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In the video Cassini at Titan: A World Unveiled after about 01:56 Linda Spilker, Cassini Project Scientist, Jet Propulsion Laboratory says:

Not only was Titan fascinating in its own right, a moon the size of the planet Mercury, it was also Cassini’s “gas tank”. It allowed us to change the shape and orientation of the orbit in order to explore the poles of Saturn and the rings and all of the icy moons, by carrying a lot less fuel than we would have to have carried otherwise.

It gave us the energy to go all the way across the rings, and fly between the gap; between the rings and the planet.

Immediately following that, Jonathan Lunine, Cassini Titan Scientist, Cornell University says:

Because of these flyby’s of Titan, using Titan as a gravitational slingshot…

And so many of the remarkable discoveries that have been made by Cassini, for example mapping the composition of the plume of Enceladus, would not have been possible without Titan there.

We could not have gotten to these places, without using Titan.

Question: Is there a way to estimate the total delta-v that Titan contributed to the mission? Or, starting from Cassini's initial orbit, or since it's orbit dropped to say 250,000 km or so, estimate the fraction of all delta-v from then until EOM that was contributed by maneuvers using Titan?

GIF:

enter image description here

above: Teaser GIF to get you to enjoy the real thing here (since even the low-res version is larger than the stackexchange imgur's limit of 2 MB oops! MiB)

Related questions and further info on this crazy ride called the "ball of yarn":

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    $\begingroup$ If you had an idea of Cassini's mission parameters (importantly, how much velocity it left Earth with, how much velocity it eventually left Titan with) you could guesstimate the Delta-v it gained from the swingby. If you'd like to go further down the rabbit hole you could look at b-plane angles, and orbit propagation from certain known parameters. It's a tricky question you ask! $\endgroup$ – Harvey Rael Aug 25 '18 at 14:06
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    $\begingroup$ Great question! Cassini's orbit design has always amazed me - such incredible worked from the mission planners. This page has a detailed run-down of the final 23 orbits (after the final Titan flyby) and here's a list of all the flybys $\endgroup$ – Jack Aug 25 '18 at 14:10
  • $\begingroup$ @HarveyRael it's not a tricky question if someone at NASA has done this already. Let's see if a source turns up. Since state vectors for the entire mission are available in Horizons along with those of Saturn and Titan, one could just download the data, look for close encounters with Titan, and pull it out from there as well. $\endgroup$ – uhoh Aug 25 '18 at 14:10
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    $\begingroup$ All the data is there in Horizons. You can get Cassini's position and velocity relative to Saturn to, say, one minute resolution for the years of the tour. It is then easy to see the $\Delta V$s as deviations from free fall. You can add up the big ones to get the total from Titan. $\endgroup$ – Mark Adler Aug 26 '18 at 2:29
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    $\begingroup$ Nope. No different. Didn’t take the time to read the comments. Just did Seagull commenting. Swooped in, pooped all over everything, and swooped out again. $\endgroup$ – Mark Adler Aug 26 '18 at 21:05

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