The position of the sun based on a simplified model

Abstract

A simplified model for the position of the sun at any location on earth is shown to produce fairly accurate results when compared to values calculated in a spreadsheet from the United States National Oceanic and Atmospheric Administration (NOAA). A straightforward derivation of the model is presented, in which all terms and parameters have clear physical meaning. In the first version of the model, the only parameters are the tilt of the earth's axis and the date and time of the nearest northern hemisphere winter solstice. The differences between the elevation and azimuth calculated using the model and the NOAA results are typically a few degrees or less, and it is seen that the primary cause of these differences is the eccentricity of the earth's orbit. A simple correction is then added to the model, in which the only parameters are the earth's orbital eccentricity and the date and time of the perihelion nearest the solstice already in the model. This removes most of the differences between the model and the NOAA results. The model is shown to work in both the northern and southern hemispheres.