# Are Jool's moons' orbits stable?

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. – user20636 Jan 20 at 11:22
• Hence the suggested rewrite. And your reasoning is flawed because there's a difference between fictitious and hypothetical. – user20636 Jan 20 at 11:30
• @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 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 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 at 12:02

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.

Since these object have known masses and orbital parameters with physical units, the stability of the system can be 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 at 12:26
• Well, will you look at that, another question where you were wasting people's time – user20636 Jan 20 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 at 9:16
• The simple and obvious solution is to call out such bad behavior so it doesn't become normalised. – user20636 Jan 21 at 9:54
• I enjoyed watching the simulation. Thank you, uhoh. – Greg Jan 22 at 23:26