Why Phi? – a luni-solar link

This was a surprise, but whatever the interpretation, the numbers speak for themselves.

‘Richard Christopher Carrington determined the solar rotation rate from low latitude sunspots in the 1850s and arrived at 25.38 days for the sidereal rotation period. Sidereal rotation is measured relative to the stars, but because the Earth is orbiting the Sun, we see this period as 27.2753 days.’ – Wikipedia.

What happens if we relate this period to the lunar draconic year?

‘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).’ – Wikipedia

How many Carrington rotations in a draconic year?

346.620075883 / 27.2753 = 12.708204
12.708204 / 3 = 4.236068 = Phi³
[1.618034(Phi) + 2.618034(Phi²) = 4.236068]

So the ratio of the Carrington rotation to the draconic year is exactly (3*Phi³):1

We saw in an earlier post that the full moon cycle occurs around 3 * Phi² per lunar apsidal cycle, and that this was about the same as the number of quasi-biennial oscillations (QBO) per lunar nodal cycle.

There’s also another very similar correlation with a planetary element to it, which will appear in a later post.

Phi: the golden ratio.