Estimation of solar zenith passage on the Earth's surface by a simple harmonic motion

TL;DR

This paper models the solar zenith passage on Earth as a simple harmonic motion using a uniform circular motion approach, comparing it with Stellarium data to validate the analytical model.

Contribution

It introduces a simple harmonic motion model for solar zenith passage based on Earth's rotation and compares it with software data for validation.

Findings

Uncertainty of about 1 day in the model's predictions

Model effectively describes solar zenith passage as simple harmonic motion

Provides a basis for further kinematic studies of Earth's solar interactions

Abstract

The kinematics of the Solar zenith passage on the Earth was shown as a simple harmonic motion. This analytical model used the uniform circular motion to describe the Earth's rotation relative to its axis and relative to the Sun, also this model considered the sunlight beams parallel and constant the obliquity of the ecliptic. We made a contrast between some data taken from of the software Stellarium 0.12.1 and the model, we obtained an uncertainty $\Delta t=1d$; this result allow to project the model as an astronomical context conducive to develop the kinematics of simple harmonic motion.