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Cassini's final flyby of Titan in April 2017 sealed it's fate in September of that year. This is described further in answers to What force is bringing Cassini down into Saturn's atmosphere in another 145 days; drag, or…?

Question: If Cassini's final flyby of Saturn's moon Titan is the 127th Titan flyby, why is it called "T-126"?

So Long, and Thanks for All the Fish Science (slightly edited for "clarity")

Cassini’s 127th and final close flyby of Titan marks the end of Cassini’s Ring-Grazing Orbits and sets the stage for the mission’s Grand Finale.

The spacecraft made its 127th and final close approach to Titan on April 21 at 11:08 p.m. PDT (2:08 a.m. EDT on April 22), passing at an altitude of about 608 miles (979 kilometers) above the moon's surface.

From the first link:

Date: April 22, 2017
Altitude: 608 miles (979 km)
Speed (relative to Titan): 13,000 mph (5.8 km/sec)
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    $\begingroup$ Not really sure. The first three were T-A, T-B, and T-C, followed by T-3, T-4, ... T-C was the Huygens problem deployment. $\endgroup$
    – Mark Adler
    Oct 20 '18 at 1:45
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    $\begingroup$ @MarkAdler they were forward-thinking folks and so used zero-based indexing ;-) $\endgroup$
    – uhoh
    Oct 20 '18 at 1:47
  • $\begingroup$ @MarkAdler if you think that suffices as an answer, let's go for it! $\endgroup$
    – uhoh
    Mar 23 '19 at 8:31
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Because they started at 0.

From An Apparent Increase in Flux from a Surface Feature on Titan: Implications for Surface and Atmosphere...

We observed an apparent increase in flux from a region of Titan's surface between the time of the initial Titan flyby in July 2004 (T0)

Astronomers like starting at 0 because it means the number line is contiguous. You can do very simple math before and after the start of the event. The familiar launch countdown is a simple countdown from T-5 [seconds], T-4, T-3, T-2, T-1, T0 is the liftoff event, and T1 is the first second after liftoff.

If T1 was liftoff their counters would have to know to skip 0, and T2 would be the first second after liftoff, T3 would be the second, and so on.

Similarly, for astronomers, whereas we would count years 2 BC, 1 BC, 1 AD, 2 AD, they would say Year -1, 0, 1, 2.

This logic doesn't apply to counting flybys, there's no T-1 flyby, but likely they did it to remain consistent with how they count elsewhere.

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