Lunar Node Calculator

What the mean and true node are

For the models, accuracy and data behind these figures, see the methodology and sources page.

The Moon's orbit is tilted about 5 degrees to the ecliptic, the plane of Earth's own orbit, so it crosses that plane at exactly two points on opposite sides of the sky: the ascending node, where the Moon climbs from south of the ecliptic to north, and the descending node, half an orbit later, where it sinks back from north to south. Because the Sun's gravity constantly tugs on the tilted orbit, the whole line joining the two nodes slowly turns westward, a full circuit every 18.6 years, the regression of the nodes. See the lunar nodes explained for the full picture with a scrubbable 3-D view.

The mean node is a polynomial that models only the steady average regression and ignores the smaller wobbles; it is the figure this site's eclipse year page and Celestial Return Calculator use as "the node". Jean Meeus's version (Astronomical Algorithms, chapter 47) is the one used here. But the Moon does not actually follow the smooth mean curve. Solar gravity perturbs the Moon's orbital plane on a shorter rhythm as well as the long one, so the point where the Moon truly crosses the ecliptic, the true node, oscillates around the mean position by roughly 1.5 degrees, nearly 2 at the extremes, and occasionally appears to pause or even move briefly forward before the regression resumes. This calculator finds the true node directly: by searching the vendored astronomy engine for the actual instants the Moon's ecliptic latitude passes through zero, then reading the Moon's own longitude at that moment. It is the same lunar theory that positions the Moon everywhere else on this site, evaluated at the crossing itself. Ephemerides that print a true node for every day usually give the osculating node, the orbital element fitted to the Moon's position and velocity at that instant: it coincides with the crossing longitude at the crossing itself and drifts from it by up to about a degree in between, so this page reports the true node only at its crossings.

Why the difference is worth showing

Eclipses depend on the Moon's real position, not a smoothed average: the gap between the two is not a rounding error, and it can shift a marginal eclipse season in or out of range.

It answers a narrow question, for any date from 1700 to 2200: what the Moon's node is actually doing, from the same engine that drives this site's eclipse pages, and what that means for the next eclipse season.

How this tool works

The mean node comes from Meeus's published polynomial (Astronomical Algorithms, chapter 47). The true node comes from the vendored Astronomy Engine's own search for the Moon crossing the ecliptic plane, refined to about a second of time, the search tolerance rather than the error; right ascension and declination are geocentric, referred to the true equator and equinox of date (precession and nutation applied). The mean node is Meeus's mean-equinox figure and the crossing longitude is true-equinox, a nutation difference under 0.005 degrees, below the two decimals shown. Light-time and aberration are not applied: at the Moon's distance they together amount to about 0.7 arcsecond, far below the arcminute shown. Positions come from the open-source Astronomy Engine, running entirely in your browser, and the model is reliable for roughly the years 1700 to 2200, with future crossing times carrying the delta-T uncertainty described in the accuracy study. The zodiac positions are the tropical ecliptic longitude of date, with 0° at the spring equinox, the same convention used across CycleCalcs.