[masklinn]

> why not do the calculating all other days than Friday and Saturday?

Note that assuming UTC reference point you need to bleed into sunday: Kiribati is on UTC+14, and you need to wait until some time after sunset (stars should be visible).

Though that makes me wonder how shabbat works in northerly latitude, how does shabbat work within the arctic circle?

[llimos]

Been there, done that. The commonly accepted ruling is to take the time that the sun is at its lowest point as simultaneous sunset/nightfall/midnight/dawn/sunrise (each of which has its own significance in Jewish law). So shabbat is from around midnight Friday to midnight Saturday.

It also means one can pray the afternoon, evening, and morning prayers one after the other.