Gravity assist

A gravity assist, gravity assist maneuver, swing-by, or generally a gravitational slingshot in orbital mechanics, is a type of spaceflight flyby which makes use of the relative movement and gravity of a planet or other astronomical object to alter the path and speed of a spacecraft, typically to save propellant and reduce expense.
Gravity assistance can be used to accelerate a spacecraft, that is, to increase or decrease its speed or redirect its path. The "assist" is provided by the motion of the gravitating body as it pulls on the spacecraft. Any gain or loss of kinetic energy and linear momentum by a passing spacecraft is correspondingly lost or gained by the gravitational body, in accordance with Newton's Third Law. The gravity assist maneuver was first used in 1959 when the Soviet probe Luna 3 photographed the far side of Earth's Moon, and it was used by interplanetary probes from Mariner 10 onward, including the two Voyager probes' notable flybys of Jupiter and Saturn.

Explanation

A gravity assist around a planet changes a spacecraft's velocity by entering and leaving the gravitational sphere of influence of a planet. The sum of the kinetic energies of both bodies remains constant. A slingshot maneuver can therefore be used to change the spaceship's trajectory and speed relative to the Sun.
A close terrestrial analogy is provided by a tennis ball bouncing off the front of a moving train. Imagine standing on a train platform, and throwing a ball at 30 km/h toward a train approaching at 50 km/h. The driver of the train sees the ball approaching at 80 km/h and then departing at 80 km/h after the ball bounces elastically off the front of the train. Because of the train's motion, however, that departure is at 130 km/h relative to the train platform; the ball has added twice the train's velocity to its own.
Translating this analogy into space: in the planet reference frame, the spaceship has a vertical velocity of v relative to the planet. After the slingshot occurs the spaceship is leaving on a course 90 degrees to that which it arrived on. It will still have a velocity of v, but in the horizontal direction. In the Sun reference frame, the planet has a horizontal velocity of v, and by using the Pythagorean Theorem, the spaceship initially has a total velocity of v. After the spaceship leaves the planet, it will have a velocity of v + v = 2v, gaining approximately 0.6v.
This oversimplified example cannot be refined without additional details regarding the orbit, but if the spaceship travels in a path which forms a hyperbola, it can leave the planet in the opposite direction without firing its engine. This example is one of many trajectories and gains of speed the spaceship can experience.
This explanation might seem to violate the conservation of energy and momentum, apparently adding velocity to the spacecraft out of nothing, but the spacecraft's effects on the planet must also be taken into consideration to provide a complete picture of the mechanics involved. The linear momentum gained by the spaceship is equal in magnitude to that lost by the planet, so the spacecraft gains velocity and the planet loses velocity. However, the planet's enormous mass compared to the spacecraft makes the resulting change in its speed negligibly small even when compared to the orbital perturbations planets undergo due to interactions with other celestial bodies on astronomically short timescales. For example, one metric ton is a typical mass for an interplanetary space probe whereas Jupiter has a mass of almost 2 x 10²⁴ metric tons. Therefore, a one-ton spacecraft passing Jupiter will theoretically cause the planet to lose approximately 5 x 10⁻²⁵ km/s of orbital velocity for every km/s of velocity relative to the Sun gained by the spacecraft. For all practical purposes the effects on the planet can be ignored in the calculation.
Realistic portrayals of encounters in space require the consideration of three dimensions. The same principles apply as above except 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 reduce the speed of a spacecraft. Both Mariner 10 and MESSENGER performed this maneuver to reach Mercury.
If more speed is needed than available from gravity assist alone, a rocket burn near the periapsis uses the least fuel. A given rocket burn always provides the same change in velocity, but the change in kinetic energy is proportional to the vehicle's velocity at the time of the burn. Therefore the maximum kinetic energy is obtained when the burn occurs at the vehicle's maximum velocity. The Oberth effect describes this technique in more detail.

