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Investigating the major lunar standstill limit event in 2006

The following subjects are handled on this page:

Project goals

In 2006 a major declination standstill limit of the moon will happen again (happens every 18.61 years) and this web page will report on the observations of this event around the world. The following ideas/questions will be covered: To do this work, the e-group Archaeocosmology@yahoogroups.com is used since Feb. 2003 for dissemination, you can join this e-group.
In the below text more context is given about the issues around the major azimuth standstill events.

The lunar azimuth standstills

Important: There is a difference in the major/minor standstill limits in declination (which is the definition of major standstill limit) and the definition I am using below, which is about major/minor azimuth standstill limit. This is because the rise/set moments of the moon do not necessarily have to be the same moments as reaching the extreme declination. The same phenomena will change dates due to changing observation location. See this link for more info.

As already studied earlier, determining the date of the real major azimuth standstills limit is not easy. From that study, the window of 0.4 is there due to the fluctuation of the azimuth value of the major azimuth standstill limit over a long period (many cycles).
Furthermore the astronomical refraction will change the azimuth of set/rise point. Between winter (1030 mbar, 0C) and summer (990 mbar, 20C) the difference in refraction can be ~0.07  (which is a small estimation; in real practice it can be larger, up to 30% of the nominal value)  in apparent altitude. This is around 0.3 change in azimuth.
So all in all it is very difficult to determine the date of the real major azimuth standstill limit using a megalithic building.

Another way of looking at it, is looking at the calculated azimuth on different dates and different locations for months around the real major azimuth standstill limit date. This was done for Maeshowe (Orkney, Scotland), Callanish I (Lewis, Scotland), Mound A, Boyne Valley (Ireland, latitude: 53o 42' N and longitude 6o 29' W, height 30 [m]), Knocknarea (Ireland), Chimney Rock (USA, longitude: 107.3115 W, latitude: 37°.1897 N, height: 2.25 [km]) and Point Lookout (Australia, longitude: 153.458 E, latitude: 27.426 S, height: 0.01 [km])
In appendix II the major azimuth standstill values are determined in the period 2005-2007 for the above mentioned locations (the form of the moon has not been evaluated in this appendix). The major azimuth standstill limits found, change slightly per location and rise/set event:

The above ideas are also worked out on this comprehensive www-page of Thomas Schmidt.

In appendix IV are the major standstill for 2007 given (they are of course not so extreme as the one in 2006, but some people still might find it interesting to investigate on these dates)

Conclusions on azimuth standstills

Comparing results for 2005-2007 period

Rise/set

So the real southern major azimuth standstill limit happens on Sept. 29th, 2006 and the northern major azimuth standstill limit on April 4th, 2006. But from the above one can also deduct that other dates are very close (at least using JPL and linear interpolation). If we take into account the 0.3 window of astronomical refraction, we have at least 4 to 5 dates in that azimuth range (these entail a period of ~1 year, with intervals between the dates of multiples of the lunar tropical month (average ~27.32 days).
This idea is also mentioned by Thom ([1973], page 18):
"The Moon, it is true, in no sense stands still, but for about a year the limiting declinations do not vary more than 20 arc minutes, so that for month after month the Moon's declination goes through almost the same cycle."

Meridian transit

The dates when the maximum and minimum meridian transits happen are also different from the azimuth and declination standstill events, see Appendix III.

Phase periods

The phase periods (each period is almost 7 days in length) used in the below text are as follows (pictures of the moon are at meridian transit moments and come from NASA site):

Phase distribution

The distribution of phases near the northern azimuth for example Calanais I can be seen below (azimuth calculated is of centre of the moon, for other positions see here):

If we only take the moons in full darkness, astronomical and nautical twilight and we take into account that the azimuth of the upper part of illumination watched is different for lunar phases <100%, we get the following picture:


In both cases: quarter-ish moons happen closer to the northern azimuth, followed by new-ish moons and then full-ish moons.
The major azimuth standstill limit though becomes 335.6 instead of 336.1 and the difference between new-ish moons and full-ish moons is some 0.6°. Remember this is only an example, other locations can have different values and sequences.

