Gravity Assist vs Direct Burning

[Superfluous J]

Closest thing I've done to a gravity assist is a free return trajectory of some Mun and Minmus probes. Otherwise, i haven't learned the math required properly align a gravity assist and therefore have never bothered.

You don't need math.

Next time you're going to Jool, get your inbound hyperbolic trajectory going around the back of Jool at about Laythe or Tylo's orbit. Then make a maneuver node once you're in the SOI, but really far out, to slow down until you get an encounter with the moon whose orbit you're near. Play with the timing just a tiny bit (and we're talking ounces of fuel here) and bam, you'll nail an orbit around Jool in no time with no aerobraking and - as a bonus - your periapsis will not be in Jool's atmosphere but out at a very workable altitude.

You'll never aerobrake at Jool again.

[Random Tank]

I'm gonna use a Jool gravity assist to get to Duna

[prophet_01]

I used slingshots for some of my satelite deployments. It was quite helpfull to get my last relais satelite up to a 40.000km polar orbit. It was a pain to get the nodes just right, but it saved my quite some fuel to use the mun for a gravity assist. Gravity assists are always nice for switching from a polar to an aequatorial orbit (if you rly have to).

It's also great to use those in the joolian system, especially tylo But for interplanetary burns they usually suck since the oberth effect in LKO helps a lot more.

I've seen that some people actually pulled of cassini style missions with multiple assists around eve and kerbin, but that's just too much planing for me. Congrats to those that actually achieved that

Edit: I forgot about free return trajectories. I just love those in career mode