Estimation of solar illumination time on the earth by an analytical model: a fertile scenery for to teach physics

TL;DR

This paper presents an analytical model to estimate Earth's solar illumination time across different latitudes and times of year, simplifying assumptions to aid physics education with minimal trigonometry.

Contribution

The authors developed a simple, analytical model for calculating Earth's illumination time that closely matches numerical results, enhancing physics teaching tools.

Findings

Maximum perceptual error of 1.6% compared to numerical data

Model estimates solar illumination time without spherical trigonometry

Applicable for any latitude and time of year

Abstract

We proposed an analytical model for the calculus of illumination time of the Earth for any time of year and any latitude, this model assumes the obliquity of the ecliptic as constant, the light beams as parallels, the Earth as spherical, the movement of translation of Earth as uniform circular, also this model showed a context of the astronomy whereby the teachers can teach the basic physics.It was built through a relationship between the movement of translation and of rotation of the wave front light, then we found the of illumination zone on the Earth and the illumination time is estimated in a particular latitude with the uniform circular movement of Earth. Present model was confronted with the numerical results of the Geoscience Australia Agency and it is found a maxim perceptual error of 1,6%, this value was assigned primarily to the difference between the circular trajectory, in this model, and the elliptical trajectory that is the real. Without the use of spherical trigonometry was obtained an analytical model that estimates very close the solar illumination time at any time of year and any latitude on earth, the model provides an authentic context for studying basic aspects of physics.