Are Jool's moons' orbits stable?

Question

The fictitious Kerbol system includes

...five planets: Moho, Eve, Kerbin, Duna and Jool; and two dwarf planets: Dres and Eeloo; orbit around it. Kerbol contains 99.97 % of the mass in the Kerbol system. This is very similar to our sun which contains 99.86 % of the mass in the real world solar system.

and

Jool is a gas giant and the sixth planet of the Kerbol star system. It is the Jupiter analog for Kerbal Space Program. Aside from Kerbol, Jool has the largest diameter and greatest mass of all celestial bodies. Its extremely high gravity makes orbital maneuvers unpleasantly expensive. While its distance from Kerbin makes it difficult to reach, it is one of the most appealing targets for missions due to its large and complex system of five moons: Laythe, Vall, Tylo, Bop, and Pol.

I am worried about Jool's moons. I believe that the KSP program propagates them in fixed, perfectly repeating and closed Kepler orbits. But if reality were to set in and they started experiencing each other's gravity, I am afraid they are too close and will start messing with each other's orbits.

Question: Are Jool's moons' orbits stable? If not, how long before the system becomes unrecognizable or one gets ejected or collides with Jool?

I’m voting to close this question because questions about fictional orbital mechanics are pointless. Next thing you know we'll have panicked browncoats asking how long they have before the Verse collapses.
Perhaps completely rewrite to ask how to calculate the orbital stability of an n-body system. — , Jan 20 '21 at 11:22
@JCRM That reasoning is flawed because most of the orbital mechanics questions here are about fictional orbits; very few are about actual orbits of actual objects. People don't learn about orbital mechanics by buying spacecraft and flying them around to see what happens, they do it by calculating hypothetical problems. — uhoh, Jan 20 '21 at 11:27
Hence the suggested rewrite. And your reasoning is flawed because there's a difference between fictitious and hypothetical. — , Jan 20 '21 at 11:30
Questions about orbits of hypothetical objects 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 — uhoh, Jan 20 '21 at 11:34
When inventing novel close reasons, one must first check to see if there is no precedent. If the objection is to something that is regularly well-accepted in the site, then it's a flawed objection. — uhoh, Jan 20 '21 at 11:36
@JCRM ten questions about Kerbin, twenty one questions about KSP, seven post about Duna If one wants to create a new close reason one should take it to meta. Apparently questions asked by users other than me about fictitious worlds are fine and well received. — uhoh, Jan 20 '21 at 11:45
@JCRM there has been no problem with fictional constructs in this site until my question: I'm writing a story..., I was writing a story..., I am writing a space sci-fi short story..., I'm writing a sci-fi story., I'm currently writing fictional story..., I'm writing sci-fi and... — uhoh, Jan 20 '21 at 11:51
I think the idea over whether its fictional or otherwise isn't that important. However I think the stability of the system is not especially relevant for this site and that this question is better suited to Astronomy SE. — Puffin, Jan 20 '21 at 11:58
@Puffin the use of numerical orbital simulators is perfectly on-topic here; it's what Space Explorers do. Any time you want to put a spacecraft in an orbit around Jupiter or Saturn with a complicated moon system you need to pay careful attention to how gravitational perturbations from all those other moons affect your orbit of interest. From a numerical integration point of view this is the same thing. And of course "better suited" is never a close reason. — uhoh, Jan 20 '21 at 12:02
Ok, I understand your point. I had looked at it that stability of a satellite orbit is one thing, mutual stability of a planetary system is quite another and I assumed that distinction (i.e. mutual interactions or not) is the dividing line that means you'll find less people with an educated opinion here and more on Astronomy SE. — Puffin, Jan 20 '21 at 12:56
@Puffin I had considered both sites and asked myself "How many previous questions about the Kerbol system and/or KSP have succeeded in Astronomy SE compared to how many here?" Since I had some insight that the answer was many more here than there, this is where I decided to post. — uhoh, Jan 20 '21 at 13:27
@uhoh, of that list of "writing a story" questions you provided, all but one ask real world questions, with the writing part being used to set the context of the question.
your list of questions about hypothetical objects includes several of the form I suggested you rewrote this one into, one that has been closed, one with the "this is a garbage question" design-alternative tag and one I've VTCed.

And of course, "better suited" is a perfectly valid close reason. — , Jan 20 '21 at 23:58
... and, of course, "other stuff exists" is never a reason not to VTC or downvote. — , Jan 21 '21 at 00:39
@JCRM I've illustrated that there is no problem with fiction here, nor hypothetical orbits nor orbits of hypothetical bodies or objects, nor KSP or the Kerbol system. The narrower and more convoluted reason one tries to craft to close only this question while avoiding all of those, the more it looks like this question is getting an undue amount of highly focused attention. That may not be the best use of one's time. — uhoh, Jan 21 '21 at 09:23
This has been answered by the KSP modding community. https://github.com/mockingbirdnest/Principia/wiki/On-the-dynamical-stability-of-Principia's-modified-Jool-system — Anton Hengst, Jan 21 '21 at 17:35
Jools moons are rather famous among the KSP community precisely because they are hilariously unstable as soon as you add 3-body physics. — Polygnome, Jan 22 '21 at 16:47

uhoh · Answer 1 · 2021-12-24T13:33:34.833

Since these object have known masses and orbital parameters with physical units, the stability of the system can be investigated numerically.

