kerbal-space-program
I parked a space station in Jool's equatorial orbit and inclinated a little to avoid collisions with Tylo or Laythe.
After a 5 year tourist contract mission near Duna, I opened the mission control to find my space station "in an escape trajectory away from the Sun". I know that either Tylo or Laythe must have slingshoted my station.
Question : How to be sure that my ship/station will not meet the SoI of a nearby moon ?
Vanilla/stock answer prefered but I have KER and MechJeb installed.
There are several steps to successful dockings. Click on images for larger view.
As a side note, I screwed up this particular approach because I wasn't paying attention and didn't reduce my speed as I closed in. I shot past the target ship and had to correct. Additionally, you'll note that I didn't in fact change to docking mode. This is a personal preference, and I use both hands on the keyboard to control my attitude with my left had (WASDQE) and translation with my right hand (IJKLHN).
So you're correct in using Jool for a gravitational slingshot into a high inclination, and you're also correct in assuming that you can only get about 40° from an encounter prior to switching the spheres of influence. Trying to set up burns prior to switching SoI is an exercise in futility. What you do want to do is set up your encounter so that you're coming in close to over a pole. 200m/s early (about a month out from switching SoI) can save a lot down the road.
Getting your trans-Joolian burn correct is actually one of the biggest factors for saving fuel. Not only do you minimize delta-V on the transfer burn, but you'll also minimize delta-V on the polar injection burn. You want to start your transfer about 65° after crossing the terminator into night when Jool is leading Kerbin by about 95°. When it comes to the phase angle, burning too early is really bad, as delta-V costs go up exponentially with the amount of time before optimal. Burning late isn't so bad, as costs go up much slower (quadratically maybe? Don't know for sure). This is a utility for determining optimal burn patterns.
So you've done your transfer burn, and you've done your final correction burn before switching SoI, and you're just waiting those last few seconds before that Jool orbit line changes from yellow to green. When that happens, you'll want to immediately plop down a maneuver node not too far in front of you. You're basically going to be doing a bunch of min-maxing to get your inclination into the high eighties. First, set your incoming inclination for best result inclination. Next, add about 500m/s of prograde velocity. You're doing this because you essentially have to kill something like 4000m/s of horizontal velocity and turn that into vertical. Next, reduce your periapse using the ground vector until optimal. Rinse and repeat, adding the most velocity in the prograde direction. Eventually, you'll get to a point where the inclination of the resulting orbit is correct, but the periapse will be in the sun, or the apoapse will be way out of the system. You're three options are to try and fix it now, try to fix it at Jool periapse, or (easily) fix it once you achieve polar orbit.
It's a tough operation, but with patience and experimentation, you should be able to get it every time.
Best Answer
The most practical approach is to simply park in an orbit which does not intersect with the orbit of any of the moons.
A reasonable rule of thumb I use is to simply park halfway between them, maybe adjusting a bit towards the smaller moon.
If you want to be sure, though, you can look up the moon characteristics and calculate the safe altitudes. For example, taking Tylo and Vall, we can see that Vall has an apoapsis of 43.2Mm and a sphere of influence of 2.4Mm, and Tylo has a periapsis of 68.5Mm and a SoI of 10.9Mm. So an orbit around Jool with an Ap under 68.5-10.9=57.6Mm and Pe above 43.2+2.4=45.6Mm will not intersect any of the moons' orbits.
Alternatively, you can manage your orbital periods to make sure you don't encounter the moon.
The simplest example is to simply have your orbit period match the orbit period of the moon. E.g. if you parked on the other side of Jool from Tylo, and you took exactly the same amount of time to orbit Jool as Tylo, then neither of you would catch each other, and no encounters would happen.
There are more complicated alternatives, e.g. if you had an elliptic orbit with a period of exactly 1.5 (3/2) times Tylo's orbit, you would get into the same position every 2 orbits (2 ship orbits, 3 Tylo orbits), so as long as the match is exact and your positions do not drift, if you did not encounter Tylo in 2 orbits, you will not encounter Tylo.
If you want to get fancy, you can even exploit the fact that Laythe-Vall-Tylo have an orbital resonance of 1:2:4, and set up a safe elliptic orbit floating among all of them.
Both of these approaches are safe to use on the same orbital plane as the moon, but if your orbit is significantly inclined, you only need to worry about these things at the time your orbital plane crosses the orbital plane of the moon. Inclination alone will only slightly reduce your chances of an encounter, and does not offer significant protection, though.