Historical origins

In his paper "To Those Who Will Be Reading in Order to Build", published in 1938 but dated 1918–1919, Yuri Kondratyuk suggested that a spacecraft traveling between two planets could be accelerated at the beginning and end of its trajectory by using the gravity of the two planets' moons. The portion of his manuscript considering gravity-assists received no later development and was not published until the 1960s. In his 1925 paper "Problems of Flight by Jet Propulsion: Interplanetary Flights", Friedrich Zander showed a deep understanding of the physics behind the concept of gravity assist and its potential for the interplanetary exploration of the Solar System.
Italian engineer Gaetano Crocco was first to calculate an interplanetary journey considering multiple gravity-assists in 1956.
The gravity assist maneuver was first used in 1959 when the Soviet probe Luna 3 photographed the far side of the Moon. The maneuver relied on research performed under the direction of Mstislav Keldysh at the Keldysh Institute of Applied Mathematics.
In 1961, Michael Minovitch, UCLA graduate student who worked at NASA's Jet Propulsion Laboratory, developed a gravity assist technique, that would later be used for the Gary Flandro's Planetary Grand Tour idea.
During the summer of 1964 at the NASA JPL, Gary Flandro was assigned the task of studying techniques for exploring the outer planets of the Solar System. In this study he discovered the rare alignment of the outer planets and conceived the Planetary Grand Tour multi-planet mission utilizing gravity assist to reduce mission duration from forty years to less than ten.

Purpose

A spacecraft traveling from Earth to an inner planet will increase its relative speed because it is falling toward the Sun, and a spacecraft traveling from Earth to an outer planet will decrease its speed because it is leaving the vicinity of the Sun.
Rocket engines can certainly be used to increase and decrease the speed of the spacecraft. However, rocket thrust takes propellant, propellant has mass, and even a small change in velocity translates to a far larger requirement for propellant needed to escape Earth's gravity well. This is because not only must the primary-stage engines lift the extra propellant, they must also lift the extra propellant beyond that which is needed to lift that additional propellant. The liftoff mass requirement increases exponentially with an increase in the required delta-v of the spacecraft.
Because additional fuel is needed to lift fuel into space, space missions are designed with a tight propellant "budget", known as the "delta-v budget". The delta-v budget is in effect the total propellant that will be available after leaving the earth, for speeding up, slowing down, stabilization against external buffeting, or direction changes, if it cannot acquire more propellant. The entire mission must be planned within that capability. Therefore, methods of speed and direction change that do not require fuel to be burned are advantageous, because they allow extra maneuvering capability and course enhancement, without spending fuel from the limited amount which has been carried into space. Gravity assist maneuvers can greatly change the speed of a spacecraft without expending propellant, and can save significant amounts of propellant, so they are a useful technique to save fuel.

Limits

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 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 scattered in unsuitable parts of their orbits.
Another limitation is the distance of closest approach to the planet. The magnitude of the change in velocity depends on the spacecraft's approach velocity and the planet's escape velocity at the point of closest approach. The closer to the center of the planet that approach is, the greater the achievable change in velocity. The atmosphere, if any, of the available planet will set a limit to the approach distance; for bodies with no atmosphere, like the moon, the closest approach is set by the constraint that the trajectory must not intersect the surface. For planets with atmosphere, as a spacecraft gets deep into the atmosphere, the energy lost to drag can exceed that gained from the planet's velocity.. There have also been theoretical proposals to use aerodynamic lift as the spacecraft flies through the atmosphere. This maneuver, called an aerogravity assist, 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 a related effect, the Oberth effect. This has the potential to magnify a spacecraft's thrusting power enormously, but is limited by the spacecraft's ability to resist the heat. For planetary gravity assists, a thrust applied near the closest approach can add the Oberth effect to the gravity slingshot effect, producing a larger change in orbital velocity than either effect by itself.
A rotating black hole might provide additional assistance, if its spin axis is aligned the right way. General relativity predicts that a large spinning frame-dragging—close to the object, space itself is dragged around in the direction of the spin. Any ordinary rotating object produces this effect. Although attempts to measure frame dragging about the Sun have produced no clear evidence, experiments performed by Gravity Probe B have detected frame-dragging effects caused by Earth. General relativity predicts that a spinning black hole is surrounded by a region of space, called the ergosphere, within which standing still 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.