Gravitational slingshot

# Gravitational slingshot

Discussion

Encyclopedia

In orbital mechanics and aerospace engineering
Aerospace engineering
Aerospace engineering is the primary branch of engineering concerned with the design, construction and science of aircraft and spacecraft. It is divided into two major and overlapping branches: aeronautical engineering and astronautical engineering...

, a gravitational slingshot, gravity assist maneuver, or swing-by is the use of the relative movement and gravity of a planet
Planet
A planet is a celestial body orbiting a star or stellar remnant that is massive enough to be rounded by its own gravity, is not massive enough to cause thermonuclear fusion, and has cleared its neighbouring region of planetesimals.The term planet is ancient, with ties to history, science,...

or other celestial body to alter the path
In navigation, a vehicle's course is the angle that the intended path of the vehicle makes with a fixed reference object . Typically course is measured in degrees from 0° clockwise to 360° in compass convention . Course is customarily expressed in three digits, using preliminary zeros if needed,...

and speed
Speed
In kinematics, the speed of an object is the magnitude of its velocity ; it is thus a scalar quantity. The average speed of an object in an interval of time is the distance traveled by the object divided by the duration of the interval; the instantaneous speed is the limit of the average speed as...

of a spacecraft
Spacecraft
A spacecraft or spaceship is a craft or machine designed for spaceflight. Spacecraft are used for a variety of purposes, including communications, earth observation, meteorology, navigation, planetary exploration and transportation of humans and cargo....

, typically in order to save propellant
Propellant
A propellant is a material that produces pressurized gas that:* can be directed through a nozzle, thereby producing thrust ;...

, time
Time
Time is a part of the measuring system used to sequence events, to compare the durations of events and the intervals between them, and to quantify rates of change such as the motions of objects....

, and expense. Gravity assistance can be used to accelerate, decelerate and/or re-direct the path of a spacecraft.

The "assist" is provided by the motion (orbital angular momentum
Angular momentum
In physics, angular momentum, moment of momentum, or rotational momentum is a conserved vector quantity that can be used to describe the overall state of a physical system...

) 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
Mariner 10 was an American robotic space probe launched by NASA on November 3, 1973, to fly by the planets Mercury and Venus. It was launched approximately two years after Mariner 9 and was the last spacecraft in the Mariner program...

onwards, including Voyagers' notable fly-bys of Jupiter and Saturn.

## Explanation

A gravity assist or slingshot maneuver around a planet changes a spacecraft's velocity
Velocity
In physics, velocity is speed in a given direction. Speed describes only how fast an object is moving, whereas velocity gives both the speed and direction of the object's motion. To have a constant velocity, an object must have a constant speed and motion in a constant direction. Constant ...

relative to the Sun
Sun
The Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...

, though the spacecraft's speed
Speed
In kinematics, the speed of an object is the magnitude of its velocity ; it is thus a scalar quantity. The average speed of an object in an interval of time is the distance traveled by the object divided by the duration of the interval; the instantaneous speed is the limit of the average speed as...

relative to the planet on effectively entering and leaving its gravitational field, will remain the same—as it must according to the law of conservation of energy
Conservation of energy
The nineteenth century law of conservation of energy is a law of physics. It states that the total amount of energy in an isolated system remains constant over time. The total energy is said to be conserved over time...

. To a first approximation, from a large distance, the spacecraft appears to have bounced off the planet. Physicists call this an elastic collision
Elastic collision
An elastic collision is an encounter between two bodies in which the total kinetic energy of the two bodies after the encounter is equal to their total kinetic energy before the encounter...

even though no actual contact occurs. A slingshot maneuver can therefore be used to change the spaceship's trajectory and speed relative to the Sun.

Suppose that you are a "stationary" observer and that you see: a planet moving left at speed U; a spaceship moving right at speed v. If the spaceship has the proper trajectory, it will pass close to the planet, moving at speed U + v relative to the planet's surface because the planet is moving in the opposite direction at speed U. When the spaceship leaves orbit, it is still moving at U + v relative to the planet's surface but in the opposite direction, to the left; and since the planet is moving left at speed U, the total velocity of the rocket relative to you will be the velocity of the moving planet plus the velocity of the rocket with respect to the planet. So the velocity will be U + ( U + v ), that is 2U + v.

