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Archaeoastronomy


Equinox Observations at Atlatl Rock


Valley of Fire State Park, NV, USA

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Analysis and Results

    Definition of Terms

    Analysis of the 2008 "Observation"
    Analysis of the 2010 Observations
    Analysis of the 2011 Observations (summer solstice):   see   My Visits
    Analysis of the 2015 Observations (too early terminated daily):   see   My Visits
    Analysis of the 2017 and 2018 Observations
    Sunrise Observations
    Timetable of Primary Shadow Events


 

Definition of Terms

Time

Nevada: Pacific Daylight saving Time (PDT) = UT - 7h;
(daylight saving time in effect from mid March to begin of November)
|T10|

Due to the equation of time, local noon is different in March and September (|T07|):
Local noon (Sun due south from Atlatl Rock) in March/April:
      March 20:   12:46 a.m. PDT
      March 30:   12:43 a.m. PDT
      April   10:   12:39 a.m. PDT
Local noon (Sun due south from Atlatl Rock) in September:
      September   1:   12:38 a.m. PDT
      September 10:   12:35 a.m. PDT
      September 20:   12:32 a.m. PDT
time to/from astronomical equinox:
        E ± fraction of days
        (e.g. E - 1.44 is 1 day and 10 hours and 34 minutes before equinox)
 

Correction of the Clock Drift of the Camera

The time of my camera always had been set to UT.
Like almost each clock, this clock has a drift that has to be taken into accout if it is ≥ 1 minute to calculate the proper coordinates of the Sun (Az, El).
If times quoted have been corrected, they are marked with "tc".

Horizontal Coordinate System

For the position of the Sun the horizontal coordinate system is used where:
      - the azimuth (Az) of the Sun is the angle in degrees from North; measured   N -> E -> S -> W
      - the elevation (El) is the height of the Sun in degrees above the horizon
 

Equinoxes and Solar Quarter Days

The astronomical equinox is defined as the moment when the plane of the Earth's equator, which is tilted with respect to the orbital plane of the Earth around the Sun (the ecliptic) passes through the center of the Sun. This happens twice a year: in spring around March 20 (vernal equinox) when the Sun apparently crosses the plane of the earth equator from south to north, and in fall around September 22/23 (autumnal equinox) when the Sun apparently crosses the plane of the earth equator from north to south.

The astronomical equinoxes are not directly observable by the naked eye nor could the equal lenght of day and night (= equinox) be determined with sufficient accuracy by the sunwatchers of ancient times.

However, the astronomical equinoxes are close to the middle (in days) between the summer and winter solstices which could be determined by counting the days from a solstice. These "middle" days are sometimes called quarter days as together with the solstices they divide a year into four quarters of equal length.
I prefer to call them solar quarter days as not to confuse them with the quarter days used in England and Ireland which have a different definition.
Due to the variable speed of the Earth in its elliptical orbit around the Sun, which is a little bit faster in winter, the astronomical equinoxes are off by about two days from the solar quarter days. The solar quarter day in spring is two days after the astronomical vernal equinox, the solar quarter day in fall is two days before the astronomical autumnal equinox.

Throughout this web pages I use the term "equinox" for a time span of a couple of days around the astronomical equinox including the solar quarter days.
 

The Markers

At the Atlatl Rock site there are three outstanding petroglyphs which are proposed to indicate the time around the equinoxes by showing some "interaction" with a shadow edge in the hours before and around local noon. They belong to a group of petroglyps which, among other pictures, show an atlatl, giving the rock its name.

The proposed equinox markers are four concentric circles (known to be a sun marker) and an outlined cross (proposed to be an equinox marker at least at this site). In addition, there is a (left?) "foot" that may have also some function. All petroglyps (exept the "foot") are to the left of an imaginary line tangent to the upper edge of the concentric circles and the outlinded cross.

The "foot" is the only petroglyp that is in interaction with the shadow edge closest to the solar quarter days and the equinoxes.

