Gravitational slingshot - AbsoluteAstronomy.com

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

Course (navigation)

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

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

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...

made a similar argument.

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

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

. 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

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

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)

Voyager 1 – furthest human-made object

As of January 21, 2010, Voyager 1

Voyager 1

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

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

), 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)

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

External links

The source of this article is wikipedia, the free encyclopedia. The text of this article is licensed under the GFDL.

Explanation

Historical origins of the method

Why gravitational slingshots are used

Limits to slingshot use

Mariner 10 – first use

Voyager 1 – furthest human-made object

Galileo – a change of plan

The Ulysses probe changed the plane of its trajectory

MESSENGER

The Cassini probe – multiple gravity assists

Solar Probe+

Powered slingshots

See also

External links