From the Scale Model of the Sky to the Armillary Sphere

TL;DR

This paper demonstrates the equivalence between a simple scale model of the sky and traditional armillary spheres, highlighting their educational value for illustrating celestial movements.

Contribution

It introduces a straightforward construction linking the scale model and armillary sphere, enhancing their use as teaching tools for celestial motion.

Findings

The scale model and armillary sphere are mathematically equivalent.

A simple construction can demonstrate their equivalence.

Armillary spheres can be effectively used in educational settings.

Abstract

It is customary to employ a semi-spherical scale model to describe the apparent path of the Sun across the sky, whether it be its diurnal motion or its variation throughout the year. A flat surface and three bent semi-rigid wires (representing the three solar arcs during solstices and equinoxes) will do the job. On the other hand, since very early times, there have been famous armillary spheres built and employed by the most outstanding astronomers for the description of the celestial movements. In those instruments, many of them now considered true works of art, Earth lies in the center of the cosmos and the observer looks at the whole "from the outside." Of course, both devices, the scale model of the sky and the armillary sphere, serve to represent the movement of the Sun, and in this paper we propose to show their equivalence by a simple construction. Knowing the basics underlying the operation of the armillary sphere will give us confidence to use it as a teaching resource in school.