It might seem that this is oversimplified since the details of the orbit have not been covered, but it turns out that if the spaceship travels in a path which forms a hyperbola
Hyperbola
In mathematics a hyperbola is a curve, specifically a smooth curve that lies in a plane, which can be defined either by its geometric properties or by the kinds of equations for which it is the solution set. A hyperbola has two pieces, called connected components or branches, which are mirror...

, it can leave the planet in the opposite direction without firing its engine, the speed gain at large distance is indeed 2U once it has left the gravity of the planet far behind.

This explanation might seem to violate the conservation of energy and momentum, but we have neglected the spacecraft's effects on the planet. The linear momentum gained by the spaceship is equal in magnitude to that lost by the planet, though the planet's enormous mass compared to the spacecraft makes the resulting change in its speed negligibly small. These effects on the planet are so slight (because planets are so much more massive than spacecraft) that they can be ignored in the calculation.

Realistic portrayals of encounters in space require the consideration of three dimensions. The same principles apply, only adding the planet's velocity to that of the spacecraft requires vector addition, as shown below.

Due to the reversibility of orbits, gravitational slingshots can also be used to decelerate a spacecraft. Both Mariner 10
Mariner 10
Mariner 10 was an American robotic space probe launched by NASA on November 3, 1973, to fly by the planets Mercury and Venus. It was launched approximately two years after Mariner 9 and was the last spacecraft in the Mariner program...

and MESSENGER
MESSENGER
The MErcury Surface, Space ENvironment, GEochemistry and Ranging space probe is a robotic NASA spacecraft in orbit around the planet Mercury. The spacecraft was launched aboard a Delta II rocket in August 2004 to study the chemical composition, geology, and magnetic field of Mercury...

performed this maneuver to reach Mercury
Mercury (planet)
Mercury is the innermost and smallest planet in the Solar System, orbiting the Sun once every 87.969 Earth days. The orbit of Mercury has the highest eccentricity of all the Solar System planets, and it has the smallest axial tilt. It completes three rotations about its axis for every two orbits...

.

If even more speed is needed than available from gravity assist alone, the most economical way to utilize a rocket burn is to do it near the periapsis (closest approach). A given rocket burn always provides the same change in velocity (Δv), but the change in kinetic energy is proportional to the vehicle's velocity at the time of the burn. So to get the most kinetic energy from the burn, the burn must occur at the vehicle's maximum velocity, at periapsis. Powered slingshots describes this technique in more detail.

## Historical origins of the method

In his paper “Тем кто будет читать, чтобы строить” (To whoever will read [this paper] in order to build [an interplanetary rocket]), which he dated “1918-1919,” Yuri Kondratyuk
Yuri Kondratyuk
Yuri Vasilievich Kondratyuk , was a follower, supporter and founder of cosmism, pioneer of astronautics and spaceflight. He was a theoretician and a visionary who, in the early twentieth century, foresaw ways of reaching the moon...

suggested that a spacecraft traveling between two planets could be accelerated at the beginning of its trajectory and decelerated at the end of its trajectory by using the gravity of the two planets' moons.

In his 1925 paper “Проблема полета при помощи реактивных аппаратов: межпланетные полеты” [Problems of flight by jet propulsion: interplanetary flights], Friedrich Zander
Friedrich Zander
Friedrich Zander , often transliterated Fridrikh Arturovich Tsander, was a pioneer of rocketry and spaceflight in the Russian Empire and the Soviet Union...

However, neither investigator realized that gravitational assists from planets along a spacecraft’s trajectory could propel a spacecraft and that therefore such assists could greatly reduce the amount of propellant required to travel among the planets. That discovery was made by Michael Minovitch
Michael Minovitch
Michael Minovitch is an American mathematician who showed that spacecraft trajectories could be designed such that they could gain velocity by travelling close to a planet orbiting the sun...

in 1961.

The gravity assist maneuver was first used in 1959 when the Soviet probe Luna 3 photographed the far side of Earth's Moon. The maneuver relied on research performed at the Department of Applied Mathematics of Steklov Institute
Keldysh Institute of Applied Mathematics
The Keldysh Institute of Applied Mathematics of the Russian Academy of Sciences is a research institute specializing in computational mathematics....

