In orbital mechanics and aerospace engineering, a gravitational slingshot or gravity assist is the use of the gravity of a planet or other celestial body to alter the path and speed of a spacecraft. Passing by such a body imparts some fraction of that body's speed to the spacecraft. It is a commonly used maneuver for visiting the outer planets, which would otherwise either take far too long or require far too much fuel using our current propulsion technologies. It was first developed in 1959 at the Department of Applied Mathematics of Steklov Institute.^[1] This article or section should be merged with Celestial Mechanics Astrodynamics is the study and creation of orbits, especially those of artificial satellites. ... Aerospace engineering is the branch of engineering that concerns aircraft, spacecraft, and related topics. ... This article is about the astronomical term. ... The Space Shuttle Discovery as seen from the International Space Station. ... This article is about the astronomical term. ... The Keldysh Institute of Applied Mathematics of Russian Academy of Sciences is a research institute specializing in computational mathematics. ...

A slingshot maneuver around a planet changes a spacecraft's velocity relative to the Sun, even though it preserves the spacecraft's speed relative to the planet (as it must do, according to the law of conservation of energy). To a first approximation, from a large distance, the spacecraft appears to have bounced off the planet. (Physicists call this an elastic collision even though no contact actually occurs.) This article is about velocity in physics. ... Sol redirects here. ... This article does not cite any references or sources. ... Look up conservation of energy in Wiktionary, the free dictionary. ... As long as black-body radiation (not shown) doesn’t escape a system, atoms in thermal agitation undergo essentially elastic collisions. ...

Why gravitational slingshots are used

Interplanetary travel has to solve two problems:

• The planet from which the spaceship starts is moving around the sun at a different speed than the planet to which the spaceship is traveling, because the two planets are at different distances from the sun. So as it approaches its destination, the spaceship must increase its speed if the destination is closer to the sun, or decrease its speed if the destination is further away.
• If the destination is further away, the spaceship must lift itself "up" against the force of the sun's gravity.

Doing this by brute force – accelerating in the shortest route to the destination and then, if it is further from the sun, decelerating to match the planet's speed – would require an extremely large amount of fuel.

So journeys to the nearest planets, Mars and Venus, use a Hohmann transfer orbit, an elliptical path which starts as a tangent to one planet's orbit round the sun and finishes as a tangent to the other's. 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). Adjectives: Martian Atmosphere Surface pressure: 0. ... For other uses, see Venus (disambiguation). ... In astronautics and aerospace engineering, the Hohmann transfer orbit is an orbital maneuver that, under standard assumption, moves a spacecraft from one circular orbit to another using two engine impulses. ... For other uses, see Ellipse (disambiguation). ... For other uses, see tangent (disambiguation). ... By definition, interplanetary travel is travel between bodies in a given star system; especially the solar system. ...

Similarly it might take decades for a spaceship to travel to the outer planets (Jupiter, Saturn, Uranus, etc.) using a Hohmann transfer orbit. And it would still require far too much fuel, because the spaceship would have to travel for 500 million miles (800 million km) or more against the force of the sun's gravity. Gravitational slingshots offer a way to gain speed without using any fuel, and all missions to the outer planets have used it. For other uses, see Jupiter (disambiguation). ... This article is about the planet. ... For other uses, see Uranus (disambiguation). ...

Limits to slingshot use

The main practical limit to the use of a slingshot is that planets and other large masses are not always in the right places to help a voyage to a particular destination. For example the Voyager missions which started in the late 1970s were made possible by the "Grand Tour" 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 not in places that make slingshots useful. For the album by The Verve, see Voyager 1 (album). ... For other uses of the term Grand Tour, see Grand Tour (disambiguation) The Planetary Grand Tour was an ambitious plan to send unmanned probes to the outermost planets of the solar system. ...

Another limit is caused by the atmosphere of the available planet. The closer the craft can get, the more boost it gets, because gravity falls with the square of distance. If a craft gets too far into the atmosphere, however, the energy lost to friction can exceed that gained from the planet. On the other hand, this effect can be useful if the goal is to lose energy. See aerobraking. An artists conception of a spacecraft aerobraking Aerobraking is a technique used by spacecraft in which it uses drag within a planetary atmosphere to reduce its velocity relative to the planet. ...

Interplanetary slingshots using the sun itself are impossible 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 slingshotting around the Sun to boost its galactic travel. The energy and angular momentum would then come from the Sun's orbit around the Milky Way. The time scales involved for such an operation are considerably beyond current human capabilities, however. For other uses, see Milky Way (disambiguation). ...

