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#35: Star Trek: The Original Series, season 2, episode 12 "The Deadly Years"
Written by David P. Harmon, directed by Joseph Pevney.
Stardates 3478.2 through 3479.4 (December 2267)
"The heart is not a logical organ." - Dr. Janet Wallace
The Enterprise arrives at Gamma Hydra IV for a routine check-in of a Federation outpost and are met with silence. Investigating where everyone went, Ensign Chekov startles himself by stumbling upon the body of a very old man in a darkened room. As the landing party questions why such an old person would even be on the planet, they are greeted by two other elderly humans who insist they are only in their late 20s. When they return to the ship, issues with those who went down to the planet lead to a realization that they are all suddenly aging rapidly. All except for Chekov.
Originally released: 8 December 1967
"The Deadly Years" on Memory Alpha
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What did you think?
Commodore Decker had basically lost his mind at that point, so I don't think it's nece-celery a case of Commodores not necessarily making good captains. Other captains (Garth and Tracey) also went partially insane, and they were otherwise above-average.
So it may moreso be highlighting the idea that captaincy on star ships requires a strong collection of talents and character, and may in fact be hard on such folks, over time.
I guess I'm forgetting, but what other episodes are you thinking of?