.

## Why gravitational slingshots are used

A spacecraft traveling from Earth to an inner planet will accelerate because it is falling toward the Sun, and a spacecraft traveling from Earth to an outer planet will decelerate because it is leaving the vicinity of the Sun.

Although it is true that the orbital speed of an inner planet is greater than that of the Earth, a spacecraft traveling to an inner planet, even at the minimum speed needed to reach it, is still accelerated by the Sun's gravity to a speed notably greater than the orbital speed of that destination planet. If the spacecraft's purpose is only to fly by the inner planet, then there is typically no need to slow the spacecraft. However, if the spacecraft is to be inserted into orbit
Orbit
In physics, an orbit is the gravitationally curved path of an object around a point in space, for example the orbit of a planet around the center of a star system, such as the Solar System...

about that inner planet, then there must be some way to slow the spacecraft.

Similarly, while the orbital speed of an outer planet is less than that of the Earth, a spacecraft leaving the Earth at the minimum speed needed to travel to some outer planet is decelerated by the Sun's gravity to a speed far less than the orbital speed of that outer planet. Thus, there must be some way to accelerate the spacecraft when it reaches that outer planet if it is to enter orbit about it. However, if the spacecraft is accelerated to more than the minimum required, less total propellant will be needed to enter orbit about the target planet. Also, accelerating the spacecraft early in the flight will, of course, reduce the travel time.

Rocket engines can certainly be used to accelerate and decelerate the spacecraft. However, rocket thrust takes propellant, propellant has mass, and even a small added delta-v requirement translates to far larger amounts of propellant needed to escape Earth's gravity well. This is because not only must the primary stage engines lift that extra propellant, they must also lift more propellant still, to lift that additional propellant. Thus the liftoff mass requirement increases exponentially with an increase in the required delta-v of the spacecraft.

Since a gravity assist maneuver can change the speed of a spacecraft without expending propellant, if and when possible, combined with aerobraking
Aerobraking
Aerobraking is a spaceflight maneuver that reduces the high point of an elliptical orbit by flying the vehicle through the atmosphere at the low point of the orbit . The resulting drag slows the spacecraft...

, it can save significant amounts of propellant.

As an example, the MESSENGER
MESSENGER
The MErcury Surface, Space ENvironment, GEochemistry and Ranging space probe is a robotic NASA spacecraft in orbit around the planet Mercury. The spacecraft was launched aboard a Delta II rocket in August 2004 to study the chemical composition, geology, and magnetic field of Mercury...

mission used gravity assist maneuvering to slow the spacecraft on its way to Mercury; however, since Mercury has almost no atmosphere, aerobraking could not be used for insertion into orbit about it.

Journeys to the nearest planets, Mars
Mars
Mars is the fourth planet from the Sun in the Solar System. The planet is named after the Roman god of war, Mars. It is often described as the "Red Planet", as the iron oxide prevalent on its surface gives it a reddish appearance...

and Venus
Venus
Venus is the second planet from the Sun, orbiting it every 224.7 Earth days. The planet is named after Venus, the Roman goddess of love and beauty. After the Moon, it is the brightest natural object in the night sky, reaching an apparent magnitude of −4.6, bright enough to cast shadows...

, use a Hohmann transfer orbit
Hohmann transfer orbit
In orbital mechanics, the Hohmann transfer orbit is an elliptical orbit used to transfer between two circular orbits, typically both in the same plane....

, an elliptical
Ellipse
In geometry, an ellipse is a plane curve that results from the intersection of a cone by a plane in a way that produces a closed curve. Circles are special cases of ellipses, obtained when the cutting plane is orthogonal to the cone's axis...

path which starts as a tangent
Tangent
In geometry, the tangent line to a plane curve at a given point is the straight line that "just touches" the curve at that point. More precisely, a straight line is said to be a tangent of a curve at a point on the curve if the line passes through the point on the curve and has slope where f...

to one planet's orbit round the Sun and finishes as a tangent to the other. This method uses very nearly the smallest possible amount of fuel, but is very slow — it can take over a year to travel from Earth to Mars (fuzzy orbits use even less fuel, but are even slower).

