Are there any paths in the Interplanetary Transport Network that leave the solar system?

Question

As a (very late) follow up to this question, I wondered if there are any ITN paths that leave the solar system altogether? Articles about this seem to be concerned with low energy transfers of spacecraft to other planets. I'm not concerned about timescales just if, in principle, it's possible for an object to travel into interstellar space via the ITN?

I'm not sure if I should be asking here or in Astronomy.SE, I'm happy to move it if it's a better fit over there.

EDIT: OK, I've got a confession to make. My question specified no timescales because it was partly inspired by the Celestis flight aboard the first Vulcan Centaur, which will send the remains of some of the Star Trek TOS people into 'interplanetary space'...

DNA samples taking part in the flight are cast members of the original "Star Trek" television series — Nichelle Nichols, DeForest Kelley and James Doohan — as well as series creator Gene Roddenberry, and his wife and recurring series actor Majel Barrett Roddenberry.

According to the Celestis website, Enterprise will be the company's first "Voyager Service" option flown for its customers, which launches the DNA samples into interplanetary space.

..and I wondered if there was an established path (ITN??) which could be used to deliberately send the 'payload' into interstellar space instead. Something like the situation described by @mark_foskey where an ITN path leads to repeated gravity-assists from Jupiter.

The key to this is a known route out of the solar system, rather than an n-body solution that is so sensitive to its initial conditions that we couldn't be sure of the spacecraft's trajectory.

I do realise that I'm moving the goalposts and that this is much more specific than the original question. I'm happy to remove this edit if it confuses things too much. People have put time and effort into thinking about answers, I don't want to undermine that.

Some question the premise that the notion of useful ITN paths are meaningful at all I don't know enough about it to say either way. I think that exploiting 3-body Lagrange points and their manifolds are useful within and out of 3-body systems like Sun-Earth-Moon, but are energetically irrelevant for systems like Sun-Jupiter-Neptune for example (but I would be very happy to be wrong abou that!). Instead, good old-fashioned flybys (gravitational assists) are the actually useful things. But it's not an answer to your question, just idle comment. — uhoh, Dec 12 '23 at 01:10
More skepticism in this answer to How much of the Interplanetary Transport Network is currently known? Then again, Wikipedia's Interplanetary Transport Network talks about it like it's a real thing (albeit slow). Now I don't know what to think... Thus an existence-proof answer to your question would be wonderful! — uhoh, Dec 12 '23 at 01:20
@uhoh I have been very critical of Jarold Marsden, Shane Ross and Martin Lo saying there is little practical application. I am changing my tune. I believe the Earth Moon Lagrange 2 point may be useful And that numerous useful orbits within the Moon's Hill Sphere may have similar Jacobi constants and thus have inexpensive routes between. — HopDavid, Dec 12 '23 at 16:07
@HopDavid Every morning I like to read something "eye-opening" to augment the more mundane eye-opening effects of my coffee, that's just what I need this morning, thanks! There is one demonstrated practical use of at least a 3-body trajectory if not exactly L2-linked; the (patented!) saving of AMC-14. — uhoh, Dec 12 '23 at 22:24
@HopDavid see also https://twitter.com/GazEtc/status/1298979254244261890 and https://technology.nasa.gov/patent/TOP2-272 and https://patents.google.com/patent/US10696423B1/en — uhoh, Dec 12 '23 at 22:34
I wonder how one should define the Solar System in this context? Is a body passing through the Solar System but not on a Solar orbit part of it? Is a body balanced precisely between the Sun and some other neighbouring star part of it? — Mark Morgan Lloyd, Dec 13 '23 at 09:52

Darth Pseudonym · Answer 1 · 2023-12-12T21:20:07.280

The Interplanetary Transport Network is not a particularly useful element of human spaceflight because the paths required are mostly extremely slow. It's possibly interesting as an explanation for how rocks ejected from one body might make it to some other body after thousands of years, but for anything we want to finish within a human lifetime, it's more useful to figure out a powered trajectory.

Now that said, the ITN is defined by a series of mathematical functions that are specifically about traversal between bodies in the solar system (or rather between their Lagrange points) with no thrust. It's certainly possible for an object to be ejected from the solar system by gravitational forces alone, but that path would not be part of the ITN, as it doesn't end at another body.

As a quick metaphor: If you're in a boat somewhere in Puget Sound off of Seattle, you can get a lot of places by pointing your boat just right and letting the currents carry you. We might make a map that shows how you can get from one dock to another all across the sound based on using specific headings while the tide is at a certain state. But those specific time/position/heading sets aren't particularly special in any way -- they're notable because they go somewhere interesting, not because there's something unique about pointing your boat just-so.

Can you get washed out into the Pacific by the tides? Sure you can, but that won't be on our map, because we aren't counting all the millions of possible time/position/heading sets that don't end up getting you to a point of interest.

