This is a scenario that I have recently made up: A spacecraft is at the edge of the solar system, in orbit around Pluto, to make its journey to Alpha Centauri. The spacecraft wouldn't accelerate from Pluto to Alpha Centauri, it would go all the way back down through the solar system, doing gravitational slingshots from all of the planets and ultimately the Sun, assuming that all of the planets were in the correct alignment. Would this actually help the spacecraft, and would it take an amount of time that would be reasonable?
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3$\begingroup$ Aside from gravity assists, an interplanetary craft starting from Pluto would benefit from lowering it's solar periapsis as low as possible (without burning up) and doing it's main interplanetary ejection burn close to the sun. You get more kinetic energy for a given amount of fuel by burning that fuel close to a massive object than you do further away. This effect is known as the "Oberth effect". An efficient transfer from Pluto to low solar orbit takes decades, but if you have enough fuel to go interplanetary, you have enough to speed it up. $\endgroup$– Jack BJun 20 at 12:36
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$\begingroup$ @JackB While it's true you get a boost from the Oberth effect by doing this, the amount diminishes as the delta-v you apply increases in relation to the escape velocity. If you do a 100 km/s flyby within the orbit of Mercury to start an otherwise 100 year trip to Proxima Centauri, your gain is less than 0.4% and you only reduce the trip to 99.6 years. It's mainly relevant to maneuvering within a system, where escape velocities are similar to (and frequently larger than) the required delta-v's. $\endgroup$– Christopher James HuffJun 20 at 16:26
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1$\begingroup$ ...but if you have 500km/s of (very high acceleration) ΔV available and you dip to 5Gm, then you cut the travel time from 2500yr to 1800yr. If you have only 150km/sec available, then dipping to 5Gm cuts travel from 8500yr in half to 4250yr. I think that's much more than you could get by gravity assists - though still probably vastly longer travel times than the OP had in mind. $\endgroup$– Jack BJun 20 at 19:43
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$\begingroup$ @Daniel Shepherd, does the spaceship plan to "stop" at Proxima Centauri, or zip by, take photos, collect other readings and then head out in to the cold dark abyss of space? If going into local orbit, about Proxima Centauri, slingshots there, in reverse might be useful to slow down. $\endgroup$– chux - Reinstate MonicaJun 21 at 1:29
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1$\begingroup$ Relevant XKCD $\endgroup$– SF.Jun 21 at 8:30
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Unless I am mistaken, the amount of speed a gravitational slingshot can add is less than twice the orbital speed of the planet being used. Mercury's orbital speed is the fastest, at a little over 47 km/sec. If you could use each planet once, and each one gave you a little over twice Mercury's orbital speed (which they would not even come close to), then you would gain 800 km/sec, which is a lot. But it would still take you over 1600 years to get to Alpha Centauri.
And this is overly optimistic, perhaps by a factor of 10 or more. Adding double the speed of a planet is based on a simplified model of a ping-pong ball bouncing off the front of a semi truck, which depends on the ball going out exactly the opposite direction it came in. But actually in space the object swings behind the planet, and the faster it is going the less time it spends close to the planet and the less additional speed it can pick up. Once you are at solar system escape velocity you can't swing by repeatedly to pick up more speed, either.
Interstellar travel is just hard.
Added later: The accepted answer to this question looks at what you can accomplish with gravity assists and other techniques. It doesn't mention the specific approach you proposed, but that answer gives a sense for what can be accomplished using the best combination of maneuvers.
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9$\begingroup$ You can also only get the "2x orbital speed" boost by coming in on a parabolic course from directly "forward" in the planet's orbital motion, at precisely escape velocity relative to the planet. For Mercury, that means you can only get all of that ~95 km/s boost if you make a flyby with a maximum speed relative to Mercury of 4.25 km/s. The higher above escape velocity you go, the straighter the trajectory around Mercury and the lower the possible gain. If you're going to another star, you need a propulsion system with such high performance that none of these tricks are really relevant. $\endgroup$ Jun 20 at 16:34
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$\begingroup$ This was exactly what I was trying to convey, only in a more informal way, in my second paragraph ("depends on the ball going out exactly the opposite direction it came in"). But this comment adds good detail, thanks. $\endgroup$ Jun 20 at 18:22
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3$\begingroup$ @ChristopherJamesHuff if a simplistic/unrealistic upper limit is all it takes to answer "Would this actually help the spacecraft" (yes, but) "and would it take an amount of time that would be reasonable?" (no) then there's no reason to go further. $\endgroup$– uhohJun 21 at 4:52
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$\begingroup$ @MarkFoskey It's not really about the delta v that you can pick up by gravity assist but more about the overall energy gain that you can realize. Delta v on the outer planets is much more 'valuable' than on Mercury. To actually reach Mercury for a swing by you'd have to lose significant energy first that is very hard to regain. See the BepiColombo mission for an example. $\endgroup$– Zac67Jun 22 at 16:26