Azimuth distribution

If one takes the 15 most northern quarter-ish moons and the 15 most northern full-ish moons one gets the below distribution regardless of the twilight/darkness conditions and azimuth calculated for centre of the moon (for other positions see here):

This could provide an idea how alignments will be distributed when looking at full-ish moons and quarter-ish moon (which spans a period of 2.5 years), so this include ritual aspect (full-ish moon) and the proto-scientific aspect (quarter-ish moons), for the 2005-2007 time frame (at Calanais I).
This gives an average of 334.7 +/- 0.7 (1s), while the major azimuth standstill limit is 336.1°. So a difference of around 1.5.

The total error in lunar azimuth (near standstill limit and close to Calanais I), is a combination of:

So when measuring the average alignments of a lot of monuments, assumed to be directed to azimuth standstill limit, a resulting error of around 0.9 would be expected to be seen.

Favoured moon set/rise event at minor/major azimuth standstill events

North
The below text is copied from North [1996], page 564-567:

Fig. 209. Extreme values on the graph of the Moon's declination for a typical series of lunations
around major northern and southern standstills. The period covered is about 43 months. The lunations
are numbered consecutively and the approximate phase of the Moon is shown for each.

The new moon is strictly unobservable, lost as it is in the glare of the Sun. Although the Moon becomes visible within a day or two of new moon, the general insignificance of corresponding declinations (and thus azimuths) when it does so is noteworthy (see the points marked 6, 21, 23, 25, 34, 36). Although Semitic peoples have attached great religious importance to the first observation of the lunar crescent after the new moon, they have taken no particular notice, as far as can be seen, of lunar standstills.
The quarters give more or less the true extremes. At first quarter (the disc is shown blackened on the left half) the Moon has passed the Sun in ecliptic longitude by about 90°, so the Sun is high in the sky when the Moon rises, but has set long before the Moon sets. Only under very special atmospheric conditions is this moonrise visible. At third quarter, it is only the rising of the Moon that is likely to be visible.
Full moon is a conspicuous event, notable in its own right, and observations of its occurrence on the horizon could have been observed if they fitted readily into the scheme of standstills. Consider the alternatives: roughly speaking, if the Moon is on the horizon at full, then the Sun cannot be far from the opposite horizon. As far as visibility is concerned, refraction and parallax are of much less importance than the difference in declination of the Sun and Moon. In cases 7 and 37, at the winter solstice, the Moon is to the north of the ecliptic degree opposite the Sun, so that when the Moon is on the horizon, whether rising or setting, the Sun is a few degrees above the opposite horizon. In both cases the Moon is difficult to see. In cases like 22, however, with the Moon south of the ecliptic, it sets before the Sun rises, and rises after sunset.
This describes the ideal situation, but winter full moons like 7 and 37 should not be dismissed too readily. The Moon moves rapidly roughly thirteen degrees per dayand a day on either side of full moon makes little difference to its declination, but through change in ecliptic longitude can make all the difference between visibility and invisibility. First, therefore, some remarks from the devil's (or rather sceptic's) advocate.
Even alignments to cases like 5, 9, 35, 39, 20, and 24, while neither major standstills nor full moons, might have been recorded. There are many causes of uncertainty in the smaller details of interpretation of lunar alignments. To take two of a dozen potentially problematic instances: even after an azimuth has been converted to a declination, only a combination of an obliquity and a lunar inclination has effectively been found. Unless the obliquity is known independently (say from the year) no conclusion can be drawn about the inclination, and thus none about its difference from the mean. Secondly, the same alignment might be ambiguous, for instance, as between the direction of (1) an actual extreme of type 7, and (2) the only visible Moon in the neighbourhood of an extreme of type 15 (assuming that the weather interfered with other observations).
It seems reasonable to suppose that observations were made over periods of time long enough to stake out correctly alignments to significant standstills. As for major standstills at the winter solstice full moon, they could have been observed wherever an artificial horizon was created high enough to ensure that the Sun had well and truly set by the time the Moon rose. It might have been twilight still, but the Moon would have been visible, given the right atmospheric conditions.

