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 (e.g. orbit around the Sun) 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. In Simple word it involves a spacecraft flying close to a planet or moon to use its gravity and motion to alter the spacecraft’s path and speed.
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 liner 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.
In the planet's frame of reference, the space probe leaves with the exact same speed at which it had arrived. But when observed in the reference frame of the Solar System (fixed to the Sun), the benefit of this maneuver becomes apparent. Here it can be seen how the probe gains speed by tapping energy from the speed of the planet as it orbits the Sun. (If the trajectory is designed to pass in front of the planet instead of behind it, the gravity assist can be used as a braking maneuver rather than accelerating.) Because the mass of the probe is many orders of magnitude smaller than that of the planet, while the result on the probe is quite significant, the deceleration reaction experienced by the planet, according to Newton’s third law, is utterly imperceptible.
Possible outcomes of a gravity assist maneuver depending on the velocity vector and flyby position of the incoming spacecraft.
The spacecraft taps into the planet’s orbital energy. While the spacecraft gains kinetic energy, the planet loses an equal amount—though the effect on the planet is negligible due to its massive size.
A tennis ball bouncing off a moving train illustrates the concept. The ball gains speed relative to the ground by rebounding off the moving train, just as a spacecraft gains speed relative to the Sun.
The maneuver alters the spacecraft’s velocity vector. Depending on the flyby angle and direction, it can accelerate, decelerate, or redirect the spacecraft.
The process respects conservation of energy and momentum. The spacecraft’s gain is offset by the planet’s loss, though the latter is imperceptible
Two-dimensional schematic of gravitational slingshot. The arrows show the direction in which the spacecraft is traveling before and after the encounter. The length of the arrows shows the spacecraft's speed.
Real-world applications require vector addition in three dimensions to account for the planet’s motion and the spacecraft’s trajectory.
Gravity assists can also be used to reduce speed, as demonstrated by missions like Mariner 10 and MESSENGER en route to Mercury.
Gravity assists are not measured by a linear acceleration or deceleration from the spot where the gravity assist occurs. The momentum you gain while approaching the planet is lost as you leave (conservation of momentum).
The acceleration is measured in terms of orbital velocity.
If a spacecraft is traveling away from the sun, the sun's gravity will slow the craft down. Using a gravity assist from an outer planet let's you steal some angular momentum from that planet's own orbital velocity and increases your own. The greater your orbital velocity allows for a 'higher' orbit increasing your distance from the sun without using your own power.
Example_
Animation of Voyager 1's trajectory from September 1977 to 31 December 1981 Voyager 1, Earth, Saturn, Jupiter, Sun
Purpose
Gravity assists allow spacecraft to change speed and direction without using additional propellant, conserving fuel for other mission needs.
Space missions have a limited fuel supply (delta-v budget). Gravity assists help stay within this budget by providing free velocity changes.
By using planetary flybys, missions can reach distant targets or adjust orbits that would otherwise require large fuel expenditures.
Limits
Gravity assists depend on the positions of planets. Favorable alignments (like the Voyager “Grand Tour”) are rare and time-sensitive.
The effectiveness depends on how close the spacecraft can safely pass a planet. Atmospheric drag or surface impact limits this.
For planets with atmospheres, too close an approach can cause energy loss due to drag, though this can be used intentionally (aerobraking).
The Sun can’t be used for gravity assists since it’s stationary relative to the Solar System, but thrusting near it can exploit the Oberth effect. Theoretical ideas like using rotating black holes (via frame-dragging) exist but are not practical with current technology.
More examples and related images_
Animation of Voyager2 's trajectory from 20 August 1977 to 31 December 2000.Voyager, Earth, Jupiter, Saturn, Uranus, Neptune, Sun.
Plot of Voyager 2's heliocentric velocity against its distance from the Sun, illustrating the use of gravity assist to accelerate the spacecraft by Jupiter, Saturn and Uranus. To observe Triton, Voyager 2 passed over Neptune's north pole resulting in an acceleration out of the plane of the ecliptic and reduced velocity away from the Sun.
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.
The trajectories that enabled NASA's twin Voyager spacecraft to tour the four giant planets and achieve velocity to escape the Solar System
_Cassini's Interplanetary trajectectory, converted to SVG by timecop from NASA.gov.
The Cassini-Huygens spacecraft was launched from Earth on 15 October 1997, followed by gravity assist flybys of Venus (26 April 1998 and 21 June 1999), Earth (18 August 1999), and Jupiter (30 December 2000). Transit to Saturn took 6.7 years, the spacecraft arrived at 1 July 2004.Its trajectory was called "the Most Complex Gravity-Assist Trajectory Flown to Date" in 2019.
Animation of Cassini trajectory from 15 October 1997 to 4 May 2008.Cassini–Huygens, Jupiter, Saturn, Earth, Venus, 2685 Masursky.
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 kilometres 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.
Animation of Rosetta's trajectory from 2 March 2004 to 9 September 2016. Rosetta, 67P/C-G, Earth, Mars, 21 Lutetia, 2876 Steins.
The Rossetta probe, launched in March 2004, used four gravity assist maneuvers (including one just 250 km from the surface of Mars, and three assists from Earth) to accelerate throughout the inner Solar System. That enabled it to flyby the asteroids 21 Lutetia and 2876 Steins as well as eventually match the velocity of the 67P/Churyumov-Gerasimenko comet at the rendezvous point in August 2014.
The Parker Solar Prob, launched by NASA in 2018, has seven planned Venus gravity assists. Each gravity assist brings the Parker Solar Probe progressively closer to the Sun. As of 2022, the spacecraft has performed five of its seven assists. The Parker Solar Probe's mission will make the closest approach to the Sun by any space mission. The mission's final planned gravity assist maneuver, completed on November 6, 2024, prepared it for three final solar flybys reaching just 3.8 million miles of the surface of the sun on December 24, 2024 (see figure).
The speed of the probe and distance from the Sun, from launch until 2026
An animation of the Parker Solar Probe's trajectory from August 7, 2018, to August 29, 2025. Parker Solar Probe, Sun, Mercury, Venus, Earth.
Conclusion
spaceship's speed relative to body must be larger but close to the escape velocity at the point of approach of the body used to do this maneuver. If it is too small, it will fall on the body or be captured in orbit. If too large, it will just pass by, barely changing its direction. .2c, for example, is much much larger for anything other then a black hole.
Assuming #1 is met, and the ship's speed is larger than escape velocity of the star at desired orbit, it is still possible to put the ship into that orbit by gravity assist IF ship speed does not exceed 2U+V where U is orbital speed of the body orbiting around star and V is less than escape velocity from the star. 2U is maximum that can be stolen away from the ship's speed in order to decelerate it. Final velocity can be adjusted by playing with angle of approach.
Trying to put yourself in orbit around a planet has nothing to do with any of this, it just requires to be in the sphere of influence of the planet with relative speed below its escape velocity. However, #2 can be used as means of accomplishing this.
~Jain Dhwani Nirmal Kumar
~BATCH_30