There's also another, theoretical limit based on general relativity. If a spacecraft gets close to the Schwarzschild radius of a black hole (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. For a less technical and generally accessible introduction to the topic, see Introduction to general relativity. ... The Schwarzschild radius (sometimes inappropriately referred to as the gravitational radius[1]) is a characteristic radius associated with every mass. ... For other uses, see Black hole (disambiguation). ...

But a rotating black hole might provide additional assistance, if its spin axis points the right way. General relativity predicts that a large spinning mass produces frame-dragging – close to the object, space itself is dragged round in the direction of the spin. In theory an ordinary star produces this effect, although attempts to measure it round the sun have produced no clear results. But general relativity predicts that a spinning black hole is surrounded by a region of space, called the ergosphere, 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 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. A rotating black hole (Kerr black hole or Kerr-Newman black hole) is a black hole that possesses angular momentum. ... For a less technical and generally accessible introduction to the topic, see Introduction to general relativity. ... According to Albert Einsteins theory of general relativity, space and time get pulled out of shape near a rotating body in a phenomenon referred to as frame-dragging. ... A rotating black hole (Kerr black hole or Kerr-Newman black hole) is a black hole that possesses angular momentum. ... To meet Wikipedias quality standards, this article or section may require cleanup. ...

Notable examples

Mariner 10 – first use

The Mariner 10 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. The Mariner 10 probe. ... This article is about the planet. ...

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 is 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), which is not within the capabilities of our current spacecraft boosters. This is an artists concept of Cassini during the Saturn Orbit Insertion (SOI) maneuver, just after the main engine has begun firing. ... In general physics, delta-v is simply the change in velocity. ... In astronautics and aerospace engineering, the Hohmann transfer orbit is an orbital maneuver that moves a spacecraft from one orbit to another using the lowest possible delta-v for the specific transfer. ... An artists conception of a spacecraft aerobraking Aerobraking is a technique used by spacecraft in which it uses drag within a planetary atmosphere to reduce its velocity relative to the planet. ...

Cassini's speed related to Sun. The various gravity assists form visible peaks on the left, while the periodic variation on the right is caused by the spacecraft's orbit around Saturn. The data was from JPL Horizons Ephemeris System. The speed above is in kilometers per second. Note also that the minimum speed achieved during Saturnian orbit is more or less equal to Saturn's own orbital velocity, which is the ~5 km/s velocity which Cassini matched to enter orbit.

Image File history File links Cassini_interplanet_trajectory. ... Image File history File links Download high resolution version (1968x802, 92 KB) Licensing I, the creator of this work, hereby grant the permission to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1. ... Image File history File links Download high resolution version (1968x802, 92 KB) Licensing I, the creator of this work, hereby grant the permission to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1. ... JPL Horizons Ephemeris System provides easy access to key solar system data and flexible production of highly accurate ephemerides for solar system objects. ...

Voyager 1 – the fastest, furthest human-made object

As of July 6, 2007, Voyager 1 is over 15.44 terameters (15.44×10¹² meters, or 15.44×10⁹ km, 103.2 AU, or 9.6 billion miles) from the Sun, and is in the boundary zone between the solar system and interstellar space. It gained the energy to escape the sun's gravity completely by performing slingshot maneuvers around Jupiter and Saturn. ^[2] is the 187th day of the year (188th in leap years) in the Gregorian calendar. ... Year 2007 (MMVII) is the current year, a common year starting on Monday of the Gregorian calendar and the AD/CE era in the 21st century. ... For the album by The Verve, see Voyager 1 (album). ... A terametre (American spelling: terameter) (symbol: Tm) is a unit of length equal to 1012 metres. ... The astronomical unit (AU or au or a. ... One thousand million (1,000,000,000) is the natural number following 999,999,999 and preceding 1,000,000,001. ... The heliosphere is a bubble in space produced by the solar wind. ... The interstellar medium (or ISM) is the name astronomers give to the tenuous gas and dust that pervade interstellar space. ...

The Ulysses probe changed the angle of its trajectory

In 1990, the ESA launched the spacecraft Ulysses to study the polar regions of the Sun. All the planets orbit approximately in a plane aligned with the equator of the Sun. To move to 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 round the sun and gain the speed needed to orbit the sun in the pole-to-pole plane – tasks which were impossible with current spacecraft propulsion systems. ESA redirects here. ... Ulysses spacecraft Ulysses is an unmanned probe designed to study the Sun at all latitudes. ... A geographical pole is either of two fixed points on the surface of a spinning body or planet, at 90 degrees from the equator, based on the axis around which a body spins. ... Sol redirects here. ... A remote camera captures a close-up view of a Space Shuttle Main Engine during a test firing at the John C. Stennis Space Center in Hancock County, Mississippi Spacecraft propulsion is any method used to change the velocity of spacecraft and artificial satellites. ...