Similarly it might take decades for a spaceship to travel to the outer planets (Jupiter
Jupiter
Jupiter is the fifth planet from the Sun and the largest planet within the Solar System. It is a gas giant with mass one-thousandth that of the Sun but is two and a half times the mass of all the other planets in our Solar System combined. Jupiter is classified as a gas giant along with Saturn,...

, Saturn
Saturn
Saturn is the sixth planet from the Sun and the second largest planet in the Solar System, after Jupiter. Saturn is named after the Roman god Saturn, equated to the Greek Cronus , the Babylonian Ninurta and the Hindu Shani. Saturn's astronomical symbol represents the Roman god's sickle.Saturn,...

, Uranus
Uranus
Uranus is the seventh planet from the Sun. It has the third-largest planetary radius and fourth-largest planetary mass in the Solar System. It is named after the ancient Greek deity of the sky Uranus , the father of Cronus and grandfather of Zeus...

, etc.) using a Hohmann transfer orbit, and it would still require far too much propellant, because the spacecraft would have to travel for 800 million km (500 million miles) or more against the force of the Sun's gravity. As gravitational assist maneuvers offer the only way to gain speed without using propellant, all missions to the outer planets have used it.

## Limits to slingshot use

The main practical limit to the use of a gravity assist maneuver is that planets and other large masses are seldom in the right places to enable a voyage to a particular destination. For example the Voyager
Voyager 1
The Voyager 1 spacecraft is a 722-kilogram space probe launched by NASA in 1977, to study the outer Solar System and eventually interstellar space. Operating for as of today , the spacecraft receives routine commands and transmits data back to the Deep Space Network. At a distance of as of...

missions which started in the late 1970s were made possible by the "Grand Tour
Planetary Grand Tour
The Planetary Grand Tour was an ambitious plan to send unmanned probes to the planets of the outer solar system. Conceived by Gary Flandro of the Jet Propulsion Laboratory in the late 1960s, the Grand Tour would have exploited the alignment of Jupiter, Saturn, Uranus, Neptune, and Pluto, an event...

" alignment of Jupiter, Saturn, Uranus and Neptune. A similar alignment will not occur again until the middle of the 22nd century. That is an extreme case, but even for less ambitious missions there are years when the planets are scattered in unsuitable parts of their orbits.

Another limitation is the atmosphere, if any, of the available planet. The closer the spacecraft can approach, the more boost it gets, because gravity falls off with the square of distance from a planet's center. If a spacecraft gets too far into the atmosphere, the energy lost to friction can exceed that gained from the planet's gravity. On the other hand, the atmosphere can be used to accomplish aerobraking
Aerobraking
Aerobraking is a spaceflight maneuver that reduces the high point of an elliptical orbit by flying the vehicle through the atmosphere at the low point of the orbit . The resulting drag slows the spacecraft...

. There have also been (so far theoretical) proposals to use aerodynamic lift
Lift (force)
A fluid flowing past the surface of a body exerts a surface force on it. Lift is the component of this force that is perpendicular to the oncoming flow direction. It contrasts with the drag force, which is the component of the surface force parallel to the flow direction...

as the spacecraft flies through the atmosphere (an aerogravity assist
Aerogravity assist
An aerogravity assist, or AGA, is a spacecraft maneuver designed to change velocity when arriving at a body with an atmosphere. A pure gravity assist uses only the gravity of a body to change the direction of the spacecraft trajectory. The change in direction is limited by the mass of the body,...

). This could bend the trajectory through a larger angle than gravity alone, and hence increase the gain in energy.

Interplanetary slingshots using the Sun itself are not possible because the Sun is at rest relative to the Solar System as a whole. However, thrusting when near the Sun has the same effect as the powered slingshot described below. This has the potential to magnify a spacecraft's thrusting power enormously, but is limited by the spacecraft's ability to resist the heat.

An interstellar slingshot using the Sun is conceivable, involving for example an object coming from elsewhere in our galaxy and swinging past the Sun to boost its galactic travel. The energy and angular momentum would then come from the Sun's orbit around the Milky Way
Milky Way
The Milky Way is the galaxy that contains the Solar System. This name derives from its appearance as a dim un-resolved "milky" glowing band arching across the night sky...