   

The alignment and the dimensions of the concentric circles and the embedded cross are such that they are parallel to the shadow edge.
The shadow is tangent to the upper edges of the two markers at the same time. This is true also for the centers and the lower edges of the markers.
This is shown here on the pictures taken September 13, 2018:



shadow at upper edge of markers
at 10:59tc a.m. PDT


shadow at center of markers
at 11:30tc a.m. PDT


shadow at lower edge of markers
at 11:59tc a.m. PDT
tc : the time has been corrected for the clock drift of the camera.

 

Self Shadow

One special feature of the wall with the petroglyps at Atlatl Rock is that once the azimuth of the Sun is larger than ~ 174 degrees, which is at about 12:15 p.m. PDT or about 15 minutes before local noon, the wall is in total shadow as the Sun is then "behind" the plane of the wall.
This I call "self shadow" to distinguish it from the shadow cast by the rock south of the wall that produces the shadow whose upper edge is the shadow line that at certain moments passes through the centers of the markers. After local noon the whole area is in shadow cast by the "tower" and the whole Atlatl Rock massiv.
 

Picture Points

All the pictures taken to document the movement of the shadow line across the petroglyps at Atlatl Rock in 2015, 2017, and 2018 were always made from the same location on the stairs to the platform, the standard picture point for the markers.
The point on the stairs from where the pictures were taken was choosen in such a way that the cross was directly visible above one of the struts of the platform to check the proper position.
The pictures taken to document the sunrise location on the eastern horizon were always made from the same point on the platform, the sunrise picture point. This point is directly at the strut that marks the proper alignment of the view to the markers.

 

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Analysis of 2008 "Observation" - The Discovery

Observation made on September 12, 2008 at 11:30 a.m. PDT.

Daylight saving time 2008 in Nevada started March 9 and ended November 2.
|T13|

Astronomical autumnal equinox:
      2008-09-22-15:44 UT   =   2008-09-22-08:44 PDT (Nevada)
|T12|

(Only two) pictures taken:
    2008-09-12-11:30 a.m. PDT (18:30 UT; view from parking lot),
        Sun azimuth 151.83 deg (i.e. east of meridian) ,
        Sun elevation 54.21 deg
    2008-09-12-11:32 a.m. PDT (18:32 UT; at the petroglyps); see right
        Sun azimuth 152.63 deg (i.e. east of meridian) ,
        Sun elevation 54.40 deg

distance from equinox:
      9.84 days before astronomical autumnal equinox
      8 days before autumnal solar quarter day

With the knowledge after the 2018 observations it is clear that the pictures were taken few minutes after the shadow line crossed the centers of the markers on its way downward to beyond the markers during the secondary shadow movement>. This is about 45 minutes before the wall with the petroglyps is in total shadow (c.f. the almost identical shadow position on September 13, 2018 at 11:31 a.m. PDT).

 

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Analysis of the 2010 Observations

Observations made on September 21, 2010 from sunrise until the petroglyphs were all in self shadow.

Daylight saving time 2010 in Nevada started March 14 and ended November 7. |T13|

Astronomical autumnal equinox:   2010-09-22-20:09 p.m. PDT;   JD 2455462.63137 |T12|

The picture shown below was the last one taken with a well defined shadow edge before the whole rock was in self shadow (which was 6 minutes later at about 12:12 p.m. PDT). The movie combines all pictures of the markers made on that day.


Picture:  2010-09-21-12:06 p.m. PDT;  JD 2455461.29583
time to/from eqinox:   E - 1d.35 ;
Sun:   azimuth   169.33 deg ,   elevation   53.64 deg
This is the only picture I have taken where the kink and the shadow of the "tower" are clearly visible!





