Solar system dynamics

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1. musgravepeterMar 2022
   L4 and L5 are stable when the smaller mass is less than about 0.0385 times the larger mass [1]. This means e.g. a typical binary star system would not have stable L4/L5 points. The reference [1] works through this in careful detail and is an excellent reference on this topic.

   [1] Solar System Dynamics, Murray and Dermott, Cambridge University Press.

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2. kartikkumarNov 2014
   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.

   [1] http://www.amazon.com/Solar-System-Dynamics-Carl-Murray/dp/0...

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