Well, obviously you'd use the network for the first n hops to get from planet to planet (and Lagrange point to Lagrange point in between), collecting more and more energy, until you use the last interaction (or perhaps the last few interactions) to eject you. Only the last one(s) will not be on the narrowly defined ITN. It's a bit like asking "can I travel to that remote village on the interstate" and you answer "obviously not, it's not on the map of interstates". But some near-by place is, and you get there on the convenient interstate, and from there you go off-interstate map. — Peter - Reinstate Monica, Dec 13 '23 at 18:07
The question was pretty clear about asking if any ITN paths leave the solar system, not "can I follow ITN paths far out and then get ejected", but I answered fully in either case. What's obvious to you may not be obvious to everyone -- it's easy to misunderstand what the ITN is and think of it as some sort of space highway rather than a mathematical construct. — Darth Pseudonym, Dec 13 '23 at 19:26

Mark Foskey · Accepted Answer · 2023-12-12T22:40:07.017

I think this basically amounts to asking whether objects can be dynamically ejected from the solar system, and, in general, whenever there is an unstable orbital configuration, eventual ejection of some body is the most likely outcome. The solar system is very stable but not perfectly stable, and so I would contend that answer is Yes, but not in a very helpful way. I think the typical pattern would be something having repeated interactions with Jupiter over many billions of years, getting lofted into higher and higher orbits until it finally doesn't come back.

Something like this is presumably what happened to 'Oumuamua, although it probably began its life further from its parent star than the an object embarking on an ITN voyage would typically be.

Added later: I'm not going to remove this because it seems to address what the OP is really getting at, but, with regard to the ITN, it seems to me that Woody is right. What I'm describing would not be an ITN trajectory. I answered above my knowledge level.

This seems like a pretty solid answer. It's sort-of the kinematic equivalent of Murphy's Law ("Anything that can go wrong will go wrong.") Slightly related (but different) in Math SE: Can there be an energetically unbounded three-body orbit where escape is impossible due to conservation of angular momentum? Still no solid answer; I've been meaning to ask it in Math Overflow, I think I'm almost ready to. — uhoh, Dec 12 '23 at 07:59
+1 'Yes, but not in a very helpful way' is actually very helpful! — Dave Gremlin, Dec 12 '23 at 21:26

score 2 · Answer 3 · answered Dec 12 '23 at 19:42

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Answer: NO

ITN manifolds always connect two LaGrange points. There are no manifolds heading out into interstellar space because there are no LaGrange points out there.

answered Dec 12 '23 at 19:42

Woody

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I don't believe your unsupported assertion. Can you add some convincing, authoritative supporting links? Exactly why can't the last manifold to go infinity? Is there a mathematical reason? is there an "Official ITN SOP" document that requires it? – uhoh Dec 13 '23 at 03:58
@uhoh ... good point. If magnetic monopoles could exist, why not ITN mono-LaGrange points? Besides, the other LaGrange point could (mathematically) be in another star system. Transport may take longer than the age of the universe, but the OP is "not concerned with timescale". I'll delete the answer once you see this comment. – Woody Dec 13 '23 at 04:39
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I'm confused by your comment, so please don't delete; let's keep going. In the CR3BP there are stable and unstable manifolds (those red and green meshes in the old Matlab plots, e.g. https://www.researchgate.net/figure/The-stable-and-unstable-manifolds-of-a-Lyapunov-orbit_fig6_285811277 For say the Sun-Earth mass ratio, don't most of the trajectories that together form the unstable manifold associated with L1 or L2 go out to heliocentric orbits rather than to the other Lagrange point? And for some mass ratios can't some of them go to infinity? – uhoh Dec 13 '23 at 09:57
@uhoh ... The contour lines on a topographic map make a useful 2-D analogy. Travelling on a contour line, you maintain the same gravitational potential. That's why railroads follow contour lines: to avoid gradients. In a complex landscape landscape, a long winding track may get you around a mountain without climbing a grade or using the brakes, but if the destination is higher than the departure point, there is no path that avoids the elevation change. – Woody Dec 13 '23 at 16:52
... Within the orbits of the planets, the gravity well of the solar system is very lumpy , Dodging and weaving can avoid spending delta-v. But the well beyond the planets is a smooth uphill climb. There are no sneaky routes. – Woody Dec 13 '23 at 16:58
Manifolds are (by definition) contour lines: paths of equal energy. They can get you somewhere without wasting delta-v climbing up one side of a mountain and sliding down the other side. – Woody Dec 13 '23 at 17:01
yes, but by that time you don't need a sneaky path, you only need some residual velocity. I guess if you can show that there's no way to leave Neptune along an unstable manifold with 7700 m/s relative to the Sun, then you've got a proof for "no". – uhoh Dec 13 '23 at 19:12
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@uhoh ... This is where my topographic map analogy breaks down. Topographic contour lines illustrate equal gravitational potential. Invariant manifolds illustrate equal total energy (potential and kinetic). I think. I'm way over my head with the math required. – Woody Dec 14 '23 at 17:21
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@uhoh ... an invariant manifold is a set of contiguous vectors, If you are "on a manifold" (in terms of origin location and vector direction) but your vector magnitude is not contiguous with the neighboring manifold vectors, you are not on the manifold. So if you have 7700m/sec, you are not on the ITN manifold even if you are in the right place, going in the right direction. We should continue this in Chat, but I can't find it in the menu structure. – Woody Dec 14 '23 at 19:38
Let us continue this discussion in chat. – uhoh Dec 14 '23 at 21:25

Are there any paths in the Interplanetary Transport Network that leave the solar system?

3 Answers3