So the craft was 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, borrowing a minute amount of momentum from the planet; after it had passed Jupiter, the velocity change had bent the probe's trajectory up out of the plane of the planetary orbits, placing it in an orbit that passed over the poles of the Sun. This manoeuvre required only enough fuel to send Ulysses to a point near Jupiter, which is well within current technologies.

Explanation

Over-simplified example of gravitational slingshot: the spacecraft's velocity changes by up to twice the planet's velocity

This is a very over-simplified explanation to show the principle. The details will be covered later. Image File history File links No higher resolution available. ... Image File history File links No higher resolution available. ...

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 is on the right path, it will pass so close to the planet that it enters a circular orbit. When it enters this orbit, it is 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 spaceship is moving left at speed U + v from your point of view – its speed has increased by 2U, twice the speed at which the planet is moving.

This example is so over-simplified that it is not realistic – the spaceship would have to fire its engine to escape from a circular orbit, and the whole point of the gravitational slingshot is to gain speed without burning fuel. But if the spaceship travels in a path which forms a hyperbola, it leaves the planet in the opposite direction without firing its engine, although the speed gain is a little less than 2U. In mathematics, a hyperbola (Greek literally overshooting or excess) is a type of conic section defined as the intersection between a right circular conical surface and a plane which cuts through both halves of the cone. ...

This explanation might seem to violate the conservation of energy and momentum, but we have neglected the spacecraft's effects on the planet. These effects on the planet are so slight (because planets are so much larger than spacecraft) that they can be ignored in the calculation.^[3]

Realistic portrayals of encounters in space require the consideration of two dimensions. In that case the same principles apply, only adding the planet's velocity requires vector addition, as shown below. A vector in physics and engineering typically refers to a quantity that has close relationship to the spatial coordinates, informally described as an object with a magnitude and a direction. The word vector is also now used for more general concepts (see also vector and generalizations below), but in this...

2 dimensional schematic of gravitational slingshot. The arrows show the direction in which the spacecraft is traveling before and after the encounter. The arrows' length shows the spacecraft's speed.

Gravitational slingshots can also be used to decelerate a spacecraft. Mariner 10 did this in 1974 and MESSENGER will also do it – both missions are to Mercury. Image File history File links No higher resolution available. ... Image File history File links No higher resolution available. ... The Mariner 10 probe. ... This article is about the NASA space mission. ... This article is about the planet. ...

If even more speed is needed, the most economical way is to fire a rocket engine near the periapsis (closest approach). A given rocket burn always provides the same change in velocity (delta-v), 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. This article is about several astronomical terms (apogee & perigee, aphelion & perihelion, generic equivalents based on apsis, and related but rarer terms. ... General In general physics delta-v is simply the change in velocity. ...

Powered slingshots

A well-established way to get more energy from a slingshot is to fire a rocket engine near the periapsis to increase the spacecraft's speed. A given rocket burn always provides the same change in velocity (delta-v), but the change in kinetic energy is proportional to the vehicle's velocity at the time of the burn. Therefore, to get the most kinetic energy from the burn, the burn must occur at the vehicle's maximum velocity, at periapsis. Energy is still conserved. The extra energy comes from the propellant being "left behind" in the planet's gravity well. This article is about several astronomical terms (apogee & perigee, aphelion & perihelion, generic equivalents based on apsis, and related but rarer terms. ... General In general physics delta-v is simply the change in velocity. ... The cars of a roller coaster reach their maximum kinetic energy when at the bottom of their path. ... This article is about several astronomical terms (apogee & perigee, aphelion & perihelion, generic equivalents based on apsis, and related but rarer terms. ...

If the ship travels at velocity v at the start of a burn that changes the velocity by Δv, then the change in specific orbital energy (SOE) is: In astrodynamics the specific orbital energy (or vis-viva energy) of an orbiting body traveling through space under standard assumptions is the sum of its potential energy () and kinetic energy () per unit mass. ...

Once the space craft is far from the planet again, the SOE is entirely kinetic, since gravitational potential energy tends to zero. Therefore, the larger the v at the time of the burn, the greater the final kinetic energy, and the higher the final velocity.

