Stabilization theory

[Souper]

If 2 Jools are orbiting eachother PERFECTLY, and Kerbin is is in the EXACT middle with no other celestial body nearby to disturb this "system"...

Is it stable?

http://i.imgur.com/OWULZjY.png

[OtherDalfite]

Considering gravity changes as you pass over a planets surface, it would PROBABLY remain steady, but has the possibility to change ever so slightly over billions of years. If you could have masses whose center of gravity is right in the middle, it would be a perfect model.

[Sillychris]

What you are describing is known as an unstable equillibrium in lagrangian mechanics. The planet between the two Jools sits carefully perched at the very top of a potential energy curve between the two large bodies... one tiny perturbation to either side (like a Kerbal farting) would send kerbal sliding down the curve.

Think of it as similar to a pencil balanced on its tip. It is technically considered equilibrium, but is extremely unstable due to energetics favoring the pencil falling down.

[Camacha]

In perfect models stability is not an issue, in reality it is a major factor.

[Everten P.]

Lets get one thing strait that I think you are ignoring KERBIN HAS MOUNTAINS! And not only the bit of gravity the mountains would create but if they where orbiting at about 1000Mm (which is small when you think of Jool) the water from Kerbin and its atmosphere would be SUCKED toward the Jools considering that all the planets rotate the amount of atmosphere and water would be split amongst the two. The as their mass increased the mountains would come into effect releasing more gravitational force towards one after this Kerbin would be near enough to a particular Jool just long enough for Jool's atmosphere to burn it to gas due to friction with the atmosphereless Kerbin to become gas. After that one Jool would have an edge over the other and when the merge that's how a star is born because Jupiter and Jool are both technically "failed" stars so when two of them collide that would create a small star a bit smaller than Kerbol. THE END hope you have a nice day.

[K^2]

No, it is not stable. It is enough to go into a rotating frame of reference to see that the effective potential has a local maximum at the center. That means that the Kerbin's location in this system is an equilibrium, but it is not a stable one. It will start falling towards one of the Jools, and either end up its moon or get knocked out of the system. The too Jools will continue orbiting each other.

If you put a ship in the center, instead of the planet. It can remain there by using very small amounts of fuel for station-keeping. Because as I've mentioned above, while it's not stable, it is an equilibrium, so you don't need a lot of force to keep something there.