Editing Gravity assist (section)

==Explanation==
[[File:GravAssis.gif|thumb|Example encounter.<ref name=":0">{{Cite web |url=http://www.planetary.org/blogs/guest-blogs/2013/20130926-gravity-assist.html |title=Gravity assist |publisher=The Planetary Society |access-date=1 January 2017}}</ref><br />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.]]
[[File:GravPoss.gif|thumb|Possible outcomes of a gravity assist maneuver depending on the velocity vector and flyby position of the incoming spacecraft]]

A gravity assist around a planet changes a spacecraft's [[velocity]] (relative to the [[Sun]]) by entering and leaving the gravitational sphere of influence of a planet.  The sum of the kinetic energies of both bodies remains constant (see [[elastic collision]]). A slingshot maneuver can therefore be used to change the spaceship's trajectory and speed relative to the Sun.<ref>{{cite web |title=Let gravity assist you ... |url=https://www.esa.int/Science_Exploration/Space_Science/Exploring_space/Let_gravity_assist_you |website=ESA |access-date=8 March 2023 }}</ref>

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&nbsp;km/h toward a train approaching at 50&nbsp;km/h. The driver of the train sees the ball approaching at 80&nbsp;km/h and then departing at 80&nbsp;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&nbsp;km/h relative to the train platform; the ball has added twice the train's velocity to its own.<ref name="auto">{{cite web |url=https://solarsystem.nasa.gov/basics/primer/ |title=A Gravity Assist Primer |series=Basics of Space Flight |publisher=NASA |access-date=21 July 2018}}</ref>

Translating this analogy into space: in the planet [[frame of reference|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.<ref name=":0" /> 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 {{sqrt|2}}''v''. After the spaceship leaves the planet, it will have a velocity of ''v + v ='' 2''v'', gaining approximately 0.6''v''.<ref name=":0" />

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 [[Perturbation (astronomy)|orbital perturbation]]s 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]] [[orders of magnitude (mass)|has a mass]] of almost 2 x 10<sup>24</sup> metric tons. Therefore, a one-ton spacecraft passing Jupiter will theoretically cause the planet to lose approximately 5 x 10<sup>−25</sup> 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.<ref>{{cite report |url=http://maths.dur.ac.uk/~dma0rcj/Psling/sling.pdf |title=The Slingshot Effect |publisher=Durham University |first=R. C. |last=Johnson |date=January 2003 |access-date=2018-07-21 |archive-date=2020-08-01 |archive-url=https://web.archive.org/web/20200801071531/http://maths.dur.ac.uk/~dma0rcj/Psling/sling.pdf }}</ref>

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.

[[File:Grav slingshot diag.svg|center|thumb|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.]]
[[File:Mdis depart anot.ogv|thumb|A view from MESSENGER as it uses Earth as a gravitational slingshot to decelerate to allow insertion into an orbit around Mercury]]

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 (planet)|Mercury]].{{Citation needed|date=May 2022}}

If more speed is needed than available from gravity assist alone, a rocket burn near the [[periapsis]] (closest planetary approach) uses the least fuel. 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. Therefore the maximum  kinetic energy is obtained when the burn occurs at the vehicle's maximum velocity (periapsis). The [[Oberth effect]] describes this technique in more detail.