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