In
spaceflight
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 or ...
, an orbital maneuver (otherwise known as a burn) is the use of
propulsion
Propulsion is the generation of force by any combination of pushing or pulling to modify the translational motion of an object, which is typically a rigid body (or an articulated rigid body) but may also concern a fluid. The term is derived from ...
systems to change the
orbit
In celestial mechanics, an orbit is the curved trajectory of an object such as the trajectory of a planet around a star, or of a natural satellite around a planet, or of an artificial satellite around an object or position in space such as a p ...
of a
spacecraft
A spacecraft is a vehicle or machine designed to fly in outer space. A type of artificial satellite, spacecraft are used for a variety of purposes, including communications, Earth observation, meteorology, navigation, space colonization, p ...
.
For spacecraft far from Earth (for example those in orbits around the Sun) an orbital maneuver is called a ''deep-space maneuver (DSM)''.
The rest of the flight, especially in a
transfer orbit
{{Astrodynamics
Orbits
Astrodynamics
In orbital mechanics, a transfer orbit is an intermediate elliptical orbit that is used to move a spacecraft in an orbital maneuver from one circular, or largely circular, orbit to another.
There are several ...
, is called ''coasting''.
General
Rocket equation
![Tsiolkovsky rocket equation](https://upload.wikimedia.org/wikipedia/commons/f/f6/Tsiolkovsky_rocket_equation.svg)
The Tsiolkovsky rocket equation, or ideal rocket equation is an equation that is useful for considering vehicles that follow the basic principle of a
rocket
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 ...
: where a device that can apply acceleration to itself (a
thrust
Thrust is a reaction force described quantitatively by Newton's third law. When a system expels or accelerates mass in one direction, the accelerated mass will cause a force of equal magnitude but opposite direction to be applied to that syst ...
) by expelling part of its mass with high speed and moving due to the conservation of
momentum
In Newtonian mechanics, momentum (more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. If is an object's mass an ...
. Specifically, it is a mathematical equation that relates the
delta-v
Delta-''v'' (more known as "change in velocity"), symbolized as ∆''v'' and pronounced ''delta-vee'', as used in spacecraft flight dynamics, is a measure of the impulse per unit of spacecraft mass that is needed to perform a maneuver such as ...
(the maximum change of speed of the rocket if no other external forces act) with the
effective exhaust velocity
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 ...
and the initial and final mass of a
rocket
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 ...
(or other
reaction engine
A reaction engine is an engine or motor that produces thrust by expelling reaction mass, in accordance with Newton's third law of motion. This law of motion is commonly paraphrased as: "For every action force there is an equal, but opposite, rea ...
.)
For any such maneuver (or journey involving a number of such maneuvers):
:
where:
:
is the initial total mass, including propellant,
:
is the final total mass,
:
is the
effective exhaust velocity
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 ...
(
where
is 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 i ...
expressed as a time period and
is
standard gravity
The standard acceleration due to gravity (or standard acceleration of free fall), sometimes abbreviated as standard gravity, usually denoted by or , is the nominal gravitational acceleration of an object in a vacuum near the surface of the Earth. ...
),
:
is delta-v - the maximum change of velocity of the vehicle (with no external forces acting).
Delta-v
The applied change in velocity of each maneuver is referred to as
delta-v
Delta-''v'' (more known as "change in velocity"), symbolized as ∆''v'' and pronounced ''delta-vee'', as used in spacecraft flight dynamics, is a measure of the impulse per unit of spacecraft mass that is needed to perform a maneuver such as ...
(
).
The delta-v for all the expected maneuvers are estimated for a mission. They are summarized in a
delta-v budget
In astrodynamics and aerospace, a delta-v budget is an estimate of the total change in velocity ( delta-''v'') required for a space mission. It is calculated as the sum of the delta-v required to perform each propulsive maneuver needed during th ...
. With a good approximation of the delta-v budget designers can estimate the fuel to payload requirements of the spacecraft using 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 ...
.
