use of the relative movement and

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. Porkchop plot (also pork-chop plot) is a chart that depicts orbital Trajectories for spacecraft 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. Launch window is a term used in Aerospace to describe a time period in which a particular Rocket must be launched ^[1]

Producing Delta-v

Delta-v is typically provided by the thrust of a rocket engine, but can be created by other reaction engines. Thrust is a reaction force described quantitatively by Newton 's Second and Third Laws. A rocket engine is a Jet engine that uses only Propellant mass for forming its high speed propulsive jet. The time-rate of change of delta-v is the magnitude of the acceleration caused by the engines, i. e. , the thrust per total vehicle mass. The actual acceleration vector would be found by adding thrust per mass on to the gravity vector and the vectors representing any other forces acting on the object.

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.

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. Spacecraft propulsion is any method used to change the velocity of Spacecraft and artificial Satellites There are many different methods

Increasing the Delta-v provided by a propulsion system can be achieved by:

• staging
• increasing specific impulse
• improving mass fraction

Additionally raising thrust levels (when close to a gravitating body) can sometimes improve delta-v. Specific impulse (usually abbreviated I sp is a way to describe the efficiency of rocket and jet engines See also Mass fraction (chemistry In Aerospace engineering, the propellant mass fraction is a measure of a vehicle's performance determined as the portion

Delta-vs around the Solar System

Delta-vs in km/s for various orbital manoeuvers^[2] 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. Lower delta-v transfers than shown can often be achieved, but involve rare transfer windows or take significantly longer, see: fuzzy orbital transfers. Orbital mechanics or astrodynamics is the application of Celestial mechanics to the practical problems concerning the motion of Rockets and other Spacecraft Not all possible links are shown.

Abbreviations used

See also

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

References

1. ^ Mars Exploration: Features
2. ^ cislunar delta-vs