Orbital Elements

 Satellite motion in space can be determined if the location of the orbit, its size and shape, orbital spatial orientation and a point in time when the satellite is at a definite point on the orbit are known. Consider the motion of a satellite around the Earth as an example. Characterization of spatial orientation of an orbit requires a base system of coordinates. Its origin coincides with the orbit's O focus (that is, with Earth's center). Equatorial plane is adopted as the base plane OXY. Satellite orbit position will be determined in respect to such plane. OX axis crosses the equator at the point with longitude 0?, which corresponds to Greenwich meridian. Ecliptic plane is traditionally selected for the tasks that related to interplanetary travel. OX axis is oriented towards the point spring equinox. The equator crosses the orbital plane in two points. Ω crossing point from southern to northern hemisphere is known as the ascending node. The opposite point Ω' is referred to as the descending node. Ω angle between OX axis and direction to the ascending node OΩ is referred to as the ascending node longitude. Ascending node longitude lies within the range of 0? to 360?. If the orbit lies in equatorial plane, the ascending node is considered to be indefinite. The direct line, along which the orbital plane crossing the OXY base plane lies, is called the nodal line. Angle i between the equatorial plane and the plane of celestial body trajectory is known as the obliquity of orbital plane. This angle ranges from 0? to 180?. If 0? < i < 90?, then the satellite rotates in the same direction as the Earth does. Such motion is called direct. Clearly, obliquity may not be less than the launch point latitude in the case of a single-pulse entry into the orbit. This value is equal to 46.5? for the Russian satellites, which are launched from the Baikonur Launch Center. The pericenter distance is the minimum distance between the orbit and the central body, whose force determines the orbit. Imagine a straight line coming from the point O to the pericenter q, and a straight line coming from the point O to the celestial body's instant position M. Consider the angles in the orbital plane that shall be formed by these lines: ω - angular distance of the pericenter from the node and ν - true anomaly. Both angles may vary from 0? to 360?. The sum of these angles u = ω + ν is known as the latitude argument. The given elements are sometimes complemented by the epoch τ - time of passage through pericenter. Angles Ω and i fully determine the orbital plane. Large semi-axis and eccentricity e determine the shape of the orbit. Pericenter direction ω determines the orbital orientation on the plane, while latitude u (either true anomaly ν or epoch τ) determines the body's position on this orbit. This model illustrates the interaction of various orbital elements. If the switch that corresponds to a particular system line or point is not selected, the element appears in red. If a corresponding switch is selected, the object will appear in a different, bright color.