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

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 illumination zone on the Earth, and the illumination time is estimated in a particular latitude with the uniform circular movement of Earth. The present model was confronted with the numerical results of the Geoscience Australia Agency and it is found a maximum percent error of 1,6%, which was due primarily to the difference between the circular trajectory, in this model, and the real elliptical trajectory. Without the use of spherical trigonometry, it was obtained an analytical model that estimates very close the solar illumination time at any time of the year and at any latitude on Earth. This model provides an authentic context for studying basic aspects of physics.

model; astronomy; physics education; teaching methods