The orbits followed by two point masses obeying Newtonian mechanics are conic sections, such as ellipses, hyperbolas, parabolas, and lines. Understanding them is important to understanding orbital mechanics. Conceptually, conic sections are formed from the intersection between a plane and a cone. More formally, it is the loci of points in a plane where the ratio of the distance from a fixed point (the focus) to a fixed line (the directix) is a constant.
Stable orbits have the shape of ellipses. Ellipses can be described by the length of the major and minor axes can also be used. These aren't useful for orbits.