The pictures for this movie were taken from 09:29 a.m. PDT (16:29 UT) till 12:11 p.m. PDT (19:11 UT); note that this are close-ups of the region of the petroglyps around the markers and are not taken from a "standard" position.
At the time of the visit I had assumed that the upper edge of the shadow would reach the center of the markers at the day of the equinox. As it turned out later (2017 and 2018 visits; see below), the last time this alignment occurs is already a couple of days before the date of the autumnal equinox. Later, like in this observation one day before astronomical autumnal equinox, the shadow edge no longer reaches the centers of the markers and is always above and the markers are always below the shadow line!.







For the 2011 (summer solstice) and 2015 observations no further detailed descriprion and analysis is necessary here. They are described in sufficient detail on the My Visits page under 2011 and 2015.


 

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Analysis of the Combined 2017 and 2018 Observations Around Autumnal Equinox

The observations that contribute to the analysis described here were all made between September 13 and 21 (2018 and 2017).

Note: all descriptions that have not been "observed" but can be derived from the observations are printed in italics.

Astronomical autumnal equinox was on
          September 22, 2017 at 01:02 p.m. PDT and on
          September 22, 2018 at 06:54 p.m. PDT.

Autumnal solar quarter day was on
          September 20, 2017 (at 3:26 p.m. PDT) and on
          September 20, 2018 (at 9:14 p.m. PDT).


Detailed Descripton of the Observations Made on the Nine Days Before Autumnal Equinox

By combining the 2018 and 2017 observations, the time span nine days before the autumnal equinox up to one day before the autumnal equinox is covered. On each of the nine days pictures have been taken every 15 minutes after 10:15 a.m. PDT until the shadow edge was no longer well defined as the wall started to be in self shadow around 12:15 p.m. PDT. They have been combined into movies for each single day (SDxx; September 13 to 21) and for the same time (STxxxx; 10:15 a.m. PDT in steps of 15 minutes to 12:15 p.m. PDT).

The numbers in the following matrix are picture (image) numbers (per year) and the time (in minutes) to be added to the time in the left column to calculate the time the picture was taken. Although I aimed to take the pictures always at the same time intervall, sometimes I missed that by few minutes.

Time
[PDT]
     date   (yyy-mm-dd)
time to equinox   [days]
same time
  2018-09-13
-9.29
2018-09-14
-8.29
2018-09-15
-7.29
2018-09-16
-6.29
2017-09-17
-5.04
2017-09-18
-4.04
2017-09-19
-3.04
2017-09-20
-2.04
2017-09-21
-1.04
 
09:45 a.m. 1272 (+4) 1448 (-1) 1642 (-1) 1823 (-5) 2636 (+1) 2781       ST0945
10:00 a.m. 1279 (+4) 1453 (-1) 1644 (-1) 1828 (-2) 2639 2789 (+1)       ST1000
10:15 a.m. 1285 (-1) 1461 (-1) 1650 (-1) 1834 (-2) 2647 (+1) 2795 (+1) 3001 (-1) 3229 (+1) 3357 (+1) ST1015
10:30 a.m. 1290 (-1) 1465 (-1) 1662 (-1) 1838 (-1) 2655 (+1) 2806 (+1) 3020 (+1) 3235 (+1) 3363 (+1) ST1030
10:45 a.m. 1294 (-1) 1471 (-1) 1665 (-1) 1844 (-2) 2658 (+1) 2813 (+2) 3024 (+1) 3244 (+1) 3369 (+1) ST1045
between 10:45 a.m. and 11:00 a.m. PDT the shadow edge starts to move downward due to the slope change of the shadow casting rock edge
11:00 a.m. 1301 (-1) 1473 (-1) 1671 (-1) 1853 (-1) 2664 (+1) 2817 3027 (+1) 3250 (+1) 3375 ST1100
11:15 a.m. 1305 (-1) 1478 (-1) 1676 1857 2671 (+1) 2825 (+1) 3034 (+1) 3262 (+1) 3382 ST1115
11:30 a.m. 1328 1481 (-1) 1688 1870 (-1) 2675 (+1) 2831 (+1) 3044 (+1) 3267 (+1) 3390 (+1) ST1130
11:45 a.m. 1343 (-1) 1492 (-1) 1697 (-6) 1880 2681 (+1) 2844 (-4) 3057 3275 3401 (+1) ST1145
12:00 p.m. 1366 (-1) 1505 (-1) 1714 (-1) 1887 (-1) 2693 (+1) 2847 (+1) 3055 (+1) 3283 3411 (+1) ST1200
12:10 p.m.     1726 (-2) 1896 2705 2860 (+1) 3074 (-1) 3298 (-2)   ST1210
12:15 p.m. 1373 1512 1729 (-3) 1900 2708 (-2)         ST1215
after 12:20 p.m. PDT the wall with the petroglyphs is in self shadow
same day SD13 SD14 SD15 SD16 SD17 SD18 SD19 SD20 SD21  
SD all nine days


