Deltav budget
In astrodynamics and aerospace, a deltav budget is an estimate of the total deltav required for a space mission. It is calculated as the sum of the deltav required for the propulsive maneuvers during the mission, and as input to the Tsiolkovsky rocket equation, determines how much propellant is required for a vehicle of given mass and propulsion system.
Deltav is a scalar quantity dependent only on the desired trajectory and not on the mass of the space vehicle. For example, although more thrust, fuel, etc. is needed to transfer a larger communication satellite from low Earth orbit to geosynchronous orbit, the deltav required is the same. Also deltav is additive, as contrasted to rocket burn time, the latter having greater effect later in the mission when more fuel has been used up.
Tables of the deltav required to move between different space venues are useful in the conceptual planning of space missions. In the absence of an atmosphere, the deltav is typically the same for changes in orbit in either direction; in particular, gaining and losing speed cost an equal effort. An atmosphere can be used to slow a spacecraft by aerodynamic braking.
A typical deltav budget might enumerate various classes of maneuvers, deltav per maneuver, and number of each maneuver required over the life of the mission, and simply sum the total deltav, much like a typical financial budget. Because the deltav needed to achieve the mission usually varies with the relative position of the gravitating bodies, launch windows are often calculated from porkchop plots that show deltav plotted against the launch time.
Contents
 General principles 1

Budget 2
 Launch/landing 2.1
 Stationkeeping 2.2
 Earth–Moon space—high thrust 2.3
 Earth–Moon space—low thrust 2.4
 Interplanetary 2.5
 Deltavs between Earth, Moon and Mars 2.6
 NearEarth objects 2.7
 See also 3
 References 4
 External links 5
General principles
The Tsiolkovsky rocket equation shows that the deltav of a rocket (stage), is proportional to the logarithm of the fuelledtoempty mass ratio of the vehicle, and to the specific impulse of the rocket engine. A key goal in designing spacemission trajectories is to minimize the required deltav to reduce the size and expense of the rocket that would be needed to successfully deliver any particular payload to its destination.
The simplest deltav budget can be calculated with Hohmann transfer, which moves from one circular orbit to another coplanar circular orbit via an elliptical transfer orbit. In some cases a bielliptic transfer can give a lower deltav.
A more complex transfer occurs when the orbits are not coplanar. In that case there is an additional deltav necessary to change the plane of the orbit. The velocity of the vehicle needs substantial burns at the intersection of the two orbital planes and the deltav is usually extremely high. However, 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. In other cases, boosting up to a relatively high altitude apoapsis gives low speed before performing the plane change and this can give lower total deltav.
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 deltav needed, because using propellant at low potential energy/high speed multiplies the effect of a burn. Thus for example the deltav for a Hohmann transfer from Earth's orbital radius to Mars's orbital radius (to overcome the Sun's gravity) is many kilometres per second, but the incremental burn from LEO over and above the burn to overcome Earth's gravity is far less if the burn is done close to Earth than if the burn to reach a Mars transfer orbit is performed at Earth's orbit, but far away from Earth.
A less used effect is low energy transfers. These are highly nonlinear effects that work by orbital resonances and by choosing trajectories close to Lagrange points. They can be very slow, but use very little deltav.
Because deltav depends on the position and motion of celestial bodies, particularly when using the slingshot effect and Oberth effect, the deltav budget changes with launch time. These can be plotted on a porkchop plot.
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.
Budget
Launch/landing
The deltav requirements for suborbital spaceflight are much lower than for orbital spaceflight. For the Ansari X Prize altitude of 100 km, Space Ship One required a deltav of roughly 1.4 km/s. To reach low Earth orbit of the space station of 300 km, the deltav is over six times higher about 9.4 km/s. Because of the exponential nature of the rocket equation the orbital rocket needs to be considerably bigger.
 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
 Reentry from LEO—the deltav required is the orbital maneuvering burn to lower perigee into the atmosphere, atmospheric drag takes care of the rest.
Stationkeeping
Maneuver  Average deltav per year [m/s]  Maximum per year [m/s] 

Drag compensation in 400–500 km LEO  < 25  < 100 
Drag compensation in 500–600 km LEO  < 5  < 25 
Drag compensation in > 600 km LEO  < 7.5  
Stationkeeping in geostationary orbit  50–55  
Stationkeeping in L_{1}/L_{2}  30–100  
Stationkeeping in lunar orbit  0–400 ^{[1]}  
Attitude control (3axis)  2–6  
Spinup or despin  5–10  
Stage booster separation  5–10  
Momentumwheel unloading  2–6 
Earth–Moon space—high thrust
Deltav needed to move inside Earth–Moon system (speeds lower than escape velocity) are given in km/s. This table assumes that the Oberth effect is being used—this is possible with high thrust chemical propulsion but not with current (As of 2011) electrical propulsion.
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 Deltav figure applies, the extra propellant is likely to be heavier than a heat shield. LEOKen refers to a low Earth orbit with an inclination to the equator of 28 degrees, corresponding to a launch from Kennedy Space Center. LEOEq is an equatorial orbit.
∆V km/s from/to  LEOKen  LEOEq  GEO  EML1  EML2  EML4/5  LLO  Moon  C3=0 

