The present article is the result of a research work of the Degree in Mathematics in the scope of the Tutorial Education Program -PET. The work deals with concepts of Spherical Trigonometry, which has several fields of applications between mathematics and physics, related to cartographic problems, navigation and astronomy. The goal is to explore problems of astronomy applications of celestial bodies by making use of trigonometry concepts in the sphere to study positions and directions of stars in terms of a celestial sphere. In order to reach this objective, the article presents concepts of a smaller distance between two points in the sphere, a triangle of position that is the spherical triangle, the fundamental relation known as law of cosines, the Celestial Sphere, its elements, its coordinates in the equatorial system, horizontal system and time system. Thus, the work seeks to encourage students and teachers to work on Spherical Geometry in the classroom