 
There are two reasons that cause the movement of the shadow edge across the Atlatl Rock wall during a day and the year and especially during the nine days documented in the above observations:

      -   the primary shadow movement is caused by the change in elevation of the Sun between following days

      -   the secondary shadow movement is caused the changing azimuth and elevation of the Sun during one day and
           the effect of the change of the slope of the shadow casting rock in the ~ 1.5 hours before noon

 
Primary Shadow Movement:

The decreasing elevation of the Sun after the summer solstice causes the upper shadow edge at Atlatl Rock to move upward between each following day. In the first couple of weeks after solstice the change in elevation is small.
Around eqionox however the change in shadow position has a maximum of about 0.36 deg each day and this causes the upper shadow edge around the autumnal equinox to move upward significantly between following days.



This is best shown in a movie that shows the shadow position for each of the nine days before astronomical autumnal equinox at the same time at 10:45 a.m. PDT. In the time span between 9:30 am PDT and 10:50 a.m. PDT each day the shadow edge is very straight and almost constant in position and thus 10:45 a.m. PDT is a good reference point in time for the description of the behaviour of the shadow edge before the downward movement of the shadow starts. From the observations in 2018 and 2017 it can be derived, that the movement of the shadow edge between following days is about one eighth the diameter of the concentric circles marker (or about one gap between the circles per day!).

From this observations it can be estimated that the date in fall when the shadow edge for the first time reaches the circles and cross markers from below is about 18 days before astronomical autumnal eqinox (~ September 4th ). Then, about 14 days before astronomical autumnal eqinox (~ September 8th), the shadow edge connects the centers of the markers for the first time since the spring eqinox. Finally, about 10 days before astronomical autumnal eqinox (~ September 12th ) is about the date when the shadow reaches the upper edge of the two markers.
 
About seven days before astronomical autumnal eqinox (~ September 15th ), the shadow edge for the first time touches the "foot" and moves over it the following five days until two days before astronomical autumnal eqinox. This is the autumnal solar quarter day and from now on all pertoglyphs at Atlatl Rock are in shadow until vernal equinox.

The following pictures have been taken at about 10:45 a.m. PDT on the days before autumnal equinox.


7.29 days
to autumnal equinox
(2018)

6.29 days
to autumnal equinox
(2018)

5.04 days
to autumnal equinox
(2017)

4.04 days
to autumnal equinox
(2017)

3.04 days
to autumnal equinox
(2017)


 
Secondary Shadow Movement - Part 1:   Between 9:30 a.m. PDT and 10:50 a.m. PDT

The rock south of the Atlatl Rock wall that casts the shadow onto the wall where the petroglyps with the atlatl are has an almost straight upper edge which casts a shadow with an straight upper edge onto the wall.

         

A complete movement of the shadow from sunrise until the rock is in shadow is shown in a movie of the September 17, 2017 data.

After the shadow tip has moved beyond the markers at about 9:30 a.m. PDT and before about 10:50 a.m. PDT the daily apparent movement of the rising Sun across the sky is almost parallel to the edge on the rock that casts the shadow on the petroglyphs. During this time span the shadow edge wiggles around and at the end of this time span it becomes an almost constant straight line.