Impulsive maneuvers
![Impulsive maneuver](https://upload.wikimedia.org/wikipedia/commons/0/04/Impulsive_maneuver.svg)
An "impulsive maneuver" is the mathematical model of a maneuver as an instantaneous change in the spacecraft's
velocity
Velocity is the directional speed of an object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time (e.g. northbound). Velocity is a ...
(magnitude and/or direction) as illustrated in figure 1. It is the limit case of a burn to generate a particular amount of delta-v, as the burn time tends to zero.
In the physical world no truly instantaneous change in velocity is possible as this would require an "infinite force" applied during an "infinitely short time" but as a mathematical model it in most cases describes the effect of a maneuver on the orbit very well.
The off-set of the velocity vector after the end of real burn from the velocity vector at the same time resulting from the theoretical impulsive maneuver is only caused by the difference in gravitational force along the two paths (red and black in figure 1) which in general is small.
In the planning phase of space missions designers will first approximate their intended orbital changes using impulsive maneuvers that greatly reduces the complexity of finding the correct orbital transitions.
Low thrust for a long time
Applying a low thrust over a longer period of time is referred to as a non-impulsive maneuver. 'Non-impulsive' refers to the momentum changing slowly over a long time, as in
electrically powered spacecraft propulsion
Spacecraft electric propulsion (or just electric propulsion) is a type of spacecraft propulsion technique that uses electrostatic or electromagnetic fields to accelerate mass to high speed and thus generate thrust to modify the velocity of a s ...
, rather than by a short impulse.
Another term is ''finite burn'', where the word "finite" is used to mean "non-zero", or practically, again: over a longer period.
For a few space missions, such as those including a
space rendezvous
A space rendezvous () is a set of orbital maneuvers during which two spacecraft, one of which is often a space station, arrive at the same orbit and approach to a very close distance (e.g. within visual contact). Rendezvous requires a precise ma ...
, high fidelity models of the trajectories are required to meet the mission goals. Calculating a "finite" burn requires a detailed model of the
spacecraft
A spacecraft is a vehicle or machine designed to fly in outer space. A type of artificial satellite, spacecraft are used for a variety of purposes, including communications, Earth observation, meteorology, navigation, space colonization, p ...
and its thrusters. The most important of details include:
mass
Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different elementar ...
,
center of mass
In physics, the center of mass of a distribution of mass in space (sometimes referred to as the balance point) is the unique point where the weighted relative position of the distributed mass sums to zero. This is the point to which a force may ...
,
moment of inertia
The moment of inertia, otherwise known as the mass moment of inertia, angular mass, second moment of mass, or most accurately, rotational inertia, of a rigid body is a quantity that determines the torque needed for a desired angular acceler ...
, thruster positions, thrust vectors, thrust curves,
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 i ...
, thrust
centroid
In mathematics and physics, the centroid, also known as geometric center or center of figure, of a plane figure or solid figure is the arithmetic mean position of all the points in the surface of the figure. The same definition extends to any ob ...
offsets, and fuel consumption.
Assists
Oberth effect
In
astronautics
Astronautics (or cosmonautics) is the theory and practice of travel beyond Earth's atmosphere into outer space. Spaceflight is one of its main applications and space science its overarching field.
The term ''astronautics'' (originally ''astronaut ...
, the Oberth effect is where the use of a
rocket engine
A rocket engine uses stored rocket propellants as the reaction mass for forming a high-speed propulsive jet of fluid, usually high-temperature gas. Rocket engines are reaction engines, producing thrust by ejecting mass rearward, in accordanc ...
when travelling at high speed generates much more useful energy than one at low speed. Oberth effect occurs because the
propellant
A propellant (or propellent) is a mass that is expelled or expanded in such a way as to create a thrust or other motive force in accordance with Newton's third law of motion, and "propel" a vehicle, projectile, or fluid payload. In vehicles, the e ...
has more usable energy (due to its kinetic energy on top of its chemical potential energy) and it turns out that the vehicle is able to employ this kinetic energy to generate more mechanical power. It is named after
Hermann Oberth
Hermann Julius Oberth (; 25 June 1894 – 28 December 1989) was an Austro-Hungarian-born German physicist and engineer. He is considered one of the founding fathers of rocketry and astronautics, along with Robert Esnault-Pelterie, Konstantin Ts ...