For example, a Hohmann transfer orbit from Earth to Jupiter brings a spacecraft into a hyperbolic flyby of Jupiter with a periapsis velocity of 60 km/s, and a final velocity (asymptotic residual velocity) of 5.6 km/s, which is 10.7 times slower. That means a burn that adds one joule of kinetic energy when far from Jupiter would add 10.7 joules at periapsis. Every 1 m/s gained at periapsis adds m/s to the spacecraft's final velocity. Thus, Jupiter's immense gravitational field has tripled the effectiveness of the space craft's propellant. In astronautics and aerospace engineering, the Hohmann transfer orbit is an orbital maneuver that, under standard assumption, moves a spacecraft from one circular orbit to another using two engine impulses. ... This article is about Earth as a planet. ... For other uses, see Jupiter (disambiguation). ... This article is about several astronomical terms (apogee & perigee, aphelion & perihelion, generic equivalents based on apsis, and related but rarer terms. ...

See also specific energy change of rockets: Tsiolkovskys rocket equation, named after Konstantin Tsiolkovsky who independently derived it, considers the principle of a rocket: a device that can apply an acceleration to itself (a thrust) by expelling part of its mass with high speed in the opposite direction, due to the conservation of momentum. ...

where ε is the specific energy of the rocket (potential plus kinetic energy) and Δv is a separate variable, not just the change in v.

A possibly life-saving use of this effect took place during the Apollo 13 mission. While on its way to the Moon the spacecraft's Service Module was disabled and the Lunar Module was used as a lifeboat. Since supplies were limited, it was desirable to return to Earth as quickly as possible. The most efficient way to use the limited rocket power available was to make a burn right after the closest approach to the Moon. Original crew photo. ...

In popular culture

• The American spacecraft Discovery One uses a gravitational slingshot around Jupiter in Arthur C. Clarke's novel 2001: A Space Odyssey.
• The alien ship in Arthur C. Clarke's novel Rendezvous with Rama uses a gravitational slingshot around the Sun.
• In Star Trek IV: The Voyage Home, time travel is achieved by a powered slingshot around the Sun. In the Star Trek: The Original Series episode, Tomorrow Is Yesterday, a slingshot around the Sun is used to return from the 20th century to the 23rd century (a more plausible result under General Relativity).
• In the Star Control series of games, "gravity whips" are common tactics to employ in order to increase a starship's velocity beyond its normal capacity.
• In the movie Armageddon, the two space shuttles carrying the drilling crews use a powered slingshot around the moon to intercept the killer asteroid.
• In the movie Sunshine, the Icarus II spacecraft uses a slingshot around Mercury to approach the sun.
• In Vernor Vinge's book The Peace War, a character wins a video game by using a slingshot maneuver.
• In an episode of the animated television series Futurama, Professor Farnsworth uses the principles of slingshot physics to guide a massive garbage ball through space in order to collide with a pre-existing garbage ball so that it might impact the Sun and not the Earth.
• In the pilot of the science-fiction series Farscape, astronaut John Crichton is attempting a powered slingshot around Earth when he encounters a wormhole that throws him to the far side of the galaxy. Later in the episode he successfully uses the technique to escape the main antagonist.

