I worked on this for my Masters thesis [1], studying the nature of low-energy transfers [2] to the Moon, using the Weak Stability Boundary (WSB) [3]. Turns out that the WSB and invariant manifolds described by Dynamical Systems Theory (DST) [4] in the N-Body problem [5] are intricately linked. There was a bit of a "war" going on when I was doing my thesis between the group at Caltech that pioneered the (DST) methods, including people like Wang-Sang Koon, Shane Ross, and Martin Lo, and Ed Belbruno, who formalized the concept of the WSB, because there was still an evolving view of chaos in the gravitational 3-body problem.
It's a fascinating area of research that has implications for planetary formation and has been exploited for space mission design. I'm currently finalizing a paper that draws attention to the fact that low-energy orbits are likely an important component of a peculiar ring system around Uranus: the mu-ring/Mab system. Mab [6] shows strange orbital behavior that's likely intimately tied to interactions with a belt of moonlets that display horseshoe-like motion.
There's been some interesting research using the concept of orbital cyclers and the coincidental proximity of Lagrange points in the Earth-Sun and Mars-Sun systems. The only issue is that these orbits are necessarily very slow, so they're not suitable for time-critical applications.
This work occupies an odd niche that piques my curiosity. I knew Ed Belbruno slightly, and I'm cordial with Martin Lo. I'm trying to figure out how to say this neutrally: the people like the ones I mentioned do not seem to have much influence on the actual world of mission trajectory design. They're off on their own.
Yet when I read the summaries of their methods, they don't discuss any drawbacks besides the large transit times required. I'm left thinking that either there is something political/historical going on that I don't know about, or that the large times in fact totally kill the idea, rendering the theory moot. Come to think of it, another option is that reducing delta-v to zero is not worth going to so much trouble over (from a mission design viewpoint).
On the other hand, the scientific angle (that these trajectories can allow long-range mass circulation in the solar system) is very interesting and something I was not aware of. Thanks for your interesting reply.
It has occupied an odd niche in my curiosity ever since my first grad-level class in astrodynamics/celestial mechanics :) . It's a fascinating problem because it's inherently tied to many physical phenomena in our Solar System and in other planetary systems, yet the statement of the 3-body problem is pretty much as simple as it gets.
And you're right, they are kinda off on their own, but that's mostly because this niche is an interesting meeting of the minds for mathematicians, astrophysicists and engineers. That means you get some "interesting" discussions to say the least.
As for the "political/historical" aspects, have a chat with Ed sometime if you get the chance. He's got an interesting backstory that's catalogued in his books too. Basically, to some extent, there was a lot of resistance at JPL to his ideas, and so he had to bypass them, which is what brought about the Hiten mission.
As an objective researcher, I can say that low-energy transfers for mission design are interesting, but really for a specific subset of scenarios. Time-critical missions, e.g. manned spaceflight, falls outside the scope of low-energy transfers. Additionally, it turns out that the maths is a bit finicky and that low-energy transfers only lead to a significant Delta-V reduction if you launch in the right "geometry". In the case of Earth-Moon transfers for instance, it turns out that if you neglect the Sun, you can't actually reach the Moon "for free", as is advertised by WSB transfers, because of KAM tori around the Moon. The Sun is crucial, as it's perturbing effect ensures that phase-space opens up and you can actually reach the Moon. This comes with a BIG caveat though that the geometry of the Earth-Moon-Sun has to meet certain requirements. Hence, launch windows are limited.
As you point out, I do think the greater interest in studying low-energy orbits, WSB and invariant manifolds in high-order gravitational problems is in using the theory to explain natural processes. This fits within the larger context of dealing with resonances in the 3-body problem. Murray and Dermott have an excellent textbook on the fundamental theory behind all of this [1]. It's a must-buy if you're interested in delving into this further.
All of this has tremendous potential to elucidate exoplanet systems. There are plenty of systems discovered by Kepler, CoRoT etc. that require a deep, fundamental understanding of the processes that shape(d) them.
It's a fascinating area of research that has implications for planetary formation and has been exploited for space mission design. I'm currently finalizing a paper that draws attention to the fact that low-energy orbits are likely an important component of a peculiar ring system around Uranus: the mu-ring/Mab system. Mab [6] shows strange orbital behavior that's likely intimately tied to interactions with a belt of moonlets that display horseshoe-like motion.
There's been some interesting research using the concept of orbital cyclers and the coincidental proximity of Lagrange points in the Earth-Sun and Mars-Sun systems. The only issue is that these orbits are necessarily very slow, so they're not suitable for time-critical applications.
[1] http://repository.tudelft.nl/view/ir/uuid%3Ae8c99c80-a25d-4c...
[2] http://en.wikipedia.org/wiki/Low-energy_transfer
[3] https://video.ias.edu/gds/belbruno
[4] http://en.wikipedia.org/wiki/Dynamical_systems_theory
[5] http://www.cds.caltech.edu/~koon/book/KoLoMaRo_DMissionBk.pd...
[6] http://en.wikipedia.org/wiki/Mab_(moon)
edit: just edited the links so they display on separate links.