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These calculations must be performed for each line of position obtained. This means that for a Navigator to obtain a fix using only celestial objects he needs to spend about an hour at the chart table (20 minutes per line, three lines for a "cocked hat" [more certain position than just two lines]).
But in the middle of the ocean with no GPS, spending an hour to get a reasonably accurate fix was well worth the time. The down side is that the navigator was generally lucky to get a fix once per day.
You see, to get a three point astro fix, you not only need to be able see at least three celestial objects in the sky at the same time, but you also need to be able to see the horizon too. If it's too light objects like planets and stars are invisible; too dark and the horizon disappears.
Morning and evening twilight is when the navigator gets the best fixes.
There are ways to obtain fixes at other times during the day, most notably midday. I won't go into that in great detail except to say that with an accurate timepiece one can accurately measure the time at which the sun crosses the southern meridian. Almanacs are then used to obtain a longitude.
Hope this answers some questions folks have about astro.
Cheers
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a big thanks for this explanation. for the mod, some details should be changed, i think. if the navigator is happy to get one fix per day, it should be the same situation in the game. perhaps, the button "get a celestial fix" is only available 3 times a day? or the conditions for beeing able to press the button must be more restricitve: best weather conditions are needed. perhaps tdw can change this?