.

Another theoretical limit is based on general relativity
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...

. If a spacecraft gets close to the Schwarzschild radius
The Schwarzschild radius is the distance from the center of an object such that, if all the mass of the object were compressed within that sphere, the escape speed from the surface would equal the speed of light...

of a black hole
Black hole
A black hole is a region of spacetime from which nothing, not even light, can escape. The theory of general relativity predicts that a sufficiently compact mass will deform spacetime to form a black hole. Around a black hole there is a mathematically defined surface called an event horizon that...

(the ultimate gravity well), space becomes so curved that slingshot orbits require more energy to escape than the energy that could be added by the black hole's motion.

A rotating black hole
Rotating black hole
A rotating black hole is a black hole that possesses spin angular momentum.-Types of black holes:There are four known, exact, black hole solutions to Einstein's equations, which describe gravity in General Relativity. Two of these rotate...

might provide additional assistance, if its spin axis is aligned the right way. General relativity
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...

predicts that a large spinning mass produces frame-dragging
Frame-dragging
Einstein's general theory of relativity predicts that non-static, stationary mass-energy distributions affect spacetime in a peculiar way giving rise to a phenomenon usually known as frame-dragging...

— close to the object, space itself is dragged around in the direction of the spin. In theory an ordinary star produces this effect, although attempts to measure frame dragging about the Sun have produced no clear evidence. Experiments performed by Gravity Probe B
Gravity Probe B
Gravity Probe B is a satellite-based mission which launched on 20 April 2004 on a Delta II rocket. The spaceflight phase lasted until 2005; its aim was to measure spacetime curvature near Earth, and thereby the stress–energy tensor in and near Earth...

looking for frame-dragging effects caused by the Earth have not revealed clear evidence either. General relativity predicts that a spinning black hole is surrounded by a region of space, called the ergosphere
Ergosphere
The ergosphere is a region located outside a rotating black hole. Its name is derived from the Greek word ergon, which means “work”. It received this name because it is theoretically possible to extract energy and mass from the black hole in this region...

, within which standing still (with respect to the black hole's spin) is impossible, because space itself is dragged at the speed of light in the same direction as the black hole's spin. The Penrose process
Penrose process
The Penrose process is a process theorised by Roger Penrose wherein energy can be extracted from a rotating black hole...

may offer a way to gain energy from the ergosphere, although it would require the spaceship to dump some "ballast" into the black hole, and the spaceship would have had to expend energy to carry the "ballast" to the black hole.

### Mariner 10 – first use

The Mariner 10
Mariner 10
Mariner 10 was an American robotic space probe launched by NASA on November 3, 1973, to fly by the planets Mercury and Venus. It was launched approximately two years after Mariner 9 and was the last spacecraft in the Mariner program...

probe was the first spacecraft to use the gravitational slingshot effect to reach another planet, passing by Venus on February 5, 1974, on its way to becoming the first spacecraft to explore Mercury
Mercury (planet)
Mercury is the innermost and smallest planet in the Solar System, orbiting the Sun once every 87.969 Earth days. The orbit of Mercury has the highest eccentricity of all the Solar System planets, and it has the smallest axial tilt. It completes three rotations about its axis for every two orbits...

.

### Voyager 1 – furthest human-made object

As of January 21, 2010, Voyager 1
Voyager 1
The Voyager 1 spacecraft is a 722-kilogram space probe launched by NASA in 1977, to study the outer Solar System and eventually interstellar space. Operating for as of today , the spacecraft receives routine commands and transmits data back to the Deep Space Network. At a distance of as of...

is over 16.81 terameters (1.681 meters, or 1.681 km, 112.4 AU
Astronomical unit
An astronomical unit is a unit of length equal to about or approximately the mean Earth–Sun distance....

, or 10.4 billion
1000000000 (number)
1,000,000,000 is the natural number following 999,999,999 and preceding 1,000,000,001.In scientific notation, it is written as 109....

miles) from the Sun, and is in the boundary zone between the Solar System and interstellar space
Interstellar medium
In astronomy, the interstellar medium is the matter that exists in the space between the star systems in a galaxy. This matter includes gas in ionic, atomic, and molecular form, dust, and cosmic rays. It fills interstellar space and blends smoothly into the surrounding intergalactic space...

