Before we can understand the positions and motions of celestial bodies, it is necessary to have an understanding of spherical geometry. **Spherical geometry** is the study of geometry on the surface of a sphere and is the spherical analogue of the planar geometry you will have studied at school.

We all know that the shortest path between two points on a plane is a straight line. On the surface of a sphere, however, there are no straight lines. The shortest path between two points on the surface of a sphere is given by the arc of the **great circle** passing through the two points.

A great circle is defined to be the intersection with a sphere of a plane containing the centre of the sphere. If the plane does not contain the centre of the sphere, its intersection with the sphere is known as a **small circle**.

We will meet great circles and small circles again, later in the course...

A great circle divides a sphere into two equal halves