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Lasting Lagrange points only exist where two bodies of mass dominate. But in the midst of for example the synchronous Jovian moons, is there a calendar and map for when a spacecraft can be near enough to one of the moons for a moment, that there in effect exists Lagrange points in relation to that moon and Jupiter?

Would that be useful for spaceflight? Such that when Io passes by, the spacecraft suddenly finds itself in a Lagrange like balance and could change its trajectory or orbit with less effort?

Nathan Tuggy
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LocalFluff
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  • A small-scale version of the http://en.wikipedia.org/wiki/Interplanetary_Transport_Network ? – Russell Borogove Apr 19 '15 at 16:36
  • @RussellBorogove The interplanetary transport network has recently been debunked by HopDavid who is a frequent and valuable contributor here. But locally, in a complex multi-moon system, I wonder if it would be possible. – LocalFluff Apr 19 '15 at 18:15
  • @LocalFluff I find it interesting that you say that ITN is debunked, and then ask about the possibility of exactly that (unstable, quasi-periodic manifolds), but on a smaller scale. Yes, albeit they likely wouldn't be called Lagrange points (but I guess it's fine to call them quasi-periodic, collinear,... libration points for the short duration they form), these do exist and as you mention by assuming their temporary nature, they aren't stable. But they can be periodic. One example could be the Laplace resonant moons of Jupiter. Computing a cycler around those would be... fun. – TildalWave Apr 19 '15 at 18:37
  • FWIW, an example of ITN in action are quasi-Hilda orbits, say of comet 147P/Kushida-Muramatsu. But there are others. – TildalWave Apr 19 '15 at 18:52
  • @TildalWave ITN is debunked on an inter-planetary level. HopDavid is very clear and convincing in his blog. Can't use it to go from one planet to another planet with any gain, but it is very important locally in cis-lunar space. I basically wonder here, if temporary libration points are useful for spaceflight, considering also that they recur regularly in a system such as Jupiter. – LocalFluff Apr 19 '15 at 19:13
  • @HopDavid says about Earth and Mars. But the ITN is not for human, it is for asteroids and outer planets: check page 11 of http://www.gg.caltech.edu/~mwl/publications/papers/IPSAndOrigins.pdf As I remember, it can take 100s and 1000s of years to use ITN... Wiki says "Comet Shoemaker–Levy 9 followed such a trajectory to collide with Jupiter." ITN authors have variants for multimoon too: http://www.cds.caltech.edu/~marsden/books/Mission_Design.html http://www.cds.caltech.edu/~marsden/volume/missiondesign/KoLoMaRo_DMissionBook_2011-04-25.pdf (chapter10 "Multi-Moon Orbiters") – osgx Apr 20 '15 at 03:15
  • @osgx Someone should pose a question specifically about the ITN, so that its viability could be sorted out. – LocalFluff Apr 20 '15 at 04:49
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    @LocalFluff - HopDavid is a blogger. Blogs don't count for much, scientifically. Published journal articles, published technical books -- those do count. A lot. Koon, Lo, Ross, Marsden, and others have stuck their necks out in the peer reviewed media. Has HopDavid done the same? – David Hammen Apr 20 '15 at 05:02
  • @DavidHammen I don't care for symbols of authority or anyone's prestige. The reasoning in Hops' blog is straight forward and it should be easy to point at any mistakes. It's not rocket science (oh well, as a figure of speech). – LocalFluff Apr 20 '15 at 10:34
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    Point David Hammen is making is that blogs don't have any form of peer review, unless you count comments below from those that would both 1) have to find and read it and 2) often pointlessly engage with its author that is also the sole authority of that blog. We have more rigorous peer review here, and we're still a far cry away from any serious scientific journals that 1) don't suffer visibility and scientific community subscribes to them and 2) objections are taken seriously and often lead to whole articles or individual findings / conclusions retractions. With blogs, anything goes. – TildalWave Apr 20 '15 at 15:27
  • Here's another example. It's the trajectory of S-IVB third stage of the Apollo 12 Saturn V rocket that was initially mistaken for an asteroid. It swapped from a heliocentric orbit to an Earth-Moon rosette through SEL1 and then back out again in 2003. Possibly to return back into geocentric regime in odd 30 years time. There are many other objects we know of that swap orbits. Is this an ITN? Well, no. Not on its own, but it's potentially one leg of it. That's how ITN work. A single lace doesn't make a wedding dress. – TildalWave Apr 20 '15 at 15:44
  • @TildalWave Problem with the ITN is that it is not inter-planetary, its only LTN, the Local Transportation Network. Aren't those "networks" confined to the surface of the local Hill Sphere? Libration points do allow cheap ejection from the local system, but not on any trajectory that matches the orbit of another planet (though I suppose it could happen by chance alignment...) That is how I understand it. It is for a good reason that it is I who ask the question here, hoping for those who know to share an answer. – LocalFluff Apr 20 '15 at 15:53
  • I believe this is a peer-reviewed paper: http://www.researchgate.net/profile/M_Vasile/publication/40705665_Low_Energy_Interplanetary_Transfers_Exploiting_Invariant_Manifolds_of_the_Restricted_Three-Body_Problem/links/0c960527a98426f09e000000.pdf – HopDavid Apr 20 '15 at 17:53
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    @DavidHammen Topputo, author of the above linked paper and Co-author of Belbruno's and Topputo's Mars ballistic capture paper states " Unfortunately, the R3BPs involved in this study, due to their small mass parameters, do not allow the manifolds to develop far enough to approach each other; hence in this case the manifolds do not intersect even in the configuration space." Which is exactly what I say. – HopDavid Apr 20 '15 at 17:59
  • @DavidHammen The ITN article Russell Borogrove linked to was a Wikipedia article. Peer reviewed paper? That's hilarious. Further, I haven't heard Koon, Lo, Ross or Marsden claim the ITN are "trajectories through space ... using little or no energy." So far as I can tell that's pop wisdom based on misinterpretation of their papers. Sadly, Ross et al have done little to correct this exaggerated view of the ITN benefits. – HopDavid Apr 20 '15 at 18:10
  • @TildalWave Sun-Uranus and sun-Neptune mass parameters are comparable to Jupiter and a Galilean moon. And of course Sun-Jupiter and Sun-Saturn have even larger $\mu$ s. Manifold tubes from the gas giant Lagrange necks likely overlap. Kuiper Belt objects might use ITN to migrate towards Jupiter. – HopDavid Apr 22 '15 at 16:17
  • ITNs between gas giants are interesting when it comes to modeling evolution of the solar system. But routes that take eons are of little use to us humans. What about the inner system? The mass parameter for the sun and an inner system rocky planet are quite a lot smaller. As Topputo said, the Mars and Earth tubes don't overlap. So is LocalFluff naive to inquire about an ITN for Jovian moons while questioning the usefulness of a planetary ITN? In my opinion LocalFluff has taken a sensible view. – HopDavid Apr 22 '15 at 16:33
  • related but different L2 point in multi-moon system – uhoh Jan 20 '19 at 15:38