From Jool I clicked on the five links to its moons and compiled the numbers here. The mean anomaly at epoch ("0 UT") is likely to be in radians and is less precise than all the other values for some reason.

name       a (km)      e       i(°)   ω (°)    Ω (°)     M (rad?)     mass (kg)
------   -------     -----    -----   -----    -----     -------     ------------
Jool (central body)                                                  4.2332127E+24
Laythe    27,184     0         0        0        0         3.14      2.9397311E+22
Vall      43,152     0         0        0        0         0.9       3.1087655E+21
Tylo      68,500     0         0.025    0        0         3.14      4.2332127E+22
Bop      128,500     0.235    15.      25       10         0.9       3.7261090E+19
Pol      179,890     0.171     4.25    15        0         0.9       1.0813507E+19

It is not surprising then that someone has done so, and in keeping with our sites heritage of taking questions about the Kerbol system very seriously I'll reference this wonderful calculation.

From the notes below the video N-body simulation of KSP's solar system -- closeup of Jool's moons (hat tip to @Elaskanator)

I recently uploaded a video showing the results of an n-body simulation of Kerbal Space Program's solar system. Over a time-frame of 100 years the system is stable, all except for Jool's moons. Vall gets ejected from Jool very quickly, and Pol eventually follows a few decades later.

This video shows the motion of Jool's moons for the first 3 Ms of the simulation so that Vall's ejection can be seen clearly. After a number of close passes by Laythe, Vall's orbit is pushed high enough that it encounters Tylo, which boosts it into a much higher elliptical orbit. A few orbits later it has another close encounter Tylo and gets ejected from Jool entirely, and thereafter orbits Kerbol independently. By 2.4 Ms it's gone.

This simulation was performed using Dormand and Prince's RK5(4)7M fifth-order embedded Runge Kutta scheme with a local position error limit of 0.1 mm. The simulation of the 3 Ms of motion of the Kerbol system took just a couple of seconds.

Normally I don't answer my own questions, but in this case it seemed prudent. It's likely that better answers will be forthcoming, but this should get the ball rolling. — uhoh, Jan 20 '21 at 12:26
Well, will you look at that, another question where you were wasting people's time — , Jan 20 '21 at 23:32
@JCRM any user who reads or interacts with a stack exchange post does so on a voluntary basis, it's done because they want to do it. If you feel your time is not spent well interacting at length with this post, then there is a simple and obvious solution to that, right? — uhoh, Jan 21 '21 at 09:16
The simple and obvious solution is to call out such bad behavior so it doesn't become normalised. — , Jan 21 '21 at 09:54
@JCRM I've made some more space for this discussion where others can join as well: Am I really "wasting people's time" by posting a KSP-related question, then answering it when there were 4 close votes? — uhoh, Jan 21 '21 at 10:00

score 5 · Accepted Answer · answered Jan 21 '21 at 17:43

This is a studied concern for the team of KSP modders who wrote Principia, an n-body gravitational implementation. The have released a document explaining the issue with the stock system (a very close encounter between Vall and Laythe a few days into the simulation).

To remedy this, they modify the Jool system for stability when Principia is loaded. The link above spends the last 1/2 of the document discussing the stability of this modified system.

Here are the details of the modification:

[We modify the Jool system...] by increasing the size of the orbits of Vall and Tylo, thereby preventing breakdowns of the inner Jool system due to resonances; by making the orbit of Bop retrograde, as suggested by Scott Manley and @pdn4kd, so that it doesn't get boosted out of the system by Tylo (which now comes closer to it).

While the resulting system does not appear likely to break down within a century, we find that it is highly chaotic, mostly because of interactions between Bop and Tylo. In the remainder of this document, we discuss the implications of this chaotic behaviour on the predictability of the system, and look at some features of the motion of the Joolian moons.

In short, no, Jool's moons (as defined in stock KSP) are not stable.

Oh this is fascinating! Thank you for your answer and patience waiting for silly insaclose-reopen cycle. I think there's a good message here for space explorers; while they don't design systems of moons they do design orbits that move amid those moons and try to keep them there, e.g. Cassini's ball of yarn and Juno's flyby's of Jupiter's Galilean moons. — uhoh, Jan 21 '21 at 22:40
fyi I've just asked How would an n-body numerical orbit simulator use hierarchy in its Jacobian? — uhoh, Jan 22 '21 at 02:36
Any thoughts on Calculation of Orbit Accuracy (Kerbal Space Program) — uhoh, Jul 05 '21 at 00:18

Are Jool's moons' orbits stable?

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