longitude of the ascending node

Two parameters remain unknown: inclination and longitude of the ascending node.

If the orbit is retrograde the the increases and the longitude of the ascending node decreases.

A greater range of values existed for the argument of perihelion and longitude of the ascending node.

Longitude of the ascending node, one of the orbital elements used to specify the orbit of an object in space.

Longitude of the ascending node (Ω)

The two main orbital elements that are measured with respect to the plane of reference are the inclination and the longitude of the ascending node.

The orbital plane is defined by two parameters, Inclination (i) and Longitude of the ascending node (Ω).

In astrodynamics, the longitude of the ascending node can be calculated from the specific relative angular momentum vector h as follows:

This ground track is shifted east or west depending on the longitude of the ascending node, which can vary over time due to perturbations of the orbit.

This is done by specifying the longitude of the ascending node (or, sometimes, the longitude of the node.)

Adding the argument of periapsis to the longitude of the ascending node gives the longitude of the periapsis.

The longitude of the ascending node is the angle between the reference plane's 0 longitude and the planet's ascending node.

However, if the convention of setting the longitude of the ascending node Ω to 0 is followed, then the value of ω follows from the two-dimensional case:

Longitude of the ascending node () defines the angle between the reference direction and the upward crossing of the orbit on the reference plane (the ascending node).

This means that inclination is always positive and is entangled with other orbital elements primarily the argument of periapsis which is in turn connected to the longitude of the ascending node.

Newton had asserted that the longitude of the ascending node, that marked where the shower would occur, was increasing and the problem of explaining this variation attracted some of Europe's leading astronomers.

For a typical prograde (in the direction of central body rotation) satellite orbit in a about the Earth, the longitude of the ascending node decreases, i.e. node precesses westward.

The angles of inclination, longitude of the ascending node, and argument of periapsis can also be described as the Euler angles defining the orientation of the orbit relative to the reference coordinate system.

As these orbits lack nodes, the ascending node is usually taken to lie in the reference direction (usually the vernal equinox), and thus the longitude of the ascending node is taken to be zero.

The longitude of the ascending node Ω, measured in the fundamental plane counter-clockwise looking southward, from a reference direction (usually the vernal equinox) to the line where the spacecraft crosses this plane from south to north.

Longitude of the ascending node - horizontally orients the ascending node of the ellipse (where the orbit passes upward through the reference plane) with respect to the reference frame's vernal point (green angle Ω in diagram).

In describing the Keplerian elements of an orbit, is sometimes used to denote the ecliptic longitude of the ascending node, although it is more common to use Ω (capital omega), which was originally a typographical substitute for the old symbol.

In the case of orbital elements for objects within the solar system, only a few of the classical orbital elements are affected by a switch of equinox: the longitude of the ascending node, and (to a much lesser extent) the inclination.

It is a prediction of general relativity consisting of secular precessions of the longitude of the ascending node and the argument of pericenter of a test particle freely orbiting a central spinning mass endowed with angular momentum .

The longitude of the periapsis is the sum of the mean longitude and the mean anomaly ( ) and the mean longitude of the sum of the longitude of the ascending node and the argument of periapsis ( ).