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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":

BrendanLuke15
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uhoh
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    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! – Harvey Rael Aug 25 '18 at 14:06
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    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 – Jack Aug 25 '18 at 14:10
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    @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. – uhoh Aug 25 '18 at 14:10
  • @Jack that's great, thanks! There's also complementary information in this answer. – uhoh Aug 25 '18 at 14:14
  • @uhoh if thats the case once you have the data could you not just see the velocity of Cassini "at Titan" in the heliocentric frame (more like as it approaches it), and gather its velocity leaving Titan, then use the vis-viva equation combined with an average radius value and find the delta-v that way as a first order approximation? – Harvey Rael Aug 25 '18 at 14:39
  • @HarveyRael no, for each approach I would pop state vectors (converted to Saturn's frame) into a simple integrator like this and run it for a short time ("duration" of flyby) twice, once with Titan's gravity turned on, and once with it turned off, and call the magnitude of the vector difference between the two for the delta-v for that particular flyby, then add them all up. It's approximate but that would be fine for the purposes of this question. But let's see first if there is a quotable source. – uhoh Aug 25 '18 at 14:54
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    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. – Mark Adler Aug 26 '18 at 02:29
  • @MarkAdler agreed. Is that any different than what I said in the previous comment? (note: "between the two" means "between the two velocities") – uhoh Aug 26 '18 at 02:52
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    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. – Mark Adler Aug 26 '18 at 21:05
  • @MarkAdler Even so, always a pleasure! See also this comment where I failed to read words. – uhoh Aug 27 '18 at 00:03
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    There are over 140 individual spk kernels just while at Saturn, wow! – BrendanLuke15 Apr 06 '22 at 11:29

1 Answers1

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I downloaded the ~170 SPK reconstructed trajectory kernels (at Saturn) from the NAIF node of PDS and searched for instances where Cassini was within Titan's sphere of influence (~43,000 km).

Note that this construct actually excludes the third Titan flyby from the tally (T-C, Huygens probe entry; 60,000 km, blame the Italians) for a total of 126 considered flybys.

I quantified each flyby by 4 metrics (using standard hyperbolic trajectory assumptions):

  • $v_{\infty}$
  • periapsis distance of flyby
  • flyby deflection angle ($\delta = 2 \nu$ in Wikipedia nomenclature)
  • flyby $\Delta V$ (calculated with equation from a question of mine)

flyby stats (Personal work)

The total $\Delta V$ of all 126 Titan flybys was 89.4 km/s.

This is corroborated by this NASA source (that I found AFTER completing all of this work :))):

By mission’s end, Cassini achieved a delta-v of about 200,000 miles per hour (about 90,000 meters per second) from Titan flybys — roughly 37 times what it could ever have achieved by propellant alone.

Therefore Titan contributed ~97.4% of all "delta V" (while at Saturn).

Cassini-Titan "Ball of (broken) Yarn":

Cassini-Titan ball of yarn

(Personal Work, Titan base image source (Astropedia) -> MATLAB "Copper" color map)

J2000 frame, this is not where Cassini flew over Titan relative to surface features, just a neat animation :)

BrendanLuke15
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