Earth  9.3–10  
Low Earth orbit (LEOKen)  4.24  4.33  3.77  3.43  3.97  4.04  5.93  3.22  
Low Earth orbit (LEOEq)  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 (EML1)  0.77  0.77  1.38  0.14  0.33  0.64  2.52  0.14  
Lagrangian point 2 (EML2)  0.33  0.33  1.47  0.14  0.34  0.64  2.52  0.14  
Lagrangian point 4/5 (EML4/5)  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  2.74  2.74  3.92  2.52  2.53  2.58  1.87  2.80  
Earth escape velocity (C3=0)  0.00  0.00  1.30  0.14  0.14  0.43  1.40  2.80 
^{[2]} ^{[3]} ^{[4]}
Earth–Moon space—low thrust
Current electric ion thrusters produce a very low thrust (millinewtons, yielding a small fraction of a g), so the Oberth effect cannot normally be used. This results in the journey requiring a higher deltav and frequently a large increase in time compared to a high thrust chemical rocket. Nonetheless, the high specific impulse of electrical thrusters may significantly reduce the cost of the flight. For missions in the Earth–Moon system, an increase in journey time from days to months could be unacceptable for human space flight, but differences in flight time for interplanetary flights are less significant and could be favorable.
The table below presents deltav's in km/s, normally accurate to 2 significant figures and will be the same in both directions, unless aerobraking is used as described in the high thrust section above.^{[5]}
From  To  deltav (km/s) 

Low Earth orbit (LEO)  Earth–Moon Lagrangian 1 (EML1)  7.0 
Low Earth orbit (LEO)  Geostationary Earth orbit (GEO)  6.0 
Low Earth orbit (LEO)  Low Lunar orbit (LLO)  8.0 
Low Earth orbit (LEO)  Sun–Earth Lagrangian 1 (SEL1)  7.4 
Low Earth orbit (LEO)  Sun–Earth Lagrangian 2 (SEL2)  7.4 
Earth–Moon Lagrangian 1 (EML1)  Low Lunar orbit (LLO)  0.60–0.80 
Earth–Moon Lagrangian 1 (EML1)  Geostationary Earth orbit (GEO)  1.4–1.75 
Earth–Moon Lagrangian 1 (EML1)  SunEarth Lagrangian 2 (SEL2)  0.30–0.40 
^{[5]}
Interplanetary
The spacecraft is assumed to be using chemical propulsion and the Oberth effect.
From  To  Deltav (km/s) 

LEO  Mars transfer orbit  4.3 ^{[6]} 
Earth escape velocity (C3=0)  Mars transfer orbit  0.6^{[7]} 
Mars transfer orbit  Mars capture orbit  0.9^{[7]} 
Mars capture orbit  Deimos transfer orbit  0.2^{[7]} 
Deimos transfer orbit  Deimos surface  0.7^{[7]} 
Deimos transfer orbit  Phobos transfer orbit  0.3^{[7]} 
Phobos transfer orbit  Phobos surface  0.5^{[7]} 
Mars capture orbit  Low Mars orbit  1.4^{[7]} 
Low Mars orbit  Mars surface  4.1^{[7]} 
EML2  Mars transfer orbit  <1.0^{[6]} 
Mars transfer orbit  Low Mars Orbit  2.7^{[6]} 
Earth escape velocity (C3=0)  Closest NEO^{[8]}  0.8–2.0 
According to Marsden and Ross, "The energy levels of the Sun–Earth L_{1} and L_{2} points differ from those of the Earth–Moon system by only 50 m/s (as measured by maneuver velocity)."^{[9]}
Deltavs between Earth, Moon and Mars
NearEarth objects
NearEarth objects are asteroids that are within the orbit of Mars. The deltav to return from them are usually quite small, sometimes as low as 60 m/s, using aerobraking in Earth's atmosphere.^{[13]} However, heat shields are required for this, which add mass and constrain spacecraft geometry. The orbital phasing can be problematic; once rendezvous has been achieved, low deltav return windows can be fairly far apart (more than a year, often many years), depending on the body.
However, the deltav to reach nearEarth objects is usually over 3.8 km/s,^{[13]} which is still less than the deltav to reach the Moon's surface. In general bodies that are much further away or closer to the Sun than Earth have more frequent windows for travel, but usually require larger deltavs.
See also
 Bielliptic transfer
 Gravity assist
 Hohmann transfer
 Oberth effect
 Orbital speed
 Tsiolkovsky rocket equation
 Porkchop plot
 Synodic period
References
 ^ Frozen lunar orbits
 ^ list of deltav
 ^ L_{2} Halo lunar orbit
 ^ Strategic Considerations for Cislunar Space Infrastructure
 ^ ^{a} ^{b} FISO “Gateway” Concepts 2010, various authors page 26
 ^ ^{a} ^{b} ^{c} Zegler and Kutter (AIAA 20108638)
 ^ ^{a} ^{b} ^{c} ^{d} ^{e} ^{f} ^{g} ^{h} ^{i} "Rockets and Space Transportation". Retrieved June 1, 2013.
 ^ NEO list
 ^ "New methods in celestial mechanics and mission design". Bull. Amer. Math. Soc.
 ^ Atomic Rocket: Missions
 ^ cislunar deltavs
 ^ Ion Propulsion for a Mars Sample Return Mission" John R. Brophy and David H. Rodgers, AIAA2003412, Table 1""" (PDF).
 ^ ^{a} ^{b} "NearEarth Asteroid DeltaV for Spacecraft Rendezvous". JPL NASA.
External links
 Javascript Delta V calculator
 Decorative DeltaV Map
 Delft University DeltaV page
