There is of course the heavy use of spherical trigonometry in most calculations. Those of us who sweated through plane trigonometry in highschool probably just touched spherical trig. However, there are some valuable spherical astronomy relationships that can be calculated without heavy math. The sky appears as a dome over the earth. If one includes what is below the horizon, it becomes a sphere, what we call the celestial sphere.
Spherical astronomy is concerned with angles.
A complete circle contains 360 degrees. The sperical analog of the straight line is the great circle, which if it were part of a plane, would cut the sphere in half. It is the shortest spherical distance between two points. The great circle equidistant from the poles at 0 is the equator. Longitude is much more arbitrary.