Which types of lunar alignment are then most likely to have been favoured? For reasons that have now been explained, the following three bullets seem most probable:

  1. Northern lunar setting at first quarter, being more or less the ideal major standstill. Occurring near spring equinox (see case 15). Inclination (i) is increased over its mean value by 8.7' (...). In this context it is intriguing to recall Pliny's reference to the culling of mistletoe by the druids on the sixth day of the moon.
  2. Southern lunar rising at third quarter, being true major standstill. Two weeks later than the above, near the spring equinox (see case 16). Inclination as above, but declination now negative (south of equator).
  3. Southern lunar rising or setting at summer full moon. The inclination at this type of major standstill is then a minimum (10.0' below the mean, ...), but the assumption is that the brightness and general character of full moon makes it an attractive proposition.
  4. The example of Stonehenge, however, recommends a fourth bullet:
  5. Northern lunar rising or setting at winter full moon. The inclination is that under bullet 3. Given a regular horizon such will occur with the Sun above the horizon, but sunset may be guaranteed either by an artificial horizon or an unusually high lunar horizon.
These suggestions do not preclude alternatives (such as phases near full moon, or cases where the best that can be found over a short period is for a nondescript phase), but the bullets listed here do seem inherently more probable than the rest.
There remains the problem of how the perturbation affects minor standstills. From similar arguments to those given already, first-quarter spring settings and third-quarter autumn risings seem intrinsically likely to have attracted attention (as being near the absolute limit), as do summer full moons (on account of their appearance and brightness). Adjustments to the inclination are exactly as in the corresponding bullets cases for major standstills, and the corrections in azimuth are of the same order of magnitude.
Ponting
A point about observing quarter-ish moons in Ponting ([1981], page70-71): At these phases the moon has no illuminated upper limb (or lower limb). A little bit lower (at least within 0.125 degrees altitude) the moon is of course illuminated. Ponting says that this will not be a valid moon form to observe! I think Ponting assumes that the neolithic people knew the moon was round and because the upper limb existed but invisible, they dismissed that form. I think that neolithic people perhaps did not (yet) know that the moon was round, but perhaps they thought it to be a form that rotated in the sky (I think one could design such a form quiet easily that looks like the moon when using naked-eye observations, by rendering an 3D object).
So I would say that with a quarter-ish moon, the upper part of the illuminated moon form can be used for observations, see below.
Curtis
Curtis has publish a document on the Calanais major standstill limit event [Curtis [2003]). Two things are very interesting in this document:
Thom
Thom did observations at monuments and documented the declinations found (necessary when comparing multiple locations). See below picture from Thom ([1973], page 77):
Thom does not talk about different lunar shapes; he even only uses full moon forms in all his figures! So looking at the graph it seems he is working from the idea that full moons are observed (semi diameter is always 15'.9). But the strange things is that these full moons are not at the major declination ±(e±i+D), only quarter moons are!
So it needs more study why Thom did not mention this, as it is certainly not obvious from his Fig. 2.3 ([1973], page 20), where full Moons are not near the limits.
It is also clear from Thom ([1973], page 26, 106 and 110) that he was interested in the maximum of the perturbation (the perturbation cycle is 173.31 Days), because that specific moment is a danger zone for full/new moons to become eclipsed, as the Sun is in line with the lunar nodes.
The maximum of the perturbation was only measurable at standstill limit event due to the methodology proposed by Thom (the interpolation device; Thom [1973], page 83), although this maximum can be experienced of course at all local maximum lunar declination events.
Another issue with perception of the max. perturbation moment is of course the very indeterministic behavior of refraction, which can be in the order or larger then the total perturbation.

