What are the practical limitations of gravitational assists?

Question

Is there any specific, practical reason why we couldn't have a probe swing by Saturn, Uranus, Jupiter multiple times, over and over, before getting hurled into interstellar space at insane speed, overtaking Voyager and reaching neighbor solar systems within a reasonable timeframe?

From what I understand, while probes use their fuel for accelerating during gravitational loops, that's not essential - they could just use minimal amount of it to adjust route, to enter and leave the slingshot at optimal angle, and repeat it pretty much indefinitely, with a significant speed gain each time.

Is there any specific reason we don't have some probe accelerating to speeds that would leave Voyagers far behind, currently? What are the practical limitations of using this method repeatedly to bring probes to extreme speeds?

Answer 1

The easiest explanation would be that eventually you'd gain enough momentum to reach escape velocity, at which point you'd actually have to decelerate to return to orbit from what would be a hyperbolic trajectory describing your maximum delta-v gained from an Oberth maneuver (powered flyby). With unpowered flyby, your theoretical maximum delta-v gain from a slingshot would be the body's own orbital velocity, there simply isn't anything more to be gained from it in terms of accelerating the spacecraft.

It then doesn't matter if you can achieve that during your first flyby, or do a flyby past another body to later return back to the same one many times over. You could only increase efficiency of an unpowered flyby up to 100% of the momentum that the gravity assist body can lend to your spacecraft, which is your initial velocity, plus body's orbital velocity. And with Oberth maneuvers, you'd be consuming your propellants with each flyby.

There actually exist such interchanging orbits between two celestial bodies, for example the Aldrin Cyclers (here's a YouTube video of one such example). And the reason they work is because of the conservation of angular momentum, which is another way of explaining why multiple such flybys you describe wouldn't work. Well, they would work, but not in the way of gaining some additional momentum out of nothing.

The optimal trajectory for leaving the Solar System is known as the Krafft von Ehricke trajectory.

Answer 2

The practical upper velocity that can be gained by gravitational assists is limited by the number of times a spacecraft can reach another gravitational body to increase its velocity as well as the strength of the gravity well of the body. If the spacecraft is moving slowly it can alternate between two planets, increasing its velocity during each pass (and decreasing ever so slightly the orbital momentum of the planets it passes). As it moves faster and faster it will need to make passes closer closer to the planets to allow a return to the other planet. Eventually, passing closer to the planets leads to passing through an atmosphere (slowing the craft), grazing the planet (destroying the craft), or flying off away from both planets (the last pass causes a minor path deflection and not a half-orbit return to the other planet).

The limits of gravitational assists is also discussed at https://en.wikipedia.org/wiki/Gravity_assist#Limits_to_slingshot_use, where it mentions the "Grand Tour" made by Voyager, where the planets Jupiter, Saturn, Uranus and Neptune were lined up in such a way that allowed Voyager to increase its speed during the flyby of each planetary mass. If the solar system had another dozen planets that Voyager could have passed close to during its journey, it might have used them all to end up going even faster.

If you had two black holes orbiting each other, due to their extreme gravity you might, in theory, be able alternate back and forth between the two for gravitational assists until you approached the speed of light.

Another real-life limit to unlimited numbers of gravitational assists is that in order to make a pass occur along the precise path required to reach the next gravity well some reaction mass will be expended for course correction. The catch-22 here is that if you had unlimited on-board thrust you wouldn't need gravitational assists, but if you have limited thrust, after you run out you can't course correct to do the next gravitational assist.