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My understanding of gravity-assists (slingshot) is that they use some of a more-massive object's orbital energy to gain massive acceleration.

What's the upper limit on how much velocity an object coming out of one can have?

I am not interested in the max total amount of acceleration gained from a single assist. Just the highest velocity achievable.

I presume the limit here would come from the effects of frame-dragging, if trying to get an assist from a very massive object.

bobsburner
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    Your question doesn't obviously make sense... if you look at Mark Adler's answer to your linked question, you'll see he provides a handy formula. You can always get just a tiny bit faster than the velocity you arrived at, right? – Starfish Prime Nov 07 '19 at 12:46
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    So, a hair below lightspeed? – bobsburner Nov 07 '19 at 12:49
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    Perhaps, thought you'd have to be travelling at almost a hair below lightspeed to start with, so it doesn't seem like a very interesting or informative answer (and adds nothing that wasn't already said in the other question). – Starfish Prime Nov 07 '19 at 12:50
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    Realistically you will be limited by time or the availability of objects. Once you reach solar system escape velocity your ability to play cosmic billiards is extremely limited and even without that planets are months or years apart--try too many encounters and your probe will wear out before reaching it's destination. – Loren Pechtel Nov 07 '19 at 12:53
  • Not enough points to close-vote, but recommend doing so in favor of the linked question in @StarfishPrime 's comment – Carl Witthoft Nov 07 '19 at 14:42
  • @CarlWitthoft I also linked that question. Is the question not clear enough? It's about max-velocity, not max acceleration. – bobsburner Nov 07 '19 at 15:43
  • I think that this question is expected to include relativistic effects, so I am interested in knowing the answer as well. Classically it is just "the escape velocity of the object", but if, say, you are assisting via a black hole and somehow accelerated to a portion of $c$, wouldn't your increasing mass have a non-negligible effect? – Michael Stachowsky Nov 07 '19 at 16:11
  • I agree with @StarfishPrime that this question doesn't make sense. Velocity is always relative to a frame or reference. Are you asking what the maximal velocity gain around a central body is using a/many gravity assist(s) around its satellite(s)? Are propulsive maneuvers allowed? – Quietghost Nov 07 '19 at 16:12
  • @Quietghost no. I am trying to ask about total velocity. (measured from an arbitrary reference frame) The only conditions are that it be a single object, and exist within space. (i.e. propellant can be expelled, but not an infinite amount) If someone thinks they get what I'm saying, please edit the question. I don't think I can phrase it more clearly myself. – bobsburner Nov 07 '19 at 16:39
  • This is a great question but I feel that it is off-topic in Space Exploration SE as this extreme limit of gravitational assist is not something that's going to happen any time soon in the exploration of space by humans. However it is fully on-topic in Physics SE. Have a look at Could a trajectory around a large mass ever deflect by more than 180 degrees due to general relativistic effects? as an example of a relativistic orbital mechanics question that quickly received multiple high quality, authoritative answers in Physics SE. – uhoh Nov 09 '19 at 23:58

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I don't think it's easy to put a limit on the maximum achievable speed (other than $c$), without constraining the problem. There is no obvious speed, above which gravity assists can't help, if you can plan the interactions appropriately.

There are things that will make this tricky though. For example the large relative speed that bodies will likely be encountered when moving fast, and the necessity to align exit velocity with the velocity of the assisting body, you are quickly going to run into the problem of needing near infinite accelerations. I.e. skimming event horizons of progressively smaller black-holes.

This may bump into some other hard physics limit (like a black hole that small existing for long enough to complete the interaction). However I don't think there is a nice/simple statement that governs this sort of thing. Further You're starting to blur the lines of what constitutes a gravity assist when you start considering these sorts of things.

ANone
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