Orbital Elements

orbital elements [′ȯr·bəd·əl ′el·ə·məns]

(physics)

A set of seven parameters defining the orbit of a body attracted by a central, inverse-square force.

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Orbital Elements 

in astronomy, a system of quantities (parameters) that define the orientation of the orbit of a celestial object in space, the dimensions and shape of the orbit, and the position of the body in orbit at some fixed moment of time. The unperturbed orbit, in which a body moves in accordance with Kepler’s laws, is defined by six orbital elements.

(1) The inclination of the orbit i to the plane of the ecliptic or to the plane of the earth’s equator (in the case of artificial earth satellites). The inclination may have values of 0° to 180°. It is less than 90° if the body appears to be moving counterclockwise to an observer located at the north ecliptic pole or the north celestial pole and greater than 90° if the body appears to be moving in the opposite direction.

(2) The longitude of the (ascending) node ☊ or the right ascension of the (ascending) node α_☊ (in the case of artificial earth satellites); it may have values of 0° to 360°.

(3) The semimajor axis a of the orbit. The average motion of a body in an orbit n is sometimes used instead of the semi-major axis; in the case of unperturbed motion, the average motion is uniquely dependent on the semimajor axis.

(4) The orbital eccentricity e.

(5) The argument ω of perihelion or perigee (in the case of the moon or an artificial earth satellite); it may have values of 0° to 360°.

(6) The epoch (time) T at which the body is located at a certain point in the orbit, for example, at the ascending node or at perihelion or perigee. The start of the day is sometimes selected as the epoch; in this case, the orbital position is given by the mean anomaly M₀ at this epoch.

In the case of a perturbed orbit, the orbital elements are considered as functions of time and are usually represented as the power series

A = A₀ + A₁ (t – T₀) + A₂ (t – T₀)² + . . .,

where A₀ is the value of an orbital element A at time T₀.

N. P. ERPYLEV