Trying to grok the draconic year

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In summary, the draconic year is the time it takes for the Sun to complete one revolution with respect to the same lunar node. It is associated with eclipses and has an average duration of 346.620075883 days. This can 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 about the axis of the ecliptic. To calculate the 346 day duration, the formula Td = 1/(1/Te+1/Tm) is used, where Te is the period of the Earth's orbit and Tm is the period of the Moon's sidereal orbital precession. The Tropical year,
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swampwiz
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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?
 
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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.
 
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365.242
 

Related to Trying to grok the draconic year

What is a draconic year?

A draconic year is a unit of time used in astronomy and astrology, representing the time it takes for the moon to return to the same position in its orbit relative to the same star, which is approximately 27.212 days.

How is a draconic year different from a solar year?

A draconic year is shorter than a solar year, which is the time it takes for the Earth to complete one orbit around the sun. A solar year is approximately 365.24 days, making it about 13 times longer than a draconic year.

Why is it called a "draconic" year?

The term "draconic" comes from the Greek word "drakon," meaning dragon. In ancient times, the lunar nodes (the points where the moon's orbit intersects with the ecliptic) were thought to resemble the head and tail of a dragon, and the draconic year was used to track the moon's movement through these points.

How is the draconic year used in astrology?

In astrology, the draconic year is used to calculate the moon's position in relation to the lunar nodes at the time of a person's birth. This is believed to give insight into a person's soul and spiritual path.

Can the draconic year be used to predict eclipses?

Yes, the draconic year is also used to predict eclipses. Since the lunar nodes are involved in eclipses, tracking the moon's position in relation to them using the draconic year can help predict when eclipses will occur.

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