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Predicting Sunrise and Sunset Times

For a given location and day of the year, can you predict the times of sunrise and sunset? Although the solution to this problem is somewhere between old and ancient, the standard solution requires the understanding of a considerable number of preliminary ideas from celestial mechanics. The following approach uses only simple tools from trigonometry and analytic geometry to produce a fairly good set of approximations for sunrise and sunset times. One can leave it at that and have a nice project for average students or, for students with stronger backgrounds, one can pursue certain corrections that make these sunrise and sunset predictions quite accurate. These corrections can be studied at any level from a simple "Here's the source of the error and here's a term that we can add on to fix it," to a more complete analysis involving Fourier sine series and a deeper understanding of celestial mechanics.