Up with the Sun: Empirically and mathematically

Throughout time people have been measuring the rising and setting positions of celestial objects with respect to the horizon. The motivation for this paper is to provide a link between mathematical and observational approximations for the Sun’s declination (angular distance from the celestial equator). One source had students do an experiment with an apparatus to measure the altitude of the Sun each day and graph data. Another paper provided an equation where students could solve for the declination on any given day. Here we show two approaches to computing the declination, the latter of which accounts for the elliptical nature of Earth’s orbit and reveals, perhaps counterintuitively for many students, that this inclusion has very little effect on the declination results. The sequence can be used as both a practical laboratory experience and mathematical exercise accessible to teachers. It can also be an elementary introduction to computer modeling.