Similar to vehicles, you track which direction each starship is facing, called its heading. However, because the sensor map is a 1D line, there's only two options. Now here's what heading does:
A starship is off-guard to attacks made from the opposite direction of the starship’s heading. Starships in the same zone always treat each other as being in the direction of their heading. Specific rules and actions might have different results depending on starships’ headings.
That's it. (There's a whole paragraph about your starting heading when an encounter begins, but it's just "use common sense and GM discretion".) The basic actions while helming a pilot's console --specifically Boost Thrusters and Change Heading-- clearly mention that you move in the direction of your heading and change that heading separately.
i couldn't really find anywhere else heading comes up, but the ordinance hinges upgrade for gunneries lets you attack "in any direction, ignoring the starship’s heading" ...when neither starship weapons nor the gunnery itself mention heading at all. Ordinance hinges have no other benefit. And using a starship weapon isn't even a special station action, the gunnery just passively grants regular attacks the station trait (if you helm the gunnery and use starship weapons installed on it, oc).
(Rotate Armament (the action ordinance hinges gives you) is also just kinda odd since it lasts a single turn, i guess you're then forced to rotate back as a free action. idk why artillery would snap back.)
TLDR / My questions for you: Did i just miss the RAW for "you can only fire forwards"? Would you allow some weapons to be mounted backwards by default? How would you track firing arcs in tactical starship combat? Do you just not bother, and delete ordinance hinges?