. It gained the energy to escape the Sun's gravity completely by performing slingshot maneuvers around Jupiter and Saturn.

### Galileo – a change of plan

The Galileo spacecraft was launched by NASA
NASA
The National Aeronautics and Space Administration is the agency of the United States government that is responsible for the nation's civilian space program and for aeronautics and aerospace research...

in 1989 aboard Space Shuttle Atlantis
Space Shuttle Atlantis
The Space Shuttle Atlantis is a retired Space Shuttle orbiter in the Space Shuttle fleet belonging to the National Aeronautics and Space Administration , the spaceflight and space exploration agency of the United States...

. Its original mission was designed to use a direct Hohmann transfer. However, Galileo's intended booster, the cryogenically fueled (Hydrogen/Oxygen) Centaur
Centaur (rocket stage)
Centaur is a rocket stage designed for use as the upper stage of space launch vehicles. Centaur boosts its satellite payload to geosynchronous orbit or, in the case of an interplanetary space probe, to or near to escape velocity...

booster rocket was prohibited as a Shuttle "cargo" for safety considerations following the loss of the Space Shuttle Challenger
Space Shuttle Challenger
Space Shuttle Challenger was NASA's second Space Shuttle orbiter to be put into service, Columbia having been the first. The shuttle was built by Rockwell International's Space Transportation Systems Division in Downey, California...

. Forced to substitute a lower delta V capable solid rocket upperstage, the IUS, instead of ascending directly to Jupiter, Galileo flew by Venus once and Earth twice in order to reach Jupiter in December, 1995.

The Galileo engineering review speculated (but was never able to prove conclusively) that this longer flight time coupled with the stronger sunlight near Venus caused lubricant in Galileo's main antenna to fail, forcing the use of a much smaller backup antenna with a consequent lowering of data rate from the spacecraft.

Its subsequent tour of the Jovian moons also used numerous slingshot maneuvers with those moons to conserve fuel and maximize the number of encounters.

### The Ulysses probe changed the plane of its trajectory

In 1990, NASA launched the ESA
European Space Agency
The European Space Agency , established in 1975, is an intergovernmental organisation dedicated to the exploration of space, currently with 18 member states...

spacecraft Ulysses to study the polar
Geographical pole
A geographical pole is either of the two points—the north pole and the south pole—on the surface of a rotating planet where the axis of rotation meets the surface of the body...

regions of the Sun
Sun
The Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...

. All the planets orbit approximately in a plane aligned with the equator of the Sun. Thus, to enter an orbit passing over the poles of the Sun, the spacecraft would have to eliminate the 30 km/s speed it inherited from the Earth's orbit around the Sun and gain the speed needed to orbit the Sun in the pole-to-pole plane — tasks that are impossible with current spacecraft propulsion
Spacecraft propulsion
Spacecraft propulsion is any method used to accelerate spacecraft and artificial satellites. There are many different methods. Each method has drawbacks and advantages, and spacecraft propulsion is an active area of research. However, most spacecraft today are propelled by forcing a gas from the...

systems alone, making gravity assist maneuvers essential.

Accordingly, Ulysses was first sent towards Jupiter, aimed to arrive at a point in space just "in front of" and "below" the planet. As it passed Jupiter, the probe 'fell' through the planet's gravity field, exchanging momentum with the planet; this gravity assist maneuver bent the probe's trajectory up out of the planetary plane into an orbit that passed over the poles of the Sun. By using this maneuver, Ulysses needed only enough propellant to send it to a point near Jupiter, which is well within current capability.

### MESSENGER

The MESSENGER
MESSENGER
The MErcury Surface, Space ENvironment, GEochemistry and Ranging space probe is a robotic NASA spacecraft in orbit around the planet Mercury. The spacecraft was launched aboard a Delta II rocket in August 2004 to study the chemical composition, geology, and magnetic field of Mercury...

mission made extensive use of gravity assists to slow its speed before orbiting Mercury. The MESSENGER mission included
one flyby of Earth, two flybys of Venus, and three flybys of Mercury before finally arriving at Mercury in March 2011 with a velocity low enough to permit orbit insertion with available fuel. Although the flybys are primarily orbital maneuvers, each provided an opportunity for significant scientific observations.

