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Comparing Knowth and Calanais I

Knowth and Calanais I look to have both an easterly and an westerly direction (at Knowth it are two passages and at Calanais I it are two lines of stones). gillies macbain relates Knowth to the moon and Calanais I seems also to be strongly related to the moon (Ponting [1981]).

Calanais I

Calanais I seems closely related to two lunar events; both the southern and northern major lunar standstill limit events can be seen from this monument. But the whole region of Callanish is located in such a way that the moon rises during the southern major standstill limit from the Sleeping Beauty and then initially sets behind the Mullach an Langa and to reappear in Glen Langadale (the Clisham range) (Ponting [1981]).

Sleeping Beauty

There was a discussion on the Archaeocosmology list about lunar mid-point rises and mid-point sets (by Doug Schwartz, who found this idea in William Romain [Mysteries of the Hopewell, 2000; page 250-251]), and this stimulated me to look more into some possible lunar events former people could have investigated.
Beside the lunar standstill limit (equivalent to solstices) one could also witness perhaps equinox-like events (somewhat equivalent to solar equinoxes). I am not talking here about the strict astronomical definition of lunar equinox (declination of zero); I assume that would not be 'understood' in former times.
So what could equinox-like mean in the eyes of former people? Perhaps they could have used the same methodology as with the sun: so equal length of day and night or opposite (180º) set and rise or...
For the moon several possible equinox-like events could be defined (the azimuth graphs shown are for Knowth, Ireland between Sept. 2004 and Sept. 2007 CE [thus incl. a major standstill limit event], altitude 0º, calculations with a max. error in arc of 1º (sigma ~ 0.4º) and a max. error in time of 5 min (sigma ~ 2 min) are based on JPL HORIZON):

the moon is above (moonday) or below (moonnight) the horizon for 12 hours (12 hour moonday or 12 hour moonnight)
a moonnight has the same duration as the preceding or successive moonday (equal length moonday&night)
during a moonday the moonset is 180º from the moonrise or during a moonnight the moonrise is 180º from the moonset (180º moonday and 180º moonnight).
This one is the same as the mid-point rise/set idea quoted in Romain [2000])
Remark: Hively and Horn [1982/1984], whom are quoted by Romain, missed though the interesting dual azimuth direction (they only talked about the ~93º azimuth) seen with these 180º moonday&night!
the Spring (Equinoctial) Full Moon discussed by C. Da Silva [2004], which in its turn is mentioned by F. Silva (Equinoctial full moon models and non-Gaussianity: Portuguese dolmens as a test case, [2011]) is another possible equinox-like event (not yet evaluated in this page). The event is defined as the moment that the rise (or set) of the Sun and Full Moon have swapped location on the horizon (so at some moment the Sun rises more southern (or northern) than the Full Moon).

A few rules could be duducted from this work:

12 hour moonday:

the rise azimuth for Knowth/Calanais (lat: 53/58º) can be ~84º or ~91º (around major standstill limit) and ~85º or ~90º (around minor standstill limit).
set azimuths are some ~186º higher.

12 hour moonnight:

the rise azimuth for Knowth/Calanais (lat: 53/58º) can be ~91º or ~97º (around major standstill limit) and ~92º or ~96º (around minor standstill limit).
set azimuths are some ~174º higher.

Equal length moonday&night:
- the rise azimuth for Knowth/Calanais (lat: 53/58º) are ~85º or ~96º (around major standstill limit) and ~87º or ~95º (around minor standstill limit).
- for Octagon Earthworks (lat: 40º): ~86º or ~95º (around major standstill limit).
- the sets are at ~270º
- The equal length moonday&night matches in some cases the 12 hour moonnight&day
180º moonday&night:

the rise azimuth for Knowth/Calanais (lat: 53/58º) can be ~87º or ~93º (around major standstill limits) and ~88º or ~92º (around minor standstill limits).
for Octagon earthworks (lat: 40º) can be ~89º or ~91º (around major standstill limits) and ~88º or ~92º (around minor standstill limits).
the sets are (of course) 180º higher
the 180º moonnight is normally not following the 180º moonday.

the azimuths don't really change going back in time (so they are comparable around 2006 CE and 2995 BCE)
the rise azimuth changes with the same amount as the difference in altitude altiude_rise-altitude_set (in case of a uneven horizon).

Below a comparison between Knowth and Calanais I is made. It was hoped that these equinox-like events could perhaps explain the easterly and westerly direction, but so far no real statistically-valid results. Any constructive feedback is thus welcome on technical level and possible informed cultural/historical/ethnographical links is welcome. An interesting evaluation on lunar standstill limits has been made by B. Schaefer [1998].

	Knowth	Calanais I
Year of build	~3100 BCE	~2050 BCE
Latitude	53^o 43'	58^o 12'
Westerly direction/apparent altitude	258.6^o/0^o	267.3^o/0.5^o
Easterly direction/apparent altitude	85.0^o/0.4^o	79.7^o/0.5^o
Southern major standstill limit (rise/set)	147.6^o/213.6^o	161.7^o/198.3^o
Northern major standstill limit (rise/set)	35.8^o/325.4^o	25.3^o/334.7^o
12 hour moonday (rise/set azimuth)	84^o/270^o	84^o/270^o
12 hour moonday (rise/set azimuth)	91^o/277^o	91^o/277^o
12 hour moonnight (set/rise azimuth)	271^o/97^o	271^o/97^o
12 hour moonnight (set/rise azimuth)	265^o/91^o	265^o/91^o
Equal length moonday&night (rise/set azimuth)	85^o/270^o	85^o/270^o
Equal length moonday&night (rise/set azimuth)	96^o/270^o	96^o/270^o
180º moonday&night (rise/set azimuth)	87^o/267^o	87^o/267^o
180º moonday&night (rise/set azimuth)	93^o/273^o	93^o/273^o

assuming apparent horizon in east and west for moon night&day calculation as zero

Acknowledgements

I would like to thank the following people for their help and constructive feedback: Jo Coffey, Doug Schwartz and all other unmentioned people. Any remaining errors in methodology or results are my responsibility of course!!! If you want to provide constructive feedback, let me know.

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Major content related changes: Oct. 30th, 2004