Spherical Trigonometry

When we look into the sky, it seems that the Sun and all the stars are located on a sphere of a large but unknown radius. In other words, the location of the Sun is defined by a point on the celestial sphere. On the other hand, the surface of Earth is, to a good approximation, a sphere. Any location on Earth can be defined by a point on the terrestrial sphere; namely by the latitude and the longitude. In both cases, we are dealing with the geometry of spheres.

To study the location of the Sun with respect to a specific location on Earth, we will correlate the coordinates of the location on the terrestrial sphere of Earth with the location of the Sun on the celestial sphere. The mathematical tool of this study is spherical trigonometry. In this Appendix, we will give a brief introduction to spherical trigonometry, sufficient to deal with the problem of tracking the sunlight.

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