### The Cassini probe – multiple gravity assists

The Cassini probe passed by Venus twice, then Earth, and finally Jupiter on the way to Saturn. The 6.7-year transit was slightly longer than the six years needed for a Hohmann transfer, but cut the total amount of delta V needed to about 2 km/s, so that the large and heavy Cassini probe was able to reach Saturn even with the small boosters available. A Hohmann transfer to Saturn would require a total of 15.7 km/s delta V (disregarding Earth's and Saturn's own gravity wells, and disregarding aerobraking
Aerobraking
Aerobraking is a spaceflight maneuver that reduces the high point of an elliptical orbit by flying the vehicle through the atmosphere at the low point of the orbit . The resulting drag slows the spacecraft...

), which is not within the capabilities of current spacecraft boosters.

### Solar Probe+

The NASA Solar Probe+ mission, scheduled for launch in 2015, uses multiple gravity assists at Venus to remove the Earth's angular momentum from the orbit, in order to drop down to a distance of 9.5 solar radii from the sun. This will be the closest approach to the sun of any space mission.

## Powered slingshots

A well-established way to get more energy from a gravity assist is to fire a rocket engine at periapsis where a spacecraft is at its maximum velocity.

Rocket engines produce the same acceleration regardless of their initial velocity. A rocket acting on a fixed object, as in a static firing, does no useful work at all; the rocket's stored energy is entirely expended on its propellant. But when the rocket and its payload are free to move, the force applied by the rocket during any time interval acts through the distance the rocket and payload move during that time. Force acting through a distance is the definition of mechanical energy or work
Mechanical work
In physics, work is a scalar quantity that can be described as the product of a force times the distance through which it acts, and it is called the work of the force. Only the component of a force in the direction of the movement of its point of application does work...

. So the farther the rocket and payload move during any given interval, i.e., the faster they move, the greater the kinetic energy imparted to the payload by the rocket. (This is why rockets are seldom used on slow-moving vehicles; they're simply too inefficient when used in that manner.)

Energy is still conserved, however. The additional energy imparted to the payload is exactly matched by a decrease in energy imparted to the propellant being expelled behind the rocket. This is because the velocity of the rocket is being subtracted from the propellant exhaust velocity. But we don't care about what happens to the propellant, so the faster we can move the rocket during a burn, the better.

To impart the most kinetic energy
Kinetic energy
The kinetic energy of an object is the energy which 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 acceleration, the body maintains this kinetic energy unless its speed changes...

to a spacecraft whose free-fall velocity varies with time, we must do it when it's moving the fastest. As this occurs at periapsis, the closest approach to the planet, that's when we do the burn.

Another way to look at this is to note that by bringing in propellant as we fall into the planet's gravity well and leaving it behind there, we are able to extract much of the gravitational potential energy that was contained in that propellant.

There are also proposals to use aerodynamic lift
Lift (force)
A fluid flowing past the surface of a body exerts a surface force on it. Lift is the component of this force that is perpendicular to the oncoming flow direction. It contrasts with the drag force, which is the component of the surface force parallel to the flow direction...

at the point of closest approach (an aerogravity assist), to achieve a larger deflection and hence more energy gain.

• 3753 Cruithne
3753 Cruithne
3753 Cruithne is an asteroid in orbit around the Sun in approximate 1:1 orbital resonance with the Earth. It is a periodic inclusion planetoid orbiting the Sun in an apparent horseshoe orbit. It has been incorrectly called "Earth's second moon", but it is only a quasi-satellite. Cruithne never...

: an asteroid which periodically has gravitational slingshot encounters with Earth.
• Delta-v budget
Delta-v budget
In the astrodynamics and aerospace industry, a delta-v budget is the estimated delta-v requirements for the various propulsive tasks and orbital maneuvers over one or more phases of a space mission.Sample delta-v budget will enumerate various classes of maneuvers, delta-v per maneuver, number of...

• Dynamical friction
Dynamical friction
Dynamical friction is a term in astrophysics related to loss of momentum and kinetic energy of moving bodies through a gravitational interaction with surrounding matter in space...

