# Do Lagrange-like regions temporarily appear around planets with multiple moons?

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?

• A small-scale version of the 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 - 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 5:02
• 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
• @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

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 $\mu$:

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:

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:

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.