Delta-v budget

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Delta-v budget (or velocity change budget) is an astrogation term used in astrodynamics and aerospace industry for velocity change (or delta-v) requirements for the various propulsive tasks and orbital maneuvers over phases of a space mission.

Sample delta-v budget will enumerate various classes of maneuvers, delta-v per maneuver, number of maneuvers required over the time of the mission.

In the absence of an atmosphere, the delta-v is typically the same for changes in orbit in either direction; in particular, gaining and losing speed cost an equal effort.

General principles

The delta-v requirements for sub-orbital spaceflight can be surprising. For the Ansari X Prize altitude of 100 km, Space Ship One required a delta-v of roughly 1.4 km/s. To reach low earth orbit of the space station of 300 km, the delta-v is over six times higher about 9.4 km/s.

Course corrections usually also require some propellant budget. Propulsion systems never provide precisely the right propulsion in precisely the right direction at all times and navigation also introduces some uncertainty. Some propellant needs to be reserved to correct variations from the optimum trajectory.

The simplest budget can be calculated with Hohmann transfer, which moves from one circular orbit to another coplanar circular orbit via an elliptical transfer orbit.

A more complex transfer occurs when the orbits are not coplanar, in that case there is an additional delta-v necessary to change the plane of the orbit, the velocity of the vehicle needs a substantial change and the delta-v is usually high. These plane changes can be almost free in some cases if the gravity and mass of a planetary body is used to perform the deflection.

From the rocket equation, the delta-v of a rocket is logarithmically related to the mass ratio of the vehicle, minimising the delta-v budget as far as possible is usually very important to avoid the necessity for infeasibly big and expensive rockets.

The slingshot effect can be used in some cases to give a boost of speed/energy; if a vehicle goes past a planetary or lunar body, it is possible to pick up (or lose) much of that body's orbital speed relative to the Sun or a planet.

Another effect is the Oberth effect- this can be used to greatly decrease the delta-v needed, as using propellant at low potential energy/high speed multiplies up the effect of a burn. Thus for example the delta-v for a Hohmann transfer from Earth's orbital radius to Mars' orbital radius is many kilometres per second, but the incremental burn from LEO over and above that to reach Earth escape velocity is far less than if the burn to reach a Mars transfer orbit is performed outside the Earth's gravity.

Launch/landing budget

• Launch to LEO — this not only requires an increase of velocity from 0 to 7.8 km/s, but also typically 1.5–2 km/s for atmospheric drag and gravity drag
• Re-entry from LEO — the delta-v required is the orbital maneuvering burn to lower perigee into the atmosphere, atmospheric drag takes care of the rest.

Earth-Moon space budget

Delta-v needed to move inside Earth Moon system (speeds lower than escape velocity) in km/s

The return to LEO figures assume that a heat shield and aerobraking/aerocapture is used to reduce the speed by up to 3.2 km/s. The heat shield increases the mass, possibly by 15%. Where a heat shield is not used the higher from LEO Delta-v figure applies.

From\To LEO-Ken LEO-Eq GEO EML-1 EML-2 EML-4/5 LLO Moon C3
Earth 9.3 - 10
Low Earth Orbit (LEO-Ken) 4.24 4.33 3.77 3.43 3.97 4.04 5.93 3.22
Low Earth Orbit (LEO-Eq) 4.24 3.90 3.77 3.43 3.99 4.04 5.93 3.22
Geostationary Orbit (GEO) 2.06 1.63 1.38 1.47 1.71 2.05 3.92 1.30
Lagrangian point 1 (EML-1) 0.77 0.77 1.38 0.14 0.33 0.64 2.52 0.14
Lagrangian point 2 (EML-2) 0.33 0.33 1.47 0.14 0.34 0.64 2.52 0.14
Lagrangian point 4/5 (EML-4/5) 0.84 0.98 1.71 0.33 0.34 0.98 2.58 0.43
Low Lunar orbit (LLO) 1.31 1.31 2.05 0.64 0.65 0.98 1.87 1.40
Moon (Moon) 2.74 2.74 3.92 2.52 2.53 2.58 1.87 2.80
Earth Escape velocity (C3) 0.00 0.00 1.30 0.14 0.14 0.43 1.40 2.80

Interplanetary budget

From To delta-v in km/s
Earth Escape velocity (C3) Mars Transfer Orbit 0.6 [5]
Mars Transfer Orbit Mars Capture Orbit 0.9 [5]
Mars Capture Orbit Deimos Transfer Orbit 0.2 [5]
Deimos Transfer Orbit Deimos surface 0.7 [5]
Deimos Transfer Orbit Phobos Transfer Orbit 0.3 [5]
Phobos Transfer Orbit Phobos surface 0.5 [5]
Mars Capture Orbit Low Mars Orbit 1.4 [5]
Low Mars Orbit Mars surface 4.1 [5]
Earth Escape velocity (C3) Closest NEO Asteroids[6] 0.8 - 2.0

According to Marsden and Ross, "The energy levels of the Sun-Earth L1 and L2 points differ from those of the Earth-Moon system by only 50 m/s (as measured by maneuver velocity)."

Delta-vs between Earth and Mars

Delta-v's in km/s for various orbital maneuvers 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. Not all possible links are shown.

Abbreviations used

 C3 Escape orbit GEO Geosynchronous orbit GTO Geostationary transfer orbit L5 Earth-Moon fifth Lagrangian point LEO-Eq Low Earth orbit - equatorial LEO-Ken Low Earth orbit - "Kennedy inclination orbit"

Published - July 2009