# Length of the ascending node

In celestial mechanics, the **length of the ascending node** ( **node length for** short ; symbol *Ω* ) of an orbit around the sun is the heliocentric angle to be measured in the ecliptic ( reference plane or reference plane) between the ascending node ☊ and the spring point ♈.

The length of the ascending node is one of the six orbit elements (see graphic) that suffice for a sufficient description of an - ideal - Kepler orbit. Together with the inclination *i* and the argument of the periapsis *ω* , it belongs to that subgroup of orbit elements that defines the *position of* the orbit plane in space .

## Other central bodies or reference planes

In the case of central bodies other than the sun and / or other reference planes than the ecliptic, “length” generally means the first polar coordinate of a spherical coordinate system .

Depending on the type of object whose path is specified, they, the following reference are flat usual:

- for solar orbital objects of the solar system , d. H. for planets , asteroids , comets : the ecliptic
- where the length of the ascending node is its ecliptical length (
*longitude of the ascending node, LOAN*), measured from the vernal equinox .

- where the length of the ascending node is its ecliptical length (
- for objects that do
*not*orbit the sun: the equatorial plane of the central body that the object orbits instead; For example, for earth satellites with a uniform orbit semi-axis : the plane of the earth or celestial equator (see satellite orbit elements ).- where the length of the ascending node is its right ascension (i.e. the equatorial length, English
*right ascension of the ascending node, RAAN*), again measured from the vernal equinox, but this time along the equator.

- where the length of the ascending node is its right ascension (i.e. the equatorial length, English
- for the earth's moon : the ecliptic
- where the length of the ascending node is its ecliptical length , measured geocentrically from the vernal equinox .

## Time dependence

In the case of Kepler orbits (only *two bodies* in a vacuum ) the length of the knot is constant and the orbital plane remains stable in its alignment under the fixed stars .

In the case of gravitational disturbances from third bodies , the length of the node suffers small, sometimes periodic changes. The orbit element is therefore given as a series of oscillating terms with respect to an epoch , i.e. as an approximate solution that is valid at a certain point in time .

As a first approximation, the value for the length of the lunar knot is given as

- with
*T*as time argument in Julian centuries since the epoch J2000.0 ( Lit .: Vollmann, 3.5 p. 26).

The approximately 19.34 ° in a Julian year (365.25 days) correspond to one complete rotation of the knot line in 18.61 years, the nutation period .

## literature

- Andreas Guthman:
*Introduction to celestial mechanics and ephemeris*calculation*, theory, algorithms, numerics*, 2nd edition. Spectrum Academic Publishing House, 2000 - Jean Meeus:
*Astronomical Algorithms*. Willmann-Bell Inc., 2009 - Wolfgang Vollmann:
*Changing star locations*. In: Hermann Mucke (Hrsg.):*Modern astronomical phenomenology.*20th Sternfreunde Seminar, 1992/93. Planetarium of the City of Vienna - Zeiss Planetarium of the City of Vienna - Zeiss Planetarium and Austrian Astronomical Association , 1992, pp. 55–102 ( online )