![ApolloEnergyRequirementsMSC1966](https://upload.wikimedia.org/wikipedia/commons/7/7a/ApolloEnergyRequirementsMSC1966.png)
In
astrodynamics
Orbital mechanics or astrodynamics is the application of ballistics and celestial mechanics to the practical problems concerning the motion of rockets and other spacecraft. The motion of these objects is usually calculated from Newton's laws of ...
and
aerospace
Aerospace is a term used to collectively refer to the atmosphere and outer space. Aerospace activity is very diverse, with a multitude of commercial, industrial and military applications. Aerospace engineering consists of aeronautics and astr ...
, a delta-v budget is an estimate of the total change in velocity (
delta-''v'') required for a
space mission
Spaceflight (or space flight) is an application of astronautics to fly spacecraft into or through outer space, either with or without humans on board. Most spaceflight is uncrewed and conducted mainly with spacecraft such as satellites in o ...
. It is calculated as the sum of the delta-v required to perform each
propulsive maneuver
Maneuver (American English), manoeuvre (British English), manoeuver, manœuver (also spelled, directly from the French, as manœuvre) denotes one's tactical move, or series of moves, that improves or maintains one's strategic situation in a compet ...
needed during the mission. As input to the
Tsiolkovsky rocket equation
Konstantin Eduardovich Tsiolkovsky (russian: Константи́н Эдуа́рдович Циолко́вский , , p=kənstɐnʲˈtʲin ɪdʊˈardəvʲɪtɕ tsɨɐlˈkofskʲɪj , a=Ru-Konstantin Tsiolkovsky.oga; – 19 September 1935) ...
, it determines how much propellant is required for a vehicle of given empty mass and propulsion system.
Delta-''v'' is a
scalar quantity dependent only on the desired trajectory and not on the mass of the space vehicle. For example, although more fuel is needed to transfer a heavier communication satellite from
low Earth orbit
A low Earth orbit (LEO) is an orbit around Earth with a period of 128 minutes or less (making at least 11.25 orbits per day) and an eccentricity less than 0.25. Most of the artificial objects in outer space are in LEO, with an altitude never mor ...
to
geosynchronous orbit than for a lighter one, the delta-''v'' required is the same. Delta-''v'' is also 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 delta-''v'' required to move between different space regime are useful in the conceptual planning of space missions. 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. An atmosphere can be used to slow a spacecraft by
aerobraking
Aerobraking is a spaceflight maneuver that reduces the high point of an elliptical orbit ( apoapsis) by flying the vehicle through the atmosphere at the low point of the orbit ( periapsis). The resulting drag slows the spacecraft. Aerobraking ...
.
A typical delta-''v'' budget might enumerate various classes of maneuvers, delta-''v'' per maneuver, and number of each maneuver required over the life of the mission, then simply sum the total delta-''v'', much like a typical financial budget. Because the delta-v needed to achieve the mission usually varies with the relative position of the gravitating bodies,
launch window
In the context of spaceflight, launch period is the collection of days and launch window is the time period on a given day during which a particular rocket must be launched in order to reach its intended target. If the rocket is not launched wit ...
s are often calculated from
porkchop plot
In orbital mechanics, a porkchop plot (also pork-chop plot) is a chart that shows contours of equal characteristic energy (C3) against combinations of launch date and arrival date for a particular interplanetary flight.
By examining the results ...
s that show delta-''v'' plotted against the launch time.
General principles
The
Tsiolkovsky rocket equation
Konstantin Eduardovich Tsiolkovsky (russian: Константи́н Эдуа́рдович Циолко́вский , , p=kənstɐnʲˈtʲin ɪdʊˈardəvʲɪtɕ tsɨɐlˈkofskʲɪj , a=Ru-Konstantin Tsiolkovsky.oga; – 19 September 1935) ...
shows that the delta-v of a rocket (stage) is proportional to the logarithm of the fuelled-to-empty
mass ratio
In aerospace engineering, mass ratio is a measure of the efficiency of a rocket. It describes how much more massive the vehicle is with propellant than without; that is, the ratio of the rocket's ''wet mass'' (vehicle plus contents plus propellan ...
of the vehicle, and to the
specific impulse
Specific impulse (usually abbreviated ) is a measure of how efficiently a reaction mass engine (a rocket using propellant or a jet engine using fuel) creates thrust. For engines whose reaction mass is only the fuel they carry, specific impulse is ...
of the rocket engine. A key goal in designing space-mission trajectories is to minimize the required delta-v to reduce the size and expense of the rocket that would be needed to successfully deliver any particular payload to its destination.
