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I'll keep it short but please read through!

Gravitation's $1/r$ potential means everything in the solar system is pulling on everything all the time.

Gravitational slingshot maneuvers are normally though of as passing fairly close to a massive object producing a large deflection and change in velocity, but there's no cut-off; all bodies are affecting a spacecraft orbits and if you don't take several into account your calculated trajectory will not reflect where your spacecraft ends up.

So there probably isn't a universally agreed-upon objective mathematical test to say if a particular solar-system's body's effect on a trajectory is above or below "slingshot threshold" but there may exist a particularly weak one that was still a deliberate gravitational slingshot maneuver.

Question: What was the smallest intentional, acknowledged slingshot maneuver? Does one stand out as having the lowest delta-v or smallest deflection angle, or perhaps was the least beneficial, and yet was still acknowledged as a deliberate gravitational assist?

Discussion below How fast can an orbit exist in the solar system? first got me started on this.

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    $\begingroup$ This is way too broad. Do you count a distant Lunar flyby on the way out of the Earth-Moon System? How about New Horizons flyby of 2014 MU69? There doesn't really seem to be a good answer for this... $\endgroup$
    – PearsonArtPhoto ♦
    Commented Mar 14, 2019 at 12:05
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    $\begingroup$ Better, but it still seems a bit tricky to quantify. But good enough I'll leave it open. $\endgroup$
    – PearsonArtPhoto ♦
    Commented Mar 14, 2019 at 12:21
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    $\begingroup$ An interesting source I came accross while researching this is Richard L. Dowling et al: The Effect of Gravity-Propelled Interplanetary Space Travel on the Exploration of the Solar System: Historical Survey, 1961 to 2000. In: History of Rocketry and Astronautics, AAS History Series, Vol 28. Donald C Elder, Page 339. Unfortunately, the document is not OCR'd so text search is impossible, and quickly glossing over it did not reveal a satisfactory answer. Still, the document is a fascinating read so i thought I'd share it. $\endgroup$
    – Polygnome
    Commented Mar 24, 2019 at 9:24
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    $\begingroup$ I don't like this question because it's more about 'which astrodynamics team was more nitpicky' acknowledging stuff others don't, than the maneuver itself. Asteroid fly-bys will inevitably be minuscule gravity assists. Crossing a planet's orbit while it's somewhat in sync by chance may deflect the angle by a fraction of angle second. They will be accounted for in the mission plan and trajectory, but whether the team calls them "slingshot maneuvers" or just fly-bys, depends strictly on how nitpicky the team is... $\endgroup$
    – SF.
    Commented Mar 25, 2019 at 7:09
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    $\begingroup$ Subtle gravitational assists have become quite common, for example Cassini and Juno use lots of them. $\endgroup$
    – Hobbes
    Commented Mar 25, 2019 at 10:49

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I'm going to use the definition that the object must have been within 40,000 km of the object, done only a flyby, and visited another object after. Lastly the effect must have been studied with results released to the public, via paper, website, patent, or similar.

The most likely contenders by far are one of the 3 missions to have orbited one of the outer planets. There are also a few lunar to Earth orbit missions that are worth examining.

  • Cassini - ~ 100 m/s from a Titan flyby.
  • Galileo- One with IO with 175 m/s, possibly less.
  • JUNO- No significant gravity assists due to its nearly polar trajectory.
  • HGS-1- The first had a delta-v of about 681 m/s.
  • TESS- Likely higher than HGS-1, because it passed closer, but I can't verify.

It very likely is one of the distant flybys of Titan, although it really depends on your definition. There might have been a smaller one that was used for Galileo, but Titan/ Cassini seems a clear winner.

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