Let us characterize all planetary orbits using a common Cartesian coordinate system , , , centered on the Sun. See Figure 4.6. The - plane defines a reference plane, which is chosen to be the ecliptic plane (i.e., the plane of the Earth's orbit), with the -axis pointing towards the ecliptic north pole (i.e., the direction normal to the ecliptic plane in a northward sense). Likewise, the -axis defines a reference direction, which is chosen to point in the direction of the vernal equinox (i.e., the point in the Earth's sky at which the apparent orbit of the Sun passes through the extension of the Earth's equatorial plane from south to north). Suppose that the plane of a given planetary orbit is inclined at an angle to the reference plane. The point at which this orbit crosses the reference plane in the direction of increasing is termed its ascending node. The angle subtended between the reference direction and the direction of the ascending node is termed the longitude of the ascending node. Finally, the angle, , subtended between the direction of the ascending node and the direction of the orbit's perihelion is termed the argument of the perihelion.
Let us define a second Cartesian coordinate system , , , also centered on the Sun. Let the - plane coincide with the plane of a particular planetary orbit, and let the -axis point towards the orbit's perihelion point. Clearly, we can transform from the , , system to the , , system via a series of three rotations of the coordinate system: first, a rotation through an angle about the -axis (looking down the axis); second, a rotation through an angle about the new -axis; and finally, a rotation through an angle about the new -axis. It thus follows from standard coordinate transformation theory (see Section A.6) that
In low-inclination orbits, the argument of the perihelion is usually replaced by, is often replaced by the mean longitude at —otherwise known as the mean longitude at epoch—where the mean longitude is defined
The heliocentric (i.e., as seen from the Sun) position of a planet is most conveniently expressed in terms of its ecliptic longitude, , and ecliptic latitude, . This type of longitude and latitude is referred to the ecliptic plane, with the Sun as the origin. Moreover, the vernal equinox is defined to be the zero of longitude. It follows that, , ) are the heliocentric Cartesian coordinates of the planet.