## Why Phi? – a luni-solar link

Posted: December 11, 2018 by oldbrew in moon, Phi, solar system dynamics
Tags: , , ,

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, or frequency, with a planetary element to it which will appear in a later post.

Phi: the golden ratio.

1. Curious George says:

The Sun does not rotate as a solid body, so you can pick any one of many rotation periods, to prove almost anything.

2. oldbrew says:

The Carrington rotation is the rotation period of sunspots. That’s the idea at least.

https://sohowww.nascom.nasa.gov/explore/lessons/diffrot9_12.html

3. Curious George says:

[Wikipedia] The Carrington rotation is a system for comparing locations on the Sun over a period of time, allowing the following of sunspot groups or reappearance of eruptions at a later time.

Because the Solar rotation is variable with latitude, depth and time, any such system is necessarily arbitrary and only makes comparison meaningful over moderate periods of time. Solar rotation is arbitrarily taken to be 27.2753 days for the purpose of Carrington rotations.

4. oldbrew says:

If we use the draconic month (27.21222 days) instead, the result is only marginally different.

432 draconic months = 431 Carrington rotations.
Which raises the question of why the lunar motion is so similar to the sunspot motion.

5. oldbrew says:

Study: The 27-day variation in the Mg II index of solar activity [2015]

Abstract
The 27-day variation attributed to the solar rotation is one of the most prominent periodicities of solar variations on short-term time scales.

– – –
CORONAL HOLES – SWPC @NOAA
Coronal holes can develop at any time and location on the Sun, but are more common and persistent during the years around solar minimum. The more persistent coronal holes can sometimes last through several solar rotations (27-day periods).

https://www.swpc.noaa.gov/phenomena/coronal-holes
– – –
Windows to the Universe®: Storms that Recur with the Solar Rotation (~27 Day Intervals)
https://www.windows2universe.org/spaceweather/build_storm4.html

6. oldbrew says:

Rotational Quasi-Periodicities and the Sun – Heliosphere Connection
– JPL and Calif. State Uni.

Abstract. Mutual quasi-periodicities near the solar-rotation period appear in time series based on the Earth’s magnetic field, the interplanetary magnetic field, and signed solar-magnetic fields. Dominant among these is one at 27.03 ± 0.02 days that has been highlighted by Neugebauer, et al. 2000, J. Geophys. Res., 105, 2315. Extension of their study in time and to different data reveals decadal epochs during which the ≈ 27.0 day, a ≈ 28.3 day, or other quasi-periods dominate the signal.

https://arxiv.org/ftp/arxiv/papers/0803/0803.3260.pdf
– – –
Carrington’s figure looks like an attempt at a mean value of these quasi-periodicities.