The manual page on the playership HUD doesn't mention it. Anyone know what its for?

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That's you're SETA indicator. When it's solid white/blue (whichever colour it shows up for you), SETA is available to activate, when it's spinning around, SETA is active
When it's solid red, incomming missile
Missile targeting you afaik. Had it only once, and then the spinner didn't stop spinning until game restart too.