For other uses, see Jupiter (disambiguation). ... Wikiquote has a collection of quotations related to: Arthur C. Clarke Sir Arthur Charles Clarke, CBE (born 16 December 1917) is a British science-fiction author and inventor, most famous for his novel 2001: A Space Odyssey, and for collaborating with director Stanley Kubrick on the film of the same... Wikiquote has a collection of quotations related to: Arthur C. Clarke Sir Arthur Charles Clarke, CBE (born 16 December 1917) is a British science-fiction author and inventor, most famous for his novel 2001: A Space Odyssey, and for collaborating with director Stanley Kubrick on the film of the same... Rendezvous with Rama is a novel by Arthur C. Clarke first published in 1972. ... Sol redirects here. ... Star Trek IV: The Voyage Home (Paramount Pictures, 1986; see also 1986 in film) is the fourth feature film based on the popular Star Trek science fiction television series. ... Time travel is a concept that has long fascinated humanity—whether it is Merlin experiencing time backwards, or religious traditions like Mohammeds trip to Jerusalem and ascent to heaven, returning before a glass knocked over had spilt its contents. ... Sol redirects here. ... The starship Enterprise as it appeared on Star Trek Star Trek is a culturally significant science fiction television series created by Gene Roddenberry in the 1960s. ... Tomorrow is Yesterday is a first season episode of Star Trek: The Original Series. ... (19th century - 20th century - 21st century - more centuries) Decades: 1900s 1910s 1920s 1930s 1940s 1950s 1960s 1970s 1980s 1990s As a means of recording the passage of time, the 20th century was that century which lasted from 1901–2000 in the sense of the Gregorian calendar (1900–1999... The 23rd century of the anno Domini (common) era will span the years 2201 – 2300 of the Gregorian calendar. ... For a less technical and generally accessible introduction to the topic, see Introduction to general relativity. ... The Star Control series is a trilogy of computer games with a cult following. ... The album cover Armageddon is a 1998 disaster film/science fiction film about a group of blue-collar deep-core drillers who are sent by NASA to deflect an asteroid on a collision course with Earth. ... For other uses, see Asteroid (disambiguation). ... Sunshine is a 2007 science fiction film directed by Danny Boyle from a screenplay by Alex Garland. ... This article is about the planet. ... The Peace War is a science fiction novel by Vernor Vinge about authoritarianism and technological progress. ... This article is about the television series. ... Professor Hubert Farnsworth Professor Hubert J. Farnsworth is the extremely elderly proprietor of the Planet Express delivery service in the animated television series Futurama. ... Farscape (1999–2003) is a science fiction television series, featuring a present-day astronaut who accidentally travels through a wormhole to a distant part of the galaxy. ...

See also

• 3753 Cruithne: an asteroid which periodically has gravitational slingshot encounters with Earth.
• Dynamical friction
• Flyby anomaly: an anomalous delta-v increase during gravity assists
• The Oberth effect: doing burns deep in gravity fields gain speed
• New Horizons: a gravity-assisted mission (flying past Jupiter) to reach Pluto in 2015.
• Delta-v budget
• Pioneer 10
• Pioneer 11
• Pioneer H
• Voyager 1
• Voyager 2
• Ulysses
• MESSENGER
• STEREO: a gravity-assisted mission which used Earth's Moon to eject two spacecraft from Earth's orbit into heliocentric orbit
• Michael Minovitch
• Interplanetary Superhighway
• N-body problem

3753 Cruithne (pronounced , Modern Irish ) is an asteroid in orbit around the Sun. ... This article or section is in need of attention from an expert on the subject. ... Unsolved problems in physics: What causes the unexpected change in acceleration for flybys of satellites? The flyby anomaly is an unexpected energy increase during Earth flybys of satellites. ... The Oberth effect is a feature of astronautics where using a rocket engine close to a gravitational body gives a higher final speed than the same burn executed further from the body. ... New Horizons on the launchpad New Horizons is a robotic spacecraft mission conducted by NASA. It is expected to be the first spacecraft to fly by and study the dwarf planet Pluto and its moons, Charon, Nix and Hydra. ... For other uses, see Pluto (disambiguation). ... For the video game developer, see 2015, Inc. ... Delta-v budget (or velocity change budget) is a term used in astrodynamics and aerospace industry for velocity change (or delta-v) requirements for the various propulsive tasks and orbital maneuvers over phases of the space mission. ... Pioneer 10 was the first spacecraft to travel through the asteroid belt, and was the first spacecraft to make direct observations of Jupiter. ... Position of Pioneer 10 and 11 Pioneer 11 was the second mission to investigate Jupiter and the outer solar system and the first to explore the planet Saturn and its main rings. ... Pioneer H is an unlaunched unmanned space mission that was part of the US Pioneer program. ... For the album by The Verve, see Voyager 1 (album). ... Trajectory Voyager 2 is an unmanned interplanetary spacecraft, launched on August 20, 1977. ... Ulysses spacecraft Ulysses is an unmanned probe designed to study the Sun at all latitudes. ... This article is about the NASA space mission. ... This article is about the spacecraft and the mission. ... In astronomy, heliocentrism is the theory that the Sun is at the center of the Universe and/or the Solar System. ... 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. ... Artists concept of the Interplanetary Superhighway The Interplanetary Superhighway has come to denote a set of transfer orbits between various planets and moons in the solar system. ... This article is about the problem in classical mechanics. ...

References

The Keldysh Institute of Applied Mathematics of Russian Academy of Sciences is a research institute specializing in computational mathematics. ...

External links

• Slingshot effect
• Animation of Cassini Huygens gravitational sling shot
• MathPages - Gravitational Slingshot Theory
• A Quick Gravity Assist Primer
• An artistical simulation of an unstable planetary system showing gravitational slingshots and other phenomena