Since it is a very effective Pe eject burn, the difference between arriving slowly to Jupiter (type 2 transfer) as you are setting up and heading to a faster encounter (type 1 transfer) is likely just a few m/s in the Saturn eject burn. This would eliminate the need for the burn at Jupiter and also gets the ship home about 5 years sooner.
This is where I thought I was actually saving Δv.
In the first plan you posted, at the Eject stage you have -2.8 km/s of Prograde, while mine had -1.8 km/s.
This made me think that I would save 1 km/s out of the escape plan, so I didn't mind the 0.5 km/s burn at Jupiter.
But ofcourse the relationship between the Injection Δv at stage2 and the transfer Δv at stage 3 is completely different. A few m/s difference at the Injection burn can lead to great differences at the transfer Δv.
I hadn't completely understood this, but with this thread as an incentive
I'm reading about it right now. Still havent found a definitive formula that can tell you "if the transfer Δv is x then the Injection Δv is y", but I'm understanding a lot more now.
There is much involved:the Vesc at the orbital alt. of the spacecraft, the V∞ and the orbital velocity of the planet around the sun. Cool stuff!
--------------------------EDIT---------------------------
I just finished a 2 hour Orbiter session, making a new plan.
I sticked to the same method as the first one (Titan→Jupiter direct) but in order to not have the same plane change problem again, I tried to find where to intersect with Jupiter for a Rinc ~0° at the time of the Injection burn. Sure enough, such an intersection existed, but the transfer was almost perfect Hohmann-like, meaning that I would have a low encounter velocity at Jupiter. The burn from Titan cost 1710 m/s.
Then, I tried to setup the slingshot to"hug" the planet getting all the benefit I could from Jupiter's mass and see how much Δv I still needed to make it to Earth. TransX showed that an additional 470 m/s would do the job, bringing the total Δv at 2180 m/s for a 2 burn solution.
Another great thing is that I finally figured out what the relationship is between the Transfer Δv and the Injection Δv and how to calculate both for any transfer I want, just with paper, pencil and a calculator.
Here is the plan: I have set "Plan : None" for stages 2 and 3, so it's from the burn on Titan all the way to Jupiter periapsis. I didn't setup the second burn, because it would be useless this early on, but I got the Jupiter pass pretty close to what it should be.
Code:
BEGIN_DESC
Contains the latest simulation state.
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