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]).

Rainbow at
        Calanais I
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
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):
  1. the moon is above (moonday) or below (moonnight) the horizon for 12 hours (12 hour moonday or 12 hour moonnight)
    12 hour
            moonday or moonnight
  2. a moonnight has the same duration as the preceding or successive moonday (equal length moonday&night)
    Equal duration
            of moonday and moonnight
  3. 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!
    Moon days and
            night of 180 degrees
  4. 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:
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].

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


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