, the
Austro-Hungarian
Austria-Hungary, often referred to as the Austro-Hungarian Empire,, the Dual Monarchy, or Austria, was a constitutional monarchy and great power in Central Europe between 1867 and 1918. It was formed with the Austro-Hungarian Compromise of ...
-born,
German
German(s) may refer to:
* Germany (of or related to)
**Germania (historical use)
* Germans, citizens of Germany, people of German ancestry, or native speakers of the German language
** For citizens of Germany, see also German nationality law
**Ger ...
physicist
A physicist is a scientist who specializes in the field of physics, which encompasses the interactions of matter and energy at all length and time scales in the physical universe.
Physicists generally are interested in the root or ultimate caus ...
and a founder of modern
rocket
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 ...
ry, who apparently first described the effect.
[NASA-TT-F-622: Ways to spaceflight p 200 - Herman Oberth]
/ref>
Oberth effect is used in a powered flyby or Oberth maneuver where the application of an impulse, typically from the use of a rocket engine, close to a gravitational body (where the gravity potential
In classical mechanics, the gravitational potential at a location is equal to the work (energy transferred) per unit mass that would be needed to move an object to that location from a fixed reference location. It is analogous to the electric po ...
is low, and the speed is high) can give much more change in kinetic energy
In physics, the kinetic energy of an object is the energy that it possesses due to its motion.
It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its accele ...
and final speed (i.e. higher specific energy
Specific energy or massic energy is energy per unit mass. It is also sometimes called gravimetric energy density, which is not to be confused with energy density, which is defined as energy per unit volume. It is used to quantify, for example, sto ...
) than the same impulse applied further from the body for the same initial orbit.
Since the Oberth maneuver happens in a very limited time (while still at low altitude), to generate a high impulse the engine necessarily needs to achieve high thrust (impulse is by definition the time multiplied by thrust). Thus the Oberth effect is far less useful for low-thrust engines, such as 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 a ...
s.
Historically, a lack of understanding of this effect led investigators to conclude that interplanetary travel would require completely impractical amounts of propellant, as without it, enormous amounts of energy are needed.[
]
Gravitational assist
In orbital mechanics
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 engineering
Aerospace engineering is the primary field of engineering concerned with the development of aircraft and spacecraft. It has two major and overlapping branches: aeronautical engineering and astronautical engineering. Avionics engineering is si ...
, a gravitational slingshot, gravity assist maneuver, or swing-by is the use of the relative movement and gravity
In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the stro ...
of a planet
A planet is a large, rounded astronomical body that is neither a star nor its remnant. The best available theory of planet formation is the nebular hypothesis, which posits that an interstellar cloud collapses out of a nebula to create a you ...
or other celestial body to alter the path
A path is a route for physical travel – see Trail.
Path or PATH may also refer to:
Physical paths of different types
* Bicycle path
* Bridle path, used by people on horseback
* Course (navigation), the intended path of a vehicle
* Desire p ...
and speed
In everyday use and in kinematics, the speed (commonly referred to as ''v'') of an object is the magnitude of the change of its position over time or the magnitude of the change of its position per unit of time; it is thus a scalar quanti ...
of a spacecraft
A spacecraft is a vehicle or machine designed to fly in outer space. A type of artificial satellite, spacecraft are used for a variety of purposes, including communications, Earth observation, meteorology, navigation, space colonization, p ...
, typically in order to save propellant
A propellant (or propellent) is a mass that is expelled or expanded in such a way as to create a thrust or other motive force in accordance with Newton's third law of motion, and "propel" a vehicle, projectile, or fluid payload. In vehicles, the e ...
, time
Time is the continued sequence of existence and events that occurs in an apparently irreversible succession from the past, through the present, into the future. It is a component quantity of various measurements used to sequence events, to ...
, and expense. Gravity assistance can be used to accelerate
In mechanics, acceleration is the rate of change of the velocity of an object with respect to time. Accelerations are vector quantities (in that they have magnitude and direction). The orientation of an object's acceleration is given by the ...
, decelerate and/or re-direct the path of a spacecraft.
