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Light effects with short/long line alignments

1. The disk size of the sun/moon (0.5°) will make the difference between light and dark less obvious (penumbral region). Certainly on the side walls which are in almost the same direction as the sun/moon.
2. The variation of refraction due to weather changes a apparent altitudes lower then say 0.5° (some variation of 0.18°) and the variation of the lunar parallax (0.1°) due to distance between moon and earth, can change the reproducibility. Certainly on the side walls when they are in almost the same direction as the Sun/Moon.
3. An uneven surface can make it more difficult to see where a shadows stops and starts. Certainly on the side walls which are in almost the same direction as the Sun/Moon.
4. Horizon markers or side stones can sometimes not be repositioned to the same location/slant as 5000 years ago. So erosion, vegetation growth, dilapidation and reconstruction factors (taphonomy in archaeology).

• Chamber and passage:
• If the light effect plays on the side wall (so the location of the light is important), the reproducibility (accuracy) decreases with the length of a passage.
Say we have a passage of some 35 meters long, 1 meter wide and the orientation of the passage is some 260° (like in Knowth Site I west) and relatively flat side walls (like in Maeshowe).
So looking at the above points:
1. Due to the disk size of the Sun/Moon  the penumbral region is 0.5° and the gradual change from dark to light can be some 7 m at the end of a 35 m long passage.
2. The variation of refraction and variation of lunar parallax are together in the order of 0.2°, and thus can be at least 2 m at the end of a 35 m long passage.
3. On a flat passage side (like in Maeshowe) it is already quiet difficult to see where the shadows stops and starts. With bumpy side walls like in Newgrange and Knowth this becomes even more difficult. In some cases side stones have not been repositioned at the same location/slant as 5000 years ago (like in Knowth).
   

If the celestial object is a few degrees of from the main direction of the passage; the end of shadow, the length emerging shadow area (penumbral region) and the variation due to refraction/parallax on a side wall are calculated below:



Angle between main passage direction and celestial object	End of the shadow [m]	Length of penumbral region  [m]	Variation due to refraction  [m]
2°	33	6.9	2.12
5°	12	1.1	0.4
10°	6	0.3	0.02

So if the expected light effect is on the side wall, the accuracy will diminish if it is further away from the entrance, due to the possible variation in refraction/parallax and to the fact the shadow is not hard (but gradual). The effect of dilapidation and reconstruction makes it even more unpredictable.
Shadows near the entrance will be more accurate.
A strange effect will happen when there is reflection or artificial light in the passage; the effect of the penumbral region is lessened and thus the accuracy of the passage side walls can be increased by an additional light source (there will of course be some optimum)!
• For light on planes almost perpendicular on the Sun's/Moon's rays (such as back walls or protruding side stones) the above points are less influential. The penumbral region on the back wall of Maeshowe can be seen in a simulation.
 

Location of back wall from entrance [m]	Angle between main passage direction and celestial object	Length of penumbral region [m]	Variation due to refraction  [m]
33	1°	0.31	0.12
12	2.5°	0.11	0.04
6	5°	0.06	0.02

The penumbral region is approximately 1% of the length of the passage and the effect of refraction/parallax is some 0.4%. The penumbral region is in some case smaller, because the sun is passing along an internal wall (like in a chamber, in that case the penumbral region is 1% of the chamber size).
With protruding side stones the effect of dilapidation and reconstruction is making it more unpredictable.
• To determine the sunniness of a passage, see this link.
  The number of days that a the sun is in a building is depending on its length and width. The longer and the narrower the passage, the fewer number of days the sun is inside (also covered in the above bullet). As stated above, there are these effects of refraction, but they are less important then when looking at the location the light falls on side walls.
  
• Chance of random directions with passage.
  
• Stone rows (or other earthly objects):
• Two stones on a row
  The variation of direction is determined by two view lines, see the below picture of two stones in a row:
  
  
  
  So the viewing range depends on the distance between the two objects (can be stones or circles) and the effective width of the objects (the effective width of the objects is depending on the average azimuth and the angle of the stone surfaces). The viewing range does not assume a certain observation position.
  Also here the celestial object's diameter (like moon and sun) will provide the penumbral region and thus effectively the celestial object range is at least two times half the object's diameter (0.5° minimum)  in angular width.
  A few other parameters that determine the viewing and celestial object range:
  • the size of the viewing range:
  • the effective width of the stone has a minimum value (approximately the width of the thinnest side).
    Default: 0.15 m
  • a person can stand a certain distance beside the edge of the viewing stone and still having the idea he/she is looking past the nearest stone (e.g. shoulder against nearest stone).
    Default: 0.3 m
  • the viewing line is extended with half of the celestial object's width at the remote stone, to cover the subjective idea of nearness of the celestial object to the remote object.
    Default: 0.25° in azimuth
    
  • the variability of apparent horizon altitude due to refraction.
    
  Default: 0.075° in altitude (if apparent altitude is above 0.5°).
  • the size of the celestial object range
  • half the width of the celestial object is still covering the declination (half of the penumbral region).
    Default: 0.25° in geocentric declination
    
  • the skewness of the observations (towards declination zero). Due to declination variability during plus and minus 5 days (or equivalent for lunar standstill) the actual standstill.
    Default: 0.2° in geocentric declination
    
• Several stones on a row
  If pairs of stones in a row have overlapping viewing ranges, this set of more then 2 stones is seen as a row of several stones.
  The viewing range of several stones in a row  is defined by the viewing lines on each side of the row (so not crossing the central line, but somewhat in parallel). The above parameters play the same role in this configuration.
  
  
  
• Gaps/pinholes:
• Gaps between stones/objects
  Something for to future to fill in...
• Pin hole aperture
In some cases the sky window is quiet small, at least smaller than the angular width of the Sun/Moon. These pin hole aperture alignments can be seen in some cathedrals (see Heilbron [1999]). The penumbral region is not effecting the reproducibility, because the hole is small and the reproducibility is not influenced by refraction either (because they are mainly high in the sky). They are though effected by dilapidation and reconstruction.
The effect of a  pin hole aperture was seen at Cairn L, Loughcrew (but it could be a modern one) ad Treasury of Atreus.
• Horizon marker
For a remote horizon marker the above points are less important, because the horizon marker itself will have been influenced by the refraction as are the Sun/Moon (see the reappearing sun at Orkney). And like in Maeshowe, most of the time it is not using the whole disk of the celestial object, but only a small part (so no big penumbral region). See also at the end of the animated picture (the reappearing sun light due to the steep slope (horizon marker) of Ward Hill).
A horizon marker does in principle not need a building, and thus dilapidation or reconstruction don't play a major role. Erosion and/or vegetation growth could have taken place of course.

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