The simplest delta-v budget can be calculated with
Hohmann transfer
In astronautics, the Hohmann transfer orbit () is an orbital maneuver used to transfer a spacecraft between two orbits of different altitudes around a central body. Examples would be used for travel between low Earth orbit and Moon, the Moon, ...
, which moves from one circular orbit to another coplanar circular orbit via an elliptical transfer orbit. In some cases a
bi-elliptic transfer
In astronautics and aerospace engineering, the bi-elliptic transfer is an orbital maneuver that moves a spacecraft from one orbit to another and may, in certain situations, require less delta-v than a Hohmann transfer maneuver.
The bi-ellipt ...
can give a lower delta-v.
![Hohmann transfer orbit](https://upload.wikimedia.org/wikipedia/commons/d/df/Hohmann_transfer_orbit.svg)
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 substantial burns at the intersection of the two orbital planes and the delta-v is usually extremely high. However, these plane changes can be almost free in some cases if the gravity and mass of a planetary body are used to perform the deflection. In other cases, boosting up to a relatively high altitude
apoapsis
An apsis (; ) is the farthest or nearest point in the orbit of a planetary body about its primary body. For example, the apsides of the Earth are called the aphelion and perihelion.
General description
There are two apsides in any elli ...
gives low speed before performing the plane change, thus requiring lower total delta-v.
The
slingshot effect
In orbital mechanics and aerospace engineering, a gravitational slingshot, gravity assist maneuver, or swing-by is the use of the relative movement (e.g. orbit around the Sun) and gravity of a planet or other astronomical object to alter the C ...
can be used 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) some of that body's orbital velocity relative to the sun or another planet.
Another effect is the
Oberth effect
In astronautics, a powered flyby, or Oberth maneuver, is a maneuver in which a spacecraft falls into a gravitational well and then uses its engines to further accelerate as it is falling, thereby achieving additional speed. The resulting maneuver ...
—this can be used to greatly decrease the delta-v needed, because using propellant at low potential energy/high speed multiplies the effect of a burn. Thus for example the delta-v 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
low Earth orbit
A low Earth orbit (LEO) is an orbit around Earth with a period of 128 minutes or less (making at least 11.25 orbits per day) and an eccentricity less than 0.25. Most of the artificial objects in outer space are in LEO, with an altitude never mor ...
(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 transfer
A low-energy transfer, or low-energy trajectory, is a route in space that allows spacecraft to change orbits using significantly less fuel than traditional transfers. These routes work in the Earth–Moon system and also in other systems, such as ...
s. 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 delta-v.
Because delta-v depends on the position and motion of celestial bodies, particularly when using the slingshot effect and Oberth effect, the delta-v budget changes with launch time. These can be plotted on a
porkchop plot
In orbital mechanics, a porkchop plot (also pork-chop plot) is a chart that shows contours of equal characteristic energy (C3) against combinations of launch date and arrival date for a particular interplanetary flight.
By examining the results ...
.
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 delta-v requirements for
sub-orbital spaceflight
A sub-orbital spaceflight is a spaceflight in which the spacecraft reaches outer space, but its trajectory intersects the atmosphere or surface of the gravitating body from which it was launched, so that it will not complete one orbital re ...
are much lower than for orbital spaceflight. For the
Ansari X Prize altitude of 100 km,
Space Ship One
SpaceShipOne is an experimental air-launched rocket-powered aircraft with sub-orbital spaceflight capability at speeds of up to 3,000 ft/s (900 m/s, 3240 km/h), using a hybrid rocket motor. The design features a unique "feathering" at ...
required a delta-v of roughly 1.4 km/s. To reach the initial low Earth orbit of the
International Space Station
The International Space Station (ISS) is the largest modular space station currently in low Earth orbit. It is a multinational collaborative project involving five participating space agencies: NASA (United States), Roscosmos (Russia), JAXA ( ...
of 300 km (now 400 km), the delta-v is over six times higher, about 9.4 km/s. Because of the exponential nature of the
rocket equation
A rocket (from it, rocchetto, , bobbin/spool) is a vehicle that uses jet propulsion to accelerate without using the surrounding air. A rocket engine produces thrust by reaction to exhaust expelled at high speed. Rocket engines work entirely fr ...
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
In fluid dynamics, drag (sometimes called air resistance, a type of friction, or fluid resistance, another type of friction or fluid friction) is a force acting opposite to the relative motion of any object moving with respect to a surrounding flu ...
and
gravity drag
In astrodynamics and rocketry, gravity loss is a measure of the loss in the net performance of a rocket while it is thrusting in a gravitational field. In other words, it is the cost of having to hold the rocket up in a gravity field.