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An online 3-body text is Dynamical Systems, the Three Body Problem and Space Mission Design (big pdf).

The trajectories they look at are those with a C3 close to zero (near parabolic) in the regions of the L1 or L2 necks. If a spacecraft is traveling just under or just over the moon's escape velocity in the moon's neighborhood, there may a big variety of trajectories emanating from the moon's L1 and L2 necks.

A quantity to look at is $\mu$. No, not G * m. In 3 body mechanics $\mu$ tells you how much more massive the central body is than the orbiting one.

$\mu$ = (mass orbiting body)/(mass orbiting body + mass central body)

If you have a big $\mu$, there's all sorts of different paths out of L1 or L2.

If $\mu$ is tiny, nudging a payload from the L1 or L2 necks will result in a path nearly indistinguishable from the moon's orbit (Phobos and Deimos, I'm looking at you).

Here's a screen capture from one of my spreadsheets. I tinted the cells for $\mu$:

enter image description here

Earth's moon has a nice $\mu$. Pluto's moon Charon has a whopper $\mu$.

Jupiter's big moons have more substantial $\mu$ s than the tiny Mars-Sun and Earth-Sun $\mu$ s you've seen me complain about. Are they big enough to allow travel from moon to moon via WSBs between L1 and L2 necks?

This afternoon I had time to play with it. Here's a drawing of orbits of the 4 Galilean moons along with orbits payloads would follow if nudged from L1 or L2 necks:

enter image description here

At first glance it doesn't look like something nudged from Callisto's L1 would find it's way to Ganymede's L2.

But repeated passes by a moon will alter the orbit. Here is a screen shot where pellets are nudged from Ganymede's L1:

enter image description here

On the left side are pellets shortly after being nudged from an L1 where the sim has the same $\mu$ as Jupiter/Ganymede. On the right are the same pellets after the pellets orbit for a time. You can see repeated perturbations from Ganymede cause the pellets to wander over a larger territory.

At this time I believe payloads drifting out of one moon's Lagrange neck could possibly find their way to another moon's Lagrange neck via weak stability boundaries. And given these moons have periods on the order of days or weeks, using these paths might even be practical.

The Jovian moons are big enough that a moon swing by could drop a barely hyperbolic Jovian orbit into an elliptical Jovian capture orbit. I suspect the Jovian moons could play an interesting pinball game with such a captured object.

HopDavid
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