Mathematical modelling of photoperiod: equation to calculate the photoperiod at any location on the planetary surface

Our lives, since ancient times, have been shaped by the position of the Sun in the sky. Not only agriculture, but also the functioning of modern urban societies, depends on the presence—or absence—of light provided by our central star. In this context, the ability to determine the duration of natural daylight (photoperiod) has long held significant interest across various domains of human activity. In this work, we present a new equation that enables the calculation of the photoperiod for any location on Earth’s surface. Although approximate, the equation yields results that closely match observational data. The mathematical tools involved fall well within the scope of an undergraduate course in the exact sciences: chiefly, vector analysis and trigonometry. From astronomy, only elementary principles are employed. This makes the work accessible both for applied investigations and as a pedagogical tool to deepen the understanding of fundamental concepts encountered in undergraduate education. Although it has not yet been implemented in the classroom or developed in collaboration with students, such applications are clearly possible.