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You can get captured for literally 0 dV costs.
Aerobraking is death as you found out.
Those inflatable heatshieldsare supposed to help you not explode but then your ship will have the aerodynamic qualities of a mushroom.
For brute force captures, they say the best method is to get your periapsis as low as possible and do your capture burn there.
For a 180 degree inclination change (cw to ccw in your case), keep your eliptical orbit but push the apoapsis as far out as possible.
Then wait until you get to your apoapsis and change directions there.
Jool was always the trickiest and most rewarding system.
Bop and Pol have super low gravity so mining them for fuel is easy.
Playing pinball with the moons lets you get lots of science with just 1 flyby mission.
Ive got my eliptical orbit around jool now with only a 600 dv burn so thats good kinda
still trying to get laythe to accept my ship the d bag keeps kicking me out like a mad ex
Rewarding yes, challenging... if you haven't been here yet. I'd say, instead of challenging, that you can learn a lot from doing a mission to it. Gravity assists, safe aerobraking altitudes and velocities for your ship, all kinds of planets in that system and so on.
Doing the first maneuver for a Jool fly-by is super easy. A blind man can hit Jool due to its very high SOI. But after that, much time ought to be spent planning your maneuver nodes to get fly-bys of Laythe or Tylo that improve your orbit depending on what you wanna achieve and ofc depending on your initial orbit. I'd say more than 50% of the time spent in the Jool system is spent refining the maneuvers to get whatever effect you want.
For example, look at this:
https://www.youtube.com/watch?v=pIX3GpJCOzQ&feature=youtu.be
This ship only has 5k dV in total (if kept in one piece, unstaged), good maneuvering was pretty important to land on Laythe.
And obviously, don't have a friggin clockwise orbit when all planets go the other way :). But probably you could reverse that decently with a very high apoapsis (just burn retrograde until it becomes prograde and then some).
its pretty safe to go about 45,000m any lower and you may blow up or drop right onto the moons surface
http://steamcommunity.com/sharedfiles/filedetails/?id=1137250630
http://steamcommunity.com/sharedfiles/filedetails/?id=1137251834
http://steamcommunity.com/sharedfiles/filedetails/?id=1137252142
It is a LOT easier to do and plan these if you go into the settings file and change the conics number to 3 or 4 (its the number of projected paths through various encounters/changes of SoI it displays) that ways it will not only show your projected intercept with the moon used for braking but most importantly your projected orbit around jool post gravity assist. I have used these to also do inclination (angle of orbit) changes for free so I can get better intercepts with bop and pol
^This. Thats how I have always made it to jool. If you line up your entry to Jools SOI properly you can easily skim Laythe for aerobraking. It doesnt take much to get in to a stable Jool orbit from there.
http://steamcommunity.com/sharedfiles/filedetails/?id=758297643
Still my favourite Jool manoeuvre. I love Jool's roundabouts.
I'm a bit confused about initial trajectory you have - you meet Tylo at 180°+ from where you are right now, which means you are rather already in Jool-captured state or approaching with less speed than you would from Kerbin as far as I can tell from the curve shape.
Also you can't get Laythe capture with Laythe alone, so that last node is just a cut off of what happens next.
I played with 7 patched conics limit set in cfg file at that point and I was actually still at LKO just having fun. Not sure it goes above 6, since 6 is the limit in ingame settings, but I would recommend you to have at least those 6 too. It's even more fun at Jool :)
The closest thing to Laythe capture I have had happened during one Jool aerobraking (with like 50 passes due to 1200K low heat parts), when at some point gravity sent me into almost circular orbit close to Laythe orbit altitude. That still wouldn't give me Laythe capture, but the interception velocity was really small. The only problem with those - since your orbital velocity is so close to Laythe velocity, waiting for next natural encounter once Laythe assist sends you on that orbit may take years because you were so close to start with (during assist). So of course I did a small burn to skip all that.
http://steamcommunity.com/sharedfiles/filedetails/?id=1147692019
Not the best but its a pre-burn setup in LKO. Plan is simple, use laythe atmo to brake and if required add a braking burn to enter jool orbit.
Which will "move" Tylo or Laythe to the spot you need during optimal arrival. That way you can achieve instant Jool gravity capture without even touching Laythe atmosphere.
If you go for "after Pe" encounter, you will have to target that moon in its local SOI clockwise (pass on the inside) to achieve gravity capture for Jool as counterclockwise (pass on the outside) would accelerate you instead.
Which is not as good in case you intend aerobraking or instant landing there due to body own rotation.
Using gravity capture by closely encountering Tylo or Laythe
Before Jool Pe
inside pass (cw) - accelerating
outside pass (ccw) - decelerating
After Jool Pe
inside pass (cw) - decelerating
outside pass (ccw) - accelerating