Amount of night sky at any place at any time of year

The composition of the night sky, as well as its quantity, change slowly throughout the course of the year. While the change in the appearance of the night sky from season to season is familiar to most amateur astronomers, the amount of sky that can be seen during any night is hardly ever remarked upon (apart from the general statement that there is more sky to be seen in winter because the nights are longer). In this paper I use elementary vector methods to calculate the total solid angle of sky (in steradians) seen in the course of the night at any place (latitude) on any day of the year. The results are compared with the duration of night at that location throughout the year. The effect of twilight on these estimates is also considered.