Gravity lo ...
*
Re-entry
Atmospheric entry is the movement of an object from outer space into and through the gases of an atmosphere of a planet, dwarf planet, or natural satellite. There are two main types of atmospheric entry: ''uncontrolled entry'', such as the entr ...
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—high thrust
Delta-v needed to move inside the Earth–Moon system (speeds lower than
escape velocity
In celestial mechanics, escape velocity or escape speed is the minimum speed needed for a free, non- propelled object to escape from the gravitational influence of a primary body, thus reaching an infinite distance from it. It is typically ...
) are given in km/s. This table assumes that the
Oberth effect
In astronautics, a powered flyby, or Oberth maneuver, is a maneuver in which a spacecraft falls into a gravitational well and then uses its engines to further accelerate as it is falling, thereby achieving additional speed. The resulting maneuver ...
is being used—this is possible with high thrust chemical propulsion but not with current (as of 2018) electrical propulsion.
Earth–Moon space—low thrust
Current electric
ion thruster
An ion thruster, ion drive, or ion engine is a form of electric propulsion used for spacecraft propulsion. It creates thrust by accelerating ions using electricity.
An ion thruster ionizes a neutral gas by extracting some electrons out of ...
s produce a very low thrust (milli-newtons, yielding a small fraction of a ''g),'' so the
Oberth effect
In astronautics, a powered flyby, or Oberth maneuver, is a maneuver in which a spacecraft falls into a gravitational well and then uses its engines to further accelerate as it is falling, thereby achieving additional speed. The resulting maneuver ...
cannot normally be used. This results in the journey requiring a higher delta-''v'' and frequently a large increase in time compared to a high thrust chemical rocket. Nonetheless, the high
specific impulse
Specific impulse (usually abbreviated ) is a measure of how efficiently a reaction mass engine (a rocket using propellant or a jet engine using fuel) creates thrust. For engines whose reaction mass is only the fuel they carry, specific impulse is ...
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 delta-''vs 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.
[
][FISO “Gateway” Concepts 2010, various authors page 26]
Earth Lunar Gateway—high thrust
The Lunar Gateway
The Lunar Gateway, or simply Gateway, is the first planned extraterrestrial space station in lunar orbit intended to serve as a solar-powered communication hub, science laboratory, and short-term habitation module for government-agency astr ...
space station is planned to be deployed in a highly elliptical seven-day near-rectilinear halo orbit (NRHO) around the Moon. Spacecraft launched from Earth would perform a powered flyby of the Moon followed by a NRHO orbit insertion burn to dock with the Gateway as it approaches the apoapsis point of its orbit.
Interplanetary
The spacecraft is assumed to be using chemical propulsion and the Oberth effect
In astronautics, a powered flyby, or Oberth maneuver, is a maneuver in which a spacecraft falls into a gravitational well and then uses its engines to further accelerate as it is falling, thereby achieving additional speed. The resulting maneuver ...
.
According to Marsden and Ross, "The energy levels of the Sun–Earth and points differ from those of the Earth–Moon system by only 50 m/s (as measured by maneuver velocity)."
We may apply the formula
:
(where μ = GM is the standard gravitational parameter of the sun, see Hohmann transfer orbit
In astronautics, the Hohmann transfer orbit () is an orbital maneuver used to transfer a spacecraft between two orbits of different altitudes around a central body. Examples would be used for travel between low Earth orbit and the Moon, or ...
) to calculate the Δ''v'' in km/s needed to arrive at various destinations from Earth (assuming circular orbits for the planets, and using perihelion distance for Pluto). In this table, the column labeled "Δ''v'' to enter Hohmann orbit from Earth's orbit" gives the change from Earth's velocity to the velocity needed to get on a Hohmann ellipse whose other end will be at the desired distance from the sun. The column labeled "v exiting LEO" gives the velocity needed (in a non-rotating frame of reference centred on Earth) when 300 km above Earth's surface. This is obtained by adding to the specific kinetic energy the square of the speed (7.73 km/s) of this low Earth orbit (that is, the depth of Earth's gravity well at this LEO). The column "Δ''v'' from LEO" is simply the previous speed minus 7.73 km/s. The transit time is calculated as years.
Note that the values in the table only give the Δv needed to get to the orbital distance of the planet. The speed relative to the planet will still be considerable, and in order to go into orbit around the planet either aerocapture
Aerocapture is an orbital transfer maneuver in which a spacecraft uses
aerodynamic drag force from a single pass through a planetary
atmosphere to decelerate and achieve orbit insertion.
