The library · The other points and bodies

The true north lunar node

the true (osculating) north lunar node, the point a Western chart labels True Node, shown beside the mean node the corpus reads elsewhere

What the tradition reads

The two north nodes a chart can print are one crossing reckoned two ways. Wikipedia's orbital node page defines a node as a point where an orbiting body meets its chosen plane of reference, the ecliptic in the Moon's case, and its lunar node page gives the ascending or north node as the crossing where the Moon moves into the northern ecliptic hemisphere. The Swiss Ephemeris carries both versions as separate bodies, SE_MEAN_NODE and SE_TRUE_NODE, and its documentation sets out the difference. The mean node is a smoothed element, derived there from Moshier's lunar routine, an adjustment of the ELP2000-85 lunar theory to the JPL ephemeris, and holding to a mean orbit that leaves out the short monthly fluctuations. The true node is, in that documentation's words, "usually considered the osculating node element of the momentary lunar orbit", the intersection line of the Moon's orbital plane of the moment with the plane of the ecliptic. The same passage gives the ground for preferring it, that when the Moon is exactly conjunct the true node it does have zero latitude, not so with the mean node, and the ground for doubting it, that even the true node is "true only twice a month", at those two crossings. The pages consulted name no school of astrologers for either node, and give the true node no reading apart from the node's own.

The story

The nodes were tabulated long before they could be computed instant by instant, and the older tables gave one steady speed. Lucia Bellizia's study of the nodes, which calls such accounts legends, preserves the report of Severus Sebokht, a seventh century Syrian bishop, that eclipses were laid to a serpent named Atalia, twenty four degrees wide and one hundred and eighty long, head and tail diametrically opposed, moving from east to west by three minutes and eleven seconds a day and completing its revolution in eighteen years, seven months and sixteen days. Gerolamo Vitali's Lexicon Mathematicum, quoted in the same study, still has the Moon's nodes moving backwards about three minutes each day. Modern averages sit near those tables: Fred Espenak's NASA account gives the mean retrograde rate as 0.05295 degrees a day and one turn in 18.6 years against the fixed stars, while Wikipedia's lunar node page puts the nodal period at 18.612958 years. What the osculating reckoning added is the wobble around that average. Espenak notes that osculating elements hold for a single instant only, and that the instantaneous node's westward motion "draws to a near standstill" whenever the Sun aligns with either node, while the Swiss Ephemeris documentation lays the monthly oscillation to the Sun's strong perturbation of the lunar orbit. Neither gives a figure for the largest gap between the two nodes.

Written from

Corpus key point:TrueRahu.