Length of the ascending node

Orbit elements of the elliptical orbit of a celestial body around a central body (sun / earth)
Six orbit elements
a : Length of the major semi-axis
e : Numerical eccentricity
i : Orbital inclination, inclination
Ω: Length / right ascension of the ascending node
ω: Argument of the periapsis, periapsis distance
t : Time of the Periapsis passage, periapsis time, epoch of the periapsis passage
Further designations
M: Ellipse center. B: focus, central body, sun / earth. P: periapsis. A: Apoapsis. AP: apse line. HK: Celestial body, planet / satellite. ☋: descending node. ☊: ascending node. ☋☊: knot line. ♈: spring equinox. ν: true anomaly. r: distance of the celestial body HK from the central body B

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:

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

${\ displaystyle \ Omega = 125 {,} 0445 ^ {\ circ} -1934 {,} 1363 ^ {\ circ} \ cdot T}$
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 )