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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]
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).

Contents

Why gravitational slingshots are used

Limits to slingshot use

Notable examples

Mariner 10 – first use

The Cassini probe – multiple slingshots

Voyager 1 – the fastest, furthest human-made object

The Ulysses probe changed the angle of its trajectory

Explanation

Powered slingshots

In popular culture

See also

References

External links

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).
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.

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 were made possible by the "Grand Tour" alignment of Jupiter, Saturn, Uranus, Neptune, and Pluto which occurred in the late 1970s and 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.
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, 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.
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.
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.
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.

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 Cassini probe – multiple slingshots

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.

Voyager 1 – the fastest, furthest human-made object

As of July 6, 2007, Voyager 1 is over 15.44 terameters (15.44 meters, or 15.44 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]

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.
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

''This is a very over-simplified explanation to show the principle. The details will be covered later.''
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''.
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.

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.
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.

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.
If the ship travels at velocity $v$ at the start of a burn that changes the velocity by $Delta\; v$, then the change in specific orbital energy (SOE) is:
:
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 $sqrt\{10.7\}\; =\; 3.3$ m/s to the spacecraft's final velocity. Thus, Jupiter's immense gravitational field has tripled the effectiveness of the space craft's propellant.
See also specific energy change of rockets:
:$Delta\; epsilon\; =\; int\; v,\; d\; (Delta\; v)$
where $epsilon$ is the specific energy of the rocket (potential plus kinetic energy) and $Delta\; v$ 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.

In popular culture

★ The American spacecraft ''Discovery One'' uses a gravitational slingshot around Jupiter in Arthur C. Clarke's novel ''.

★ The alien ship in Arthur C. Clarke's novel Rendezvous with Rama uses a gravitational slingshot around the Sun.

★ In '', time travel is achieved by a powered slingshot around the Sun. In the '' 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.

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

References

1. 50th anniversary of Institute for Applied Mathematics - Applied celestial mechanics - at the website of Keldysh Institute of Applied Mathematics
2. Cassini-Huygens: Operations - Gravity Assists
3. The Slingshot Effect, Durham University

External links

★ Slingshot effect

★ Animation of Cassini Huygens gravitational sling shot

★ Gravitational Slingshot Theory

★ A Quick Gravity Assist Primer

★ An artistical simulation of an unstable planetary system showing gravitational slingshots and other phenomena