elements, orbital

elements, orbital Six quantities that describe the size, shape, and orientation of an orbit. They can be used to calculate the position of a body in its orbit at any given time. For planets orbiting the Sun, the ecliptic and the vernal equinox (the first point of Aries) are used as a reference plane and reference direction respectively (see the diagram). The orbital elements are then: the longitude of the ascending node, Ω; the inclination, i; the argument of perihelion, ω; the semimajor axis, a; the eccentricity, e; and a final number that gives the position of the planet in the orbit at a given time (or epoch). This can be the time of perihelion passage, T (or τ), the longitude at the epoch, L, or the mean anomaly at the epoch, M. For a comet with a highly eccentric orbit, the semimajor axis is usually replaced by the perihelion distance, q.

 If the orbiting body is the Moon, the orbital elements are modified; the argument of perihelion is replaced by argument of perigee, and time of perihelion passage by time of perigee passage. Furthermore, if the orbiting body is an artificial Earth satellite, the ecliptic is replaced as reference plane by the equator, and the longitude of the ascending node is replaced by the right ascension of the ascending node, α.

 For any other body with satellites, such as Jupiter or Saturn, the reference plane is either the planet's equator if the satellite is near the planet, or the planet's orbital plane if the satellite is strongly perturbed by the Sun.

 When an orbit is subject to significant perturbations, its orbital elements are given for a specified time; these are known as osculating elements.