orbital element

Orbital elements are parameters that describe an orbit (the path of an astronomical object gravitationally bound to another, particularly, a repeating pattern) according to a reference plane and a direction through that plane. Commonly used are six elements to describe a Keplerian orbit. Two of them describe shape and size of the orbit:

• eccentricity - a ratio describing the shape of the ellipse.
• semimajor axis - half the longest diameter of the ellipse.

The other four elements describe the orbit's attitude and the current phase, the latter which can be thought of as the current position of the orbiting body within its orbital path. These four are more challenging to describe so I'll use the following orbit-related terms:

• plane of reference - an otherwise-defined plane used as a basis for describing the orbit, e.g., the ecliptic.
• reference direction - an otherwise-defined direction through the plane of reference to be used in describing the orbit.
• orbital plane - plane in which the orbit resides (an undisturbed orbit is always planar).
• line of nodes - line through the plane of reference through which the orbit passes, i.e., the intersection between the orbital plane and the plane of reference.
• ascending node - the point on the line of nodes through which the orbiting body passes from the side declared "down" to that declared "up". (In the case of solar system orbits, the side to which Earth north points is also known as the north node.)
• descending node - similar point for the orbiting passing to the opposite "downward" (or south node in the solar system).

The remaining four orbital elements:

• inclination - angle at the intersection between the reference direction and the orbital plane.
• argument of periapsis - angle through the reference plane from the reference direction to the ascending node.
• longitude of ascending node (LOAN) - angle from the reference direction to the ascending node on the intersection.
• true anomaly - angle around the orbital plane from the ascending node to a line from the origin to the body's current location.

These six orbital elements are sufficient to describe the particulars of the orbit at a given moment, given a reference time (epoch), the orbit's position, a given reference plane, and a direction across the plane considered to be "upward". These givens could be provided by a given coordinate axes within a given frame of reference, a position vector to identify the orbit's position (e.g., to one of its foci), and a unit vector to identify a reference plane and the "upward" direction crossing it.