Orbital Parameters

Although a very large number of parameters may be defined, at least six are required to fully describe the motion and instantaneous position of a satellite in an orbit. These six classical Keplerian orbital elements are defined as follows:

• Semi-major axis. The semi-major axis is half the longest diameter of the orbital ellipse. It is equal to the average of the apogee and perigee radii and defines the overall size of the orbit.
• Eccentricity. The eccentricity, e, describes how much the orbit deviates from a circle. A circular orbit has e = 0; an elliptical orbit has 0 < e < 1; a parabolic trajectory has e = 1; and a hyperbolic trajectory has e > 1.
• Inclination. The inclination, i, is the angle between the orbital plane and Earth’s equatorial plane, measured at the ascending node from the equator northward.
• Right ascension of the ascending node (Ω). The right ascension of the ascending node (RAAN) is an angular measurement in the equatorial plane from the First Point of Aries eastward to the ascending node. It defines the orientation of the orbital plane around the Earth. The RAAN is undefined for an equatorial orbit with i = 0° and is sometimes referred to as the longitude of the ascending node in Earth-centered inertial (ECI) coordinates.
• Argument of perigee (ω). The argument of perigee is an angular measurement within the orbital plane from the ascending node to perigee, measured in the direction of satellite motion. It defines the orientation of the orbit within the orbital plane. This parameter is undefined for equatorial orbits (i = 0°) and for circular orbits (e = 0).
• True anomaly (ν). The true anomaly is an angular measurement within the orbital plane from perigee to the satellite’s instantaneous position, measured in the direction of motion. It specifies the satellite’s position as a function of time and is the only orbital element that varies continuously with time. The true anomaly is undefined for a perfectly circular orbit (e = 0), since there is no unique perigee.