The "assist" is provided by the motion (orbital angular momentum
In physics, angular momentum (rarely, moment of momentum or rotational momentum) is the rotational analog of linear momentum. It is an important physical quantity because it is a conserved quantity—the total angular momentum of a closed syst ...
) of the gravitating body as it pulls on the spacecraft. The technique was first proposed as a mid-course manoeuvre in 1961, and used by interplanetary probes from ''Mariner 10
''Mariner 10'' was an American Robotic spacecraft, robotic space probe launched by NASA on 3 November 1973, to fly by the planets Mercury (planet), Mercury and Venus. It was the first spacecraft to perform flybys of multiple planets.
''Ma ...
'' onwards, including the two '' Voyager'' probes' notable fly-bys of Jupiter and Saturn.
Transfer orbits
Orbit insertion
Orbit insertion is the spaceflight operation of adjusting a spacecraft’s momentum, in particular to allow for entry into a stable orbit around a planet, moon, or other celestial body. This maneuver involves either deceleration from a speed in exc ...
is a general term for a maneuver that is more than a small correction. It may be used for a maneuver to change a transfer orbit
{{Astrodynamics
Orbits
Astrodynamics
In orbital mechanics, a transfer orbit is an intermediate elliptical orbit that is used to move a spacecraft in an orbital maneuver from one circular, or largely circular, orbit to another.
There are several ...
or an ascent orbit into a stable one, but also to change a stable orbit into a descent: ''descent orbit insertion''. Also the term orbit injection is used, especially for changing a stable orbit into a transfer orbit, e.g. trans-lunar injection
A trans-lunar injection (TLI) is a propulsive maneuver used to set a spacecraft on a trajectory that will cause it to arrive at the Moon.
History
The first space probe to attempt TLI was the Soviet Union's Luna 1 on January 2, 1959 which wa ...
(TLI), trans-Mars injection
A heliocentric orbit (also called circumsolar orbit) is an orbit around the Barycentric coordinates (astronomy), barycenter of the Solar System, which is usually located within or very near the surface of the Sun. All planets, comets, and asteroi ...
(TMI) and trans-Earth injection
A trans-Earth injection (TEI) is a propulsion maneuver used to set a spacecraft on a trajectory which will intersect the Earth's sphere of influence, usually putting the spacecraft on a free return trajectory.
The maneuver is performed by a ro ...
(TEI).
Hohmann transfer
In orbital mechanics
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 ...
, the Hohmann transfer orbit is an elliptical orbit used to transfer between two circular orbit
A circular orbit is an orbit with a fixed distance around the barycenter; that is, in the shape of a circle.
Listed below is a circular orbit in astrodynamics or celestial mechanics under standard assumptions. Here the centripetal force is ...
s of different altitudes, in the same plane
Plane(s) most often refers to:
* Aero- or airplane, a powered, fixed-wing aircraft
* Plane (geometry), a flat, 2-dimensional surface
Plane or planes may also refer to:
Biology
* Plane (tree) or ''Platanus'', wetland native plant
* ''Planes' ...
.
The orbital maneuver to perform the Hohmann transfer uses two engine impulses which move a spacecraft
A spacecraft is a vehicle or machine designed to fly in outer space. A type of artificial satellite, spacecraft are used for a variety of purposes, including communications, Earth observation, meteorology, navigation, space colonization, p ...
onto and off the transfer orbit. This maneuver was named after Walter Hohmann
Walter Hohmann (; ; 18 March 1880 – 11 March 1945) was a German engineer who made an important contribution to the understanding of orbital dynamics. In a book published in 1925, Hohmann demonstrated a fuel-efficient path to move a spacecraft ...
, the German
German(s) may refer to:
* Germany (of or related to)
**Germania (historical use)
* Germans, citizens of Germany, people of German ancestry, or native speakers of the German language
** For citizens of Germany, see also German nationality law
**Ger ...
scientist who published a description of it in his 1925 book ''Die Erreichbarkeit der Himmelskörper'' (''The Accessibility of Celestial Bodies''). Hohmann was influenced in part by the German science fiction author Kurd Laßwitz
Kurd Lasswitz (german: link=no, Kurd Laßwitz; 20 April 1848 – 17 October 1910) was a German author, scientist, and philosopher. He has been called "the father of German science fiction". He sometimes used the pseudonym ''Velatus''.
