The elements of an orbit
 
In figure 1, the orbit of a planet P about the Sun S is shown. The orbit is an ellipse, for at the moment we consider the Sun to be the only mass attracting the planet. Let S be the direction of the First Point of Aries as seen from the Sun, and let the fixed reference plane be the plane of the ecliptic.
Then the planet’s orbital plane will intersect the plane of the ecliptic in some line NN₁, called the line of nodes. If motion in the orbit is described in the direction shown by the arrowhead, N is called the ascending node; N₁ is the descending node.
The angle SN is the longitude of the ascending node, usually denoted by the symbol Ω. The angle between the orbital plane and the plane of the ecliptic is called the inclination, i .

Figure 14.1. The unambiguous orientation in space of a planetary orbit by means of the orbital elements Ω, ω, i .
 
The two angles Ω and i , therefore, fix unambiguously the orientation of the planet’s orbital plane in space.
The orbit APA' lies in the orbital plane.
Let the orbit have perihelion A and aphelion A'. The line AA' is the so-called line of apsides. If SA is produced it will meet the celestial sphere in a point B. Then the orientation of the orbit in the orbital plane is given by ∠NSB, denoted by ω, and called the argument of perihelion. The size and shape of the orbit are given by the semi-major axis, a, and the eccentricity, e. It remains to fix the position P of the planet in its orbit at any given time t.
This can be done by using the formulas of the two-body problem’s solution, if any time τ at which the planet was at perihelion A is known.
The quantity τ is called the time of perihelion passage. For example, it may be 2000, April 14th, UT 22^h 47^m 12·^s4.
The six numbers, Ω, ω, i , a, e, τ , are referred to as the six elements of the planetary orbit. It is worth noting that it is the first five that describe the orientation, size and shape of the orbit. The sixth enables the planet’s position to be found within the orbit at any time.