Aerocapture uses a planet's or moon's atmosphere to accom ...
is needed using the planet's atmosphere, or more Δv is needed.
The New Horizons space probe to Pluto achieved a near-Earth speed of over 16 km/s which was enough to escape from the sun. (It also got a boost from a fly-by of Jupiter.)
To get to the sun, it is actually not necessary to use a Δ''v'' of 24 km/s. One can use 8.8 km/s to go very far away from the sun, then use a negligible Δ''v'' to bring the angular momentum to zero, and then fall into the sun. This can be considered a sequence of two Hohmann transfers, one up and one down. Also, the table does not give the values that would apply when using the moon for a gravity assist
In orbital mechanics and aerospace engineering, a gravitational slingshot, gravity assist maneuver, or swing-by is the use of the relative movement (e.g. orbit around the Sun) and gravity of a planet or other astronomical object to alter the p ...
. There are also possibilities of using one planet, like Venus which is the easiest to get to, to assist getting to other planets or the sun. The ''Galileo'' spacecraft used Venus once and Earth twice in order to reach Jupiter. The Ulysses
Ulysses is one form of the Roman name for Odysseus, a hero in ancient Greek literature.
Ulysses may also refer to:
People
* Ulysses (given name), including a list of people with this name
Places in the United States
* Ulysses, Kansas
* Ulysse ...
solar probe used Jupiter to attain polar orbit around the sun.
Delta-vs between Earth, Moon and Mars
Delta-v needed for various orbital manoeuvers using conventional rockets.
;Abbreviations key:
* Escape orbit
In astrodynamics or celestial mechanics a parabolic trajectory is a Kepler orbit with the eccentricity equal to 1 and is an unbound orbit that is exactly on the border between elliptical and hyperbolic. When moving away from the source it is ...
s with low pericentre
An apsis (; ) is the farthest or nearest point in the orbit of a planetary body about its primary (astronomy), primary body. For example, the apsides of the Earth are called the aphelion and perihelion.
General description
There are two ...
– C3 = 0
* Geostationary orbit – GEO
* Geostationary transfer orbit – GTO
* Earth–Moon Lagrangian point – L5
* low Earth orbit
A low Earth orbit (LEO) is an orbit around Earth with a period of 128 minutes or less (making at least 11.25 orbits per day) and an eccentricity less than 0.25. Most of the artificial objects in outer space are in LEO, with an altitude never mor ...
– LEO
* ''Lunar orbit'' means low lunar orbit
* Red arrows show where optional aerobraking
Aerobraking is a spaceflight maneuver that reduces the high point of an elliptical orbit ( apoapsis) by flying the vehicle through the atmosphere at the low point of the orbit ( periapsis). The resulting drag slows the spacecraft. Aerobraking ...
/aerocapture
Aerocapture is an orbital transfer maneuver in which a spacecraft uses
aerodynamic drag force from a single pass through a planetary
atmosphere to decelerate and achieve orbit insertion.
Aerocapture uses a planet's or moon's atmosphere to accom ...
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.
* Electric propulsion vehicles going from Mars C3 = 0 to Earth C3 = 0 without using the Oberth effect
In astronautics, a powered flyby, or Oberth maneuver, is a maneuver in which a spacecraft falls into a gravitational well and then uses its engines to further accelerate as it is falling, thereby achieving additional speed. The resulting maneuver ...
need a larger Delta-v of between 2.6 km/s and 3.15 km/s. Not all possible links are shown.
* The Delta-v for C3 = 0 to Mars transfer must be applied at pericentre, i.e. immediately after accelerating to the escape trajectory, and do not agree with the formula above which gives 0.4 from Earth escape and 0.65 from Mars escape.
* The figures for LEO to GTO, GTO to GEO, and LEO to GEO are inconsistent.[The sum of LEO to GTO and GTO to GEO should equal LEO to GEO. The precise figures depend on what low Earth orbit is used. According to Geostationary transfer orbit, the speed of a GTO at perigee can be just 9.8 km/s. This corresponds to an LEO at about 700 km altitude, where its speed would be 7.5 km/s, giving a delta-v of 2.3 km/s. Starting from a lower LEO would require more delta-v to get to GTO, but then the total for LEO to GEO would have to be higher.] The figure of 30 for LEO to the sun is also too high.[Earth's speed in its orbit around the sun is, on average, 29.78 km/s, equivalent to a specific kinetic energy of 443 km2/s2. One must add to this the potential energy depth of LEO, about 61 km2/s2, to give a kinetic energy close to Earth of 504 km2/s2, corresponding to a speed of 31.8 km/s. Since the LEO speed is 7.8 km/s, the delta-v is only 24 km/s. It would be possible to reach the sun with less delta-v using ]gravity assist
In orbital mechanics and aerospace engineering, a gravitational slingshot, gravity assist maneuver, or swing-by is the use of the relative movement (e.g. orbit around the Sun) and gravity of a planet or other astronomical object to alter the p ...
s. See Parker Solar Probe
The Parker Solar Probe (PSP; previously Solar Probe, Solar Probe Plus or Solar Probe+) is a NASA space probe launched in 2018 with the mission of making observations of the outer corona of the Sun. It will approach to within 9.86 solar radii ...