The following pages which are interesting (if one is member of the archaeocosmology group one can see the below links):
It has to be noted that Ruggles ([1999], page 59) was not able to reproduce the above picture (Fig 7.1) after independent assessment of horizon notches.
An evaluation
Summary on historical/ethnographic evidence for standstill limit alignments
This overview of an evaluation on historical/ethnographic evidence made on the HASTO-L list is interesting to read (Bradley Schaefer [1998]). The conclusion is that there is no evidence of any historical/ethnographic references on this. Bradley's conclusion on lunar alignments is:
"This conclusion places a heavy burden on anyone who claims that a lunar orientation is actually an alignment, as they must provide evidence of intention when all evidence shows that no one has any interest at all."

A good list of criteria is given by Schaefer [2004] concerning alignments (as I call: intentional directions).
The
author of this web page proposes a somewhat changed sequence of criteria (changes with regard to Schaefer are in purple). Intentional can be by design or by usage of the monument. The below criteria can also be used by any other discipline (like archaeoacoustics):
  1. the astronomical case for the claimed alignments, or more general; is the case properly evaluated by the discipline studied.
    Schaefer had this criteria as the last criteria in the list, but criteria A is essential to fulfil, without this no reason to continue with the following criteria.

  2. statistical significance over the null hypothesis, where a multi-site analysis is almost essential (a single site will never be able to reach a pure statistical significance). Schaefer [2004] assumes that minimally a 3 or 4-sigma threshold is needed.
    There can be chosen a few null hypothesis like:
  3. archaeological information
  4. historical documents or ethnographic information on the culture in question or more weakly, ethnographic analogy with other cultures.
    For an analogies, the argument might go something like "Almost all societies recognize the solstices while many have alignments to them, so it is plausible to think that a solsticial orientation observed for a prehistoric monument like Stonehenge is actually an alignment."
    Remember that historical documents can also be a whole new discipline (like myths or Linear A), and it might be that for these texts one needs to start again with criteria A in an iterative way.
    An example: We can even transpose Linear A to (for us) normal text symbols, but we still are not able to interprete the meaning...
  5. The above criteria B, C or D might not be the only way, in the humble opinion of the web master, to proof beyond reasonable doubt that intend is in place. It is important to be aware that art, positioning in the sky/sound/landscape, the monuments themselves, etc. all express intend by people, otherwise why do it!
    Such expression are part of this criteria E (which is comparable with criteria D, but
    criteria D is restricted to modern type of printed text). The interpretation might be lacking, but we have the same problems as in criteria D (compare it with the interpretation problems about Linear A).
    To solve
    criteria E, we need to start for that the particular discipline again with criteria A, in an iterative way (but not circular way!). Further ideas are welcome.
A paradox
There is a paradox with the above criteria and the actual classification of some recognized astronomical sites, IMHO.
If there is no possible positive evaluation for criteria D and E (say for Neolithic, prehistoric monuments), than only criteria B or C could be used for to see if there is astronomical intend. In case there is no archaeological proof and if the building is unique in its construction, no progress can be made with the above criteria on an astronomical alignment:-( Or should we just use analogy under criteria D?
One could say: "It is unique, and thus the chances are very very small it is constructed by  chance."  but that is in most cases not a valid deduction.

IMHO there is a paradox between these five criteria and looking at what people recognize as astronomically aligned monuments. A lot of pre-historic unique buildings (like Newgrange, Stonehenge, etc.) are recognized as being build by intend with astronomical guidelines. I don't think this is due to criteria B, C, D or E... So why are these buildings still recognized as being astronomically aligned by intend?

To be honest, I think that it should be possible to see a unique construction (and lacking B, C, D and E criteria) as astronomically important. A present day example: a cathedral is unique, and it stands for something that is made by intend.
So I am in principle using the analogy part of criteria D, which is very dangerous, I know.

