Celestial Sphere: 3D Astronomical Geometry and Coordinate Construction

This GeoGebra example constructs a three-dimensional celestial sphere model, demonstrating how to translate the astronomical concept of the celestial sphere into an interactive geometric visualization. The core mathematical concepts involve spherical geometry, 3D coordinate transformations, rotation and angle measurement, as well as piecewise functions for describing celestial paths. The construction uses GeoGebra commands such as Circle, Vector, Point, Intersect, Rotate, Angle, and Segment, creating key objects like the celestial sphere, equator, ecliptic, and vernal equinox, with auxiliary points (P, P', Q, Q') and equations (eq1, etc.) to precisely represent positions and motions. This model is suitable for high school or university courses in astronomy, mathematics, or physics, particularly for teaching spherical coordinates, apparent motion of celestial bodies, or 3D geometric construction. It also serves as a valuable tool for teacher demonstrations or student exploration of the celestial coordinate system and the obliquity of the ecliptic.