. It is also possible to take the long route of going far away from the sun (Δv 8.8 km/s) and then using a very small Δv to cancel the angular momentum and fall into the sun.
Near-Earth objects
Near-Earth object
A near-Earth object (NEO) is any small Solar System body whose orbit brings it into proximity with Earth. By convention, a Solar System body is a NEO if its closest approach to the Sun (perihelion) is less than 1.3 astronomical units (AU). ...
s are asteroids whose orbits can bring them within about 0.3 astronomical unit
The astronomical unit (symbol: au, or or AU) is a unit of length, roughly the distance from Earth to the Sun and approximately equal to or 8.3 light-minutes. The actual distance from Earth to the Sun varies by about 3% as Earth orbits ...
s of the Earth. There are thousands of such objects that are easier to reach than the Moon or Mars. Their one-way delta-v budgets from LEO range upwards from , which is less than 2/3 of the delta-v needed to reach the Moon's surface. But NEOs with low delta-v budgets have long synodic period
The orbital period (also revolution period) is the amount of time a given astronomical object takes to complete one orbit around another object. In astronomy, it usually applies to planets or asteroids orbiting the Sun, moons orbiting planets, ...
s, and the intervals between times of closest approach to the Earth (and thus most efficient missions) can be decades long.
The delta-v required to return from Near-Earth objects is usually quite small, sometimes as low as , with aerocapture
Aerocapture is an orbital transfer maneuver in which a spacecraft uses
aerodynamic drag force from a single pass through a planetary
atmosphere to decelerate and achieve orbit insertion.
Aerocapture uses a planet's or moon's atmosphere to accom ...
using Earth's atmosphere. 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 delta-v return windows can be fairly far apart (more than a year, often many years), depending on the body.
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 delta-vs.
See also
*Bi-elliptic transfer
In astronautics and aerospace engineering, the bi-elliptic transfer is an orbital maneuver that moves a spacecraft from one orbit to another and may, in certain situations, require less delta-v than a Hohmann transfer maneuver.
The bi-ellipt ...
*Gravity assist
In orbital mechanics and aerospace engineering, a gravitational slingshot, gravity assist maneuver, or swing-by is the use of the relative movement (e.g. orbit around the Sun) and gravity of a planet or other astronomical object to alter the p ...
*Hohmann transfer
In astronautics, the Hohmann transfer orbit () is an orbital maneuver used to transfer a spacecraft between two orbits of different altitudes around a central body. Examples would be used for travel between low Earth orbit and Moon, the Moon, ...
*Oberth effect
In astronautics, a powered flyby, or Oberth maneuver, is a maneuver in which a spacecraft falls into a gravitational well and then uses its engines to further accelerate as it is falling, thereby achieving additional speed. The resulting maneuver ...
*Orbital speed
In gravitationally bound systems, the orbital speed of an astronomical body or object (e.g. planet, moon, artificial satellite, spacecraft, or star) is the speed at which it orbits around either the barycenter or, if one body is much more mas ...
*Tsiolkovsky rocket equation
Konstantin Eduardovich Tsiolkovsky (russian: Константи́н Эдуа́рдович Циолко́вский , , p=kənstɐnʲˈtʲin ɪdʊˈardəvʲɪtɕ tsɨɐlˈkofskʲɪj , a=Ru-Konstantin Tsiolkovsky.oga; – 19 September 1935) ...
*Porkchop plot
In orbital mechanics, a porkchop plot (also pork-chop plot) is a chart that shows contours of equal characteristic energy (C3) against combinations of launch date and arrival date for a particular interplanetary flight.
By examining the results ...
*Synodic period
The orbital period (also revolution period) is the amount of time a given astronomical object takes to complete one orbit around another object. In astronomy, it usually applies to planets or asteroids orbiting the Sun, moons orbiting planets, ...
Notes
References
External links
JavaScript Delta V calculator
Long webpage on delta-v (not a source - it quotes this article)
{{DEFAULTSORT:Delta-V Budget
Astrodynamics
Spacecraft propulsion