Putting my paradox in another way:
For me both principles are valid. So there is a gap in the above criteria.
Literature on visibility
According to North, Ponting, Curtis and some other people, it is in principle possible to see the set or (and) rise of a moon's form from say 25% illumination at low apparent horizon altitudes (thought not during day time).
It is planned to change the visibility program (based on Schaefer [2000]) in such a way that it can also predict the visibility of the moon in the sky (and not only in an enclosure).
The below table of  lunar phases which happen in general at (near) majorstandstill events has been compiled using the information from Ponting ([1981], page70-71), North, others and myself. It also provides ideas about the visibility the set and rise events.
Major standstill (a)
Perturbation (b)
Near solar event
Rising Moon
Setting Moon
Southern (-e-i)
Max. (-D)
spring equinox
Southern (-e-i)
Min. (+D)
summer solstice
Southern (-e-i)
Max. (-D)
fall equinox
Southern (-e-i)
Min. (+D)
winter solstice
Northern (e+i)
Max. (+D)
spring equinox
Northern (e+i)
Min. (-D)
summer solstice
Northern (e+i)
Max. (+D)
fall equinox
Northern (e+i)
Min. (-D)
winter solstice
With d=a+b
Red cells are most probable moments favored by North
Why are blue cells not ranked by North? I would rank them also.
Green cells are less likely, but still possible, I think.
Partly lit moon
If looking at the effect of the different forms of the Moon (using SkyMap to determine the orientation of the form) and the experienced maximum azimuth (disregarding refraction):
Theoretical visibility
A graph has been made of the moon phase visibility using formula's from Schaefer [2000]:
  • using formula (12), (10), (9) and (11) to determine just the moon illuminance (Bmoon) seen on earth. Done for apparent altitude of , 0.75° and 0.5°.
  • using formula (35) (with Bsource=B+Bmoon) and (36b) or (36c)  (with z=0.2°) to determine (by iteration) which B just reveals the setting or rising moon.
  • using the table in Schlyter, horizon brightness at different twilight conditions is determined.
  • The below graph is the result (with the following important parameters; visibility range 20 km, location Ireland, height 60m, around May, 23 year observer):
    Rule of thumb
    Although the variability of the atmosphere makes it hard to predict what will be visible, one could imagine good days hopefully were more plentiful in former times;-). At this moment I don't have yet a final rule of thumb, but based on some 40 observation to hazy horizons near sea-side here in Ireland and with apparent altitudes around 0.75: This rule of thumb will be updated when more information is gained. This rule of thumb is mapping the theoretical model.

    Logging near horizon lunar observations

    One can fill in the observation form for all lunar observations you do.

    Why and when to witness celestial (lunar) events.

    Several reasons can be heard for why and when to witness a celestial (lunar) event:
    The above reasons are all valid. The above reasons are used at present, so I am sure that all these reasons (and more) were also used in pre-historic times (and thus perhaps fixed in a neolithic monument).
    Any reason is a valid intend/experience, because the reason can be the driver for human action (even if it is scientifically not correct).

    Azimuth value of major azimuth standstill events in ~3000 BCE

    The azimuths values of major azimuth standstill events in ~3000 BCE have different value than at present (~2000 CE) dates due to change in obliquity. For the Calanais I location this has an 2.4° influence on the azimuth, which has an influence of some 0.6° on the apparent altitude.

    Major azimuth standstill dates until 2100

    The following major azimuth standstill events are calculated for dates around the major standstill limit and for the location of Calanais I  (the form of the moon has not been evaluated in this appendix):

    Help for determining the limit events

    One can make one's own overview of set/rise dates of the moon near their major/minor standstill limit. A web-page show how to get the JPL data.

    If one follows the above given method (don't forget to fill in the longitude, latitude and height of the location you want to see), one gets an e-mail back from JPL with all the set and rise times.

    Save and rename the e-mail content to a file with extension .txt. Start you spreadsheet program (like Excel) and get the text file in it using File -> Open... with File of type: Text files *.txt and use Delimited option with Comma delimiters and Finish for opening the file. When the file is in the spreadsheet, select the whole worksheet and then Data -> Sort... on the Column D (Azi_ column).
    This results in an ordered file, where one can see which dates are the limit dates.

    Acknowledgements

    I would like to thank the following people for their help and constructive feedback: Margaret and Ronald Curtis, David McNaughton, Thomas Schmidt 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: March 22, 2003