Gravity Assists to Tylo Orbit?

[A_name]

I’m currently designing a Tylo mission. Let's assume I have myself a Tylo intercept straight from Kerbin with a nice and low Pe. My logic indicates that if I try to land directly from my interplanetary trajectory, since I’m going so fast, it will be more expensive than if I use gravity assists to first capture around Jool and lower my Jool orbit as much as possible. Is my logic sound? Is there any gravity assist trickery that can make my Tylo landing cheaper?

[Superfluous J]

Tylo's going to be expensive no matter what you do

But yes, you're correct. If you were to come into Tylo and gravity assist yourself in such a way that you can get a gravity assist from Vall that puts you into a Jool orbit that looks like a transfer from Vall to Tylo, you can for a scant couple m/s turn your direct Tylo intercept burn into a Vall-Tylo-transfer intercept burn.

But it's still gonna be expensive. I don't know offhand how expensive it'll be, but I do know I'm always surprised.

[Aegolius13]

Yeah, you're right on.  Tylo gravity assists are great for saving fuel into the Jool sytem.  Takes some practice but it's very satisfying when you nail it.  

One thing I've found useful: as with all transfers, you want to be near tangent to the target's orbit if you go to intercept.   In contrast, if you get an orbit similar in size to Tylo's, but has a bad intersection (think two interlocking Olympic rings), you're not going to save much fuel.  Often, with Tylo or Laythe assists, it's relatively easy to just your apo/peri low, but harder to get a good tangent approach.  

My favorite way to solve this is with resonant orbits.  For example, if you can get out of your gravity assist with an orbital period that's exactly twice that of Tylo, you and Tylo will both get back to the same place at the same time.  That usually ends up with good results.  

Also, I find its helpful to not be too stingy with using small powered maneuvers to fine-tune your assists.  

The pic below is an example going to Laythe, but the principle is the same.  I did a preliminary assist to capture (not shown), but intentionally left my apoapsis way out beyond Pol for cheap maneuvers.  That's also a good time to get your plane matched up.  Then I tweaked things until I got the blue encounter icon, which assisted me into the resonant orbit shown in green and red (with a small adjustment at the red manuever node).  Then I hit the red encounter, in about the same place as the previous encounter (and thus very close to tangent to Laythe).