Biograph ...
and his 1897 book ''Two Planets
''Two Planets'' (german: Auf zwei Planeten, lit. ''On Two Planets'', 1897) is an influential science fiction novel postulating intelligent life on Mars by Kurd Lasswitz. It was first published in hardcover by Felber in two volumes in 1897; there h ...
''.
Bi-elliptic transfer
In astronautics
Astronautics (or cosmonautics) is the theory and practice of travel beyond Earth's atmosphere into outer space. Spaceflight is one of its main applications and space science its overarching field.
The term ''astronautics'' (originally ''astronaut ...
and aerospace engineering
Aerospace engineering is the primary field of engineering concerned with the development of aircraft and spacecraft. It has two major and overlapping branches: aeronautical engineering and astronautical engineering. Avionics engineering is si ...
, the bi-elliptic transfer is an orbital maneuver that moves a spacecraft
A spacecraft is a vehicle or machine designed to fly in outer space. A type of artificial satellite, spacecraft are used for a variety of purposes, including communications, Earth observation, meteorology, navigation, space colonization, p ...
from one orbit
In celestial mechanics, an orbit is the curved trajectory of an object such as the trajectory of a planet around a star, or of a natural satellite around a planet, or of an artificial satellite around an object or position in space such as a p ...
to another and may, in certain situations, require less delta-v
Delta-''v'' (more known as "change in velocity"), symbolized as ∆''v'' and pronounced ''delta-vee'', as used in spacecraft flight dynamics, is a measure of the impulse per unit of spacecraft mass that is needed to perform a maneuver such as ...
than a 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, ...
maneuver.
The bi-elliptic transfer consists of two half elliptic orbit
In astrodynamics or celestial mechanics, an elliptic orbit or elliptical orbit is a Kepler orbit with an eccentricity of less than 1; this includes the special case of a circular orbit, with eccentricity equal to 0. In a stricter sense, it ...
s. From the initial orbit, a delta-v is applied boosting the spacecraft into the first transfer orbit with an 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 ellip ...
at some point away from the central body
A primary (also called a gravitational primary, primary body, or central body) is the main physical body of a gravitationally bound, multi-object system. This object constitutes most of that system's mass and will generally be located near the syst ...
. At this point, a second delta-v is applied sending the spacecraft into the second elliptical orbit with periapsis
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 ...
at the radius of the final desired orbit, where a third delta-v is performed, injecting the spacecraft into the desired orbit.
While they require one more engine burn than a Hohmann transfer and generally requires a greater travel time, some bi-elliptic transfers require a lower amount of total delta-v than a Hohmann transfer when the ratio of final to initial semi-major axis
In geometry, the major axis of an ellipse is its longest diameter: a line segment that runs through the center and both foci, with ends at the two most widely separated points of the perimeter. The semi-major axis (major semiaxis) is the long ...
is 11.94 or greater, depending on the intermediate semi-major axis chosen.
The idea of the bi-elliptical transfer trajectory was first published by Ary Sternfeld
Ary Sternfeld (14 May 1905 – 5 July 1980) was co-creator of the modern aerospace science. He was a Polish engineer of Jewish origin, who studied in Poland and France. From 1935 until his death he worked in Moscow.
He was the first person to ...
in 1934.
Low energy transfer
A low energy transfer, or low energy trajectory
A trajectory or flight path is the path that an object with mass in motion follows through space as a function of time. In classical mechanics, a trajectory is defined by Hamiltonian mechanics via canonical coordinates; hence, a complete traj ...
, is a route in space which allows spacecraft to change orbit
In celestial mechanics, an orbit is the curved trajectory of an object such as the trajectory of a planet around a star, or of a natural satellite around a planet, or of an artificial satellite around an object or position in space such as a p ...
s using very little fuel. These routes work in the Earth
Earth is the third planet from the Sun and the only astronomical object known to harbor life. While large volumes of water can be found throughout the Solar System, only Earth sustains liquid surface water. About 71% of Earth's surfa ...
