Using rotation matrices to calculate the locations of sunrise and sunset, the hours of daylight, observed path of the Sun, and its elevation angle for any latitude

Abstract

During the course of one year, I photographed 95 sunrises along the east bank of the Columbia River from my home on the west bank in Richland, WA (46.3° N latitude). I then calculated the seasonal phenomena listed in the title with the intention of explaining the variation of the photographed sunrises. The calculations use a simplified model of the Sun-Earth system and employ rotation matrices to predict the path of the Sun, as observed at any location in the northern hemisphere, throughout the year. These predictions are in good agreement with those listed by NOAA and also with the photographic data. The analysis presented here provides a novel way to calculate and understand the seasonal variations of visible sunlight.