Trying to grok the draconic year

[swampwiz]

From Wikipedia:

The draconic year, draconitic year, eclipse year, or ecliptic year is the time taken for the Sun (as seen from the Earth) to complete one revolution with respect to the same lunar node (a point where the Moon's orbit intersects the ecliptic). The year is associated with eclipses: these occur only when both the Sun and the Moon are near these nodes; so eclipses occur within about a month of every half eclipse year. Hence there are two eclipse seasons every eclipse year. The average duration of the eclipse year is

346.620075883 days (346 d 14 h 52 min 54 s) (at the epoch J2000.0).

So should this be interpreted as the axis of the sidereal lunar plane precessing at a rate of 346.62/366.25 of a revolution per sidereal year (i.e., the ratio of the draconic & sidereal years) about the axis of the ecliptic?

 

[Janus]

It takes ~6798 days for the Moon's orbital plane to complete a 360 day precession.
To get the 346 day draconic year, you need to use the formula:
Td = 1/(1/Te+1/Tm)*
where Te is the period of the Earth's orbit. (to be exact, the sidereal period of 365.256... days vs the Tropical year* of 265.242... days)
And Tm is the period of the Moon sidereal orbital precession.

* It is +1/Tm due to the direction the orbit precesses. If the orbit had precessed in the opposite direction, you would have needed to use -1/Tm instead.
** The Tropical year is what our calendar strives to keep in sync with.

 

[stefan r]

365.242