• Flyby anomaly
Flyby anomaly
The flyby anomaly is an unexpected energy increase during Earth-flybys of spacecraft. This anomaly has been observed as shifts in the S-Band and X-Band Doppler and ranging telemetry. Taken together it causes a significant unaccounted velocity increase of over 13 mm/s during...

: an anomalous delta-v increase during gravity assists
• Interplanetary Transport Network
Interplanetary Transport Network
The Interplanetary Transport Network 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 where trajectories through space are redirected using little...

• Gravitational keyhole
Gravitational keyhole
A gravitational keyhole, or resonance keyhole, is a small region of space that could alter the course of a passing asteroid due to a planet's gravity in a way that could cause such an asteroid to collide with that planet on its next orbital pass...

• Michael Minovitch
Michael Minovitch
Michael Minovitch is an American mathematician who showed that spacecraft trajectories could be designed such that they could gain velocity by travelling close to a planet orbiting the sun...

• N-body problem
N-body problem
The n-body problem is the problem of predicting the motion of a group of celestial objects that interact with each other gravitationally. Solving this problem has been motivated by the need to understand the motion of the Sun, planets and the visible stars...

• New Horizons
New Horizons
New Horizons is a NASA robotic spacecraft mission currently en route to the dwarf planet Pluto. It is expected to be the first spacecraft to fly by and study Pluto and its moons, Charon, Nix, Hydra and S/2011 P 1. Its estimated arrival date at the Pluto-Charon system is July 14th, 2015...

: a gravity-assisted mission (flying past Jupiter) to reach Pluto
Pluto
Pluto, formal designation 134340 Pluto, is the second-most-massive known dwarf planet in the Solar System and the tenth-most-massive body observed directly orbiting the Sun...

in 2015.
• The Oberth effect
Oberth effect
In astronautics, the Oberth effect is where the use of a rocket engine when travelling at high speed generates much more useful energy than one at low speed...

: doing burns deep in gravity fields to gain speed
• Pioneer 10
Pioneer 10
Pioneer 10 is a 258-kilogram robotic space probe that completed the first interplanetary mission to Jupiter, and became the first spacecraft to achieve escape velocity from the Solar System. The project was managed by the NASA Ames Research Center and the contract for the construction of the...

• Pioneer 11
Pioneer 11
Pioneer 11 is a 259-kilogram robotic space probe launched by NASA on April 6, 1973 to study the asteroid belt, the environment around Jupiter and Saturn, solar wind, cosmic rays, and eventually the far reaches of the solar system and heliosphere...

• Pioneer H
Pioneer H
Pioneer H is an unlaunched unmanned space mission that was part of the US Pioneer program for a planned 1974 launch. Had this mission and spacecraft been launched, it would have been designated Pioneer 12; that designation was later applied to the Pioneer Venus Orbiter.The probe would have been...

• Ulysses
Ulysses probe
Ulysses is a decommissioned robotic space probe that was designed to study the Sun as a joint venture of NASA and the European Space Agency . The spacecraft was originally named Odysseus, because of its lengthy and indirect trajectory to near Solar distance...

• Voyager 1
Voyager 1
The Voyager 1 spacecraft is a 722-kilogram space probe launched by NASA in 1977, to study the outer Solar System and eventually interstellar space. Operating for as of today , the spacecraft receives routine commands and transmits data back to the Deep Space Network. At a distance of as of...

• Voyager 2
Voyager 2
The Voyager 2 spacecraft is a 722-kilogram space probe launched by NASA on August 20, 1977 to study the outer Solar System and eventually interstellar space...

• MESSENGER
MESSENGER
The MErcury Surface, Space ENvironment, GEochemistry and Ranging space probe is a robotic NASA spacecraft in orbit around the planet Mercury. The spacecraft was launched aboard a Delta II rocket in August 2004 to study the chemical composition, geology, and magnetic field of Mercury...

• STEREO
STEREO
STEREO is a solar observation mission. Two nearly identical spacecraft were launched into orbits that cause them to respectively pull farther ahead of and fall gradually behind the Earth...

: a gravity-assisted mission which used Earth's Moon to eject two spacecraft from Earth's orbit into heliocentric orbit