-Moon
The Moon is Earth's only natural satellite. It is the fifth largest satellite in the Solar System and the largest and most massive relative to its parent planet, with a diameter about one-quarter that of Earth (comparable to the width of ...
system and also in other systems, such as traveling between the satellites of Jupiter
There are 82 known moons of Jupiter, not counting a number of moonlets likely shed from the inner moons. All together, they form a satellite system which is called the Jovian system. The most massive of the moons are the four Galilean moons: ...
. The drawback of such trajectories is that they take much longer to complete than higher energy (more fuel) transfers such as 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 ano ...
s.
Low energy transfer are also known as weak stability boundary
Weak stability boundary (WSB), including Low-energy transfer, is a concept introduced by Edward Belbruno in 1987. The concept explained how a spacecraft could change orbits using very little fuel.
Weak stability boundary is defined for the three ...
trajectories, or ballistic capture trajectories.
Low energy transfers follow special pathways in space, sometimes referred to as the Interplanetary Transport Network
The Interplanetary Transport Network (ITN) is a collection of gravitationally determined pathways through the Solar System that require very little energy for an object to follow. The ITN makes particular use of Lagrange points as locations whe ...
. Following these pathways allows for long distances to be traversed for little expenditure of delta-v
Delta-''v'' (more known as "change in velocity"), symbolized as ∆''v'' and pronounced ''delta-vee'', as used in spacecraft flight dynamics, is a measure of the impulse per unit of spacecraft mass that is needed to perform a maneuver such as ...
.
Orbital inclination change
Orbital inclination change is an orbital maneuver aimed at changing the inclination
Orbital inclination measures the tilt of an object's orbit around a celestial body. It is expressed as the angle between a Plane of reference, reference plane and the orbital plane or Axis of rotation, axis of direction of the orbiting object ...
of an orbiting body's orbit
In celestial mechanics, an orbit is the curved trajectory of an object such as the trajectory of a planet around a star, or of a natural satellite around a planet, or of an artificial satellite around an object or position in space such as a p ...
. This maneuver is also known as an orbital plane change as the plane of the orbit is tipped. This maneuver requires a change in the orbital velocity vector (delta v
Delta-''v'' (more known as "change in velocity"), symbolized as ∆''v'' and pronounced ''delta-vee'', as used in spacecraft flight dynamics, is a measure of the impulse per unit of spacecraft mass that is needed to perform a maneuver such as ...
) at the orbital nodes
An orbital node is either of the two points where an orbit intersects a plane of reference to which it is inclined. A non-inclined orbit, which is contained in the reference plane, has no nodes.
Planes of reference
Common planes of reference ...
(i.e. the point where the initial and desired orbits intersect, the line of orbital nodes is defined by the intersection of the two orbital planes).
In general, inclination changes can require a great deal of delta-v to perform, and most mission planners try to avoid them whenever possible to conserve fuel. This is typically achieved by launching a spacecraft directly into the desired inclination, or as close to it as possible so as to minimize any inclination change required over the duration of the spacecraft life.
Maximum efficiency of inclination change is achieved at 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 ellip ...
, (or apogee
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 ellip ...
), where orbital velocity is the lowest. In some cases, it may require less total delta v to raise the satellite into a higher orbit, change the orbit plane at the higher apogee, and then lower the satellite to its original altitude.
Constant-thrust trajectory
Constant-thrust and constant-acceleration trajectories involve the spacecraft firing its engine in a prolonged constant burn. In the limiting case where the vehicle acceleration is high compared to the local gravitational acceleration, the spacecraft points straight toward the target (accounting for target motion), and remains accelerating constantly under high thrust until it reaches its target. In this high-thrust case, the trajectory approaches a straight line. If it is required that the spacecraft rendezvous with the target, rather than performing a flyby, then the spacecraft must flip its orientation halfway through the journey, and decelerate the rest of the way.
