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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 do 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 this question 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 Mar 14 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 Mar 14 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 Mar 24 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. Mar 25 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 Mar 25 at 10:49

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