In the constant-thrust trajectory,[W. E. Moeckel]
Trajectories with Constant Tangential Thrust in Central Gravitational Fields
''Technical Report R-63'', NASA Lewis Research Center, 1960 (accessed 26 March 2014) the vehicle's acceleration increases during thrusting period, since the fuel use means the vehicle mass decreases. If, instead of constant thrust, the vehicle has constant acceleration, the engine thrust must decrease during the trajectory.
This trajectory requires that the spacecraft maintain a high acceleration for long durations. For interplanetary transfers, days, weeks or months of constant thrusting may be required. As a result, there are no currently available spacecraft propulsion systems capable of using this trajectory. It has been suggested that some forms of nuclear (fission or fusion based) or antimatter powered rockets would be capable of this trajectory.
More practically, this type of maneuver is used in low thrust maneuvers, for example with ion engines
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 ...
, Hall-effect thruster
In spacecraft propulsion, a Hall-effect thruster (HET) is a type of ion thruster in which the propellant is accelerated by an electric field. Hall-effect thrusters (based on the discovery by Edwin Hall) are sometimes referred to as Hall thruster ...
s, and others. These types of engines have very high specific impulse (fuel efficiency) but currently are only available with fairly low absolute thrust.
Rendezvous and docking
Orbit phasing
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 ...
orbit phasing is the adjustment of the time-position of spacecraft along its orbit
In celestial mechanics, an orbit is the curved trajectory of an object such as the trajectory of a planet around a star, or of a natural satellite around a planet, or of an artificial satellite around an object or position in space such as a p ...
, usually described as adjusting the orbiting spacecraft's true anomaly
In celestial mechanics, true anomaly is an angular parameter that defines the position of a body moving along a Keplerian orbit. It is the angle between the direction of periapsis and the current position of the body, as seen from the main focus ...
.
Space rendezvous and docking
A space rendezvous is an orbital maneuver during which two spacecraft
A spacecraft is a vehicle or machine designed to fly in outer space. A type of artificial satellite, spacecraft are used for a variety of purposes, including communications, Earth observation, meteorology, navigation, space colonization, p ...
, one of which is often a space station
A space station is a spacecraft capable of supporting a human crew in orbit for an extended period of time, and is therefore a type of space habitat. It lacks major propulsion or landing systems. An orbital station or an orbital space station i ...
, arrive at the same orbit
In celestial mechanics, an orbit is the curved trajectory of an object such as the trajectory of a planet around a star, or of a natural satellite around a planet, or of an artificial satellite around an object or position in space such as a p ...
and approach to a very close distance (e.g. within visual contact). Rendezvous requires a precise match of the orbital velocities of the two spacecraft, allowing them to remain at a constant distance through orbital station-keeping
In astrodynamics, orbital station-keeping is keeping a spacecraft at a fixed distance from another spacecraft or celestial body. It requires a series of orbital maneuvers made with thruster burns to keep the active craft in the same orbit as its t ...
. Rendezvous may or may not be followed by docking or berthing, procedures which bring the spacecraft into physical contact and create a link between them.
See also
* Clohessy-Wiltshire equations for co-orbit analysis
* Collision avoidance (spacecraft) Spacecraft collision avoidance is the implementation and study of processes minimizing the chance of orbiting spacecraft inadvertently colliding with other orbiting objects. The most common subject of spacecraft collision avoidance research and deve ...
* Flyby (spaceflight)
A flyby () is a spaceflight operation in which a spacecraft passes in proximity to another body, usually a target of its space exploration mission and/or a source of a gravity assist to impel it towards another target. Spacecraft which are specif ...
* Spacecraft propulsion
Spacecraft propulsion is any method used to accelerate spacecraft and artificial satellites. In-space propulsion exclusively deals with propulsion systems used in the vacuum of space and should not be confused with space launch or atmospheric e ...
* Orbital spaceflight
An orbital spaceflight (or orbital flight) is a spaceflight in which a spacecraft is placed on a trajectory where it could remain in space for at least one orbit. To do this around the Earth, it must be on a free trajectory which has an altit ...
References
External links
Handbook Automated Rendezvous and Docking of Spacecraft
by Wigbert Fehse
{{DEFAULTSORT:Orbital Maneuver
Astrodynamics