At this time during the movement of the Sun over the sky the tilt of the rock edge that causes the shadow changes and becomes flatter by some degrees. As the Sun continues to rise, the shadow edge, that is now very straight and parallel to the centers of the markers, starts to move downward until the wall is in self shadow shortly after ~ 12:15 p.m. PDT.

   
shadow casting rock as seen
from the platform near the markers

 
Secondary Shadow Movement - Part 2:   The Downward Movement After 10:50 a.m. PDT in Detail

The observations from each of the nine days before astronomical autumnal equinox show that around 10:50 a.m. PDT the shadow edge starts to move down from beeing above the markers. Each following day, due to the decreasing elevation of the Sun in fall (primary shadow movement), the shadow edge starts higher above the markers before it moves down.
As the timespan until the rock is in self shadow is almost fixed (10:50 a.m. PDT to 12:15 p.m. PDT) the distance the shadow edge moves down is also fixed and it (thus) moves each following day less far down over the markers before the wall is in self shadow.
It does not reach the the markers anymore after September 18th (see movie from September 18, 2017), which is four days before astronomical autumnal equinox (or two days before autumnal solar quarter day).
Compare also the two extreme movies from September 13 and September 21!

The movie from September 13 also shows, that the distance covered by the downward movement in the timespan 10:50 a.m. PDT to 12:15 p.m. PDT is almost exactly the height of the markers (concentric circles and the cross).

The last pictures taken at about 12:15 p.m. PDT on each of the nine observed days before astronomical autumnal equinox have been combined into a movie to show what happens there. Unfortunately not all pictures have been taken at the same time each day and also not frequently enough and thus they can only give a hint what can be observed in the last minute(s) before the wall is in self shadow.

During its downward movement due to the secondary shadow movement the shadow edge "dances" across the markers because the movement of the shadow edge is now not strictly in one direction and it moves up and down a little bit several times. This starts September 4th when the shadow edge due to the primary shadow movement reaches the markers the first time in fall. It ends on September 18th when the downward moving shadow starts from such a high position above the markers that it just touches the markers the last time from above before the wall is in shadow (see movie).

A special moment during those days when the shadow edge moves downward across the markers is, when it passes simultaneously right through the centers of the markers. The first time in fall that this happens during the secondary shadow movement is after September 8th. Then, on its movement down, the shadow edge again connects the centers of the markers. As it "dances" up an down during this time span, it crosses the centers several times. The last time the shadow line passes simultaneously through the centers of the two markers before the wall is in shadow occurs on September 17th (see movie), five days prior to the astronomical autumnal equinox (three days before the autumnal solar quarter day).

 

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Sunrise Observations

The location of the sunrise around autumnal equinox at the flat horizon has been determined on eight days (in different years) with different distances (in time) to the astronomical autumnal eqinox date.
The pictures taken to document the sunrise location on the eastern horizon were always made from the same point on the platform, the sunrise picture point.
The azimuth of the point at the horizon where the Sun is visible the first time at sunrise changes significantly by about 0.5 deg per day around the days of the equinoxes (this is almost exactly the apparent diameter of the Sun and also the Moon). This makes the observation of the sunrise a very good and exact tool to mark certain dates if structures on the horizon or alignments with structures in that direction are available.


# date
sunrise [PDT]

yyy-mm-dd-hh:mm
picture
JD - 2450000+
equinox
JD - 2450000+
diff. JD Azimuth
[deg]
Elevation
[deg]
S1 2018-09-13-06:23tc am 8375.05764 8384.57917 -9.52 85.39 0.44
S2 2018-09-15-06:24tc am 8377.05833 8384.57917 -7.52 86.41 0.51
S3 2017-09-17-06:27 am 8014.06042 8019.33472 -5.27 87.52 0.55
S4 2017-09-20-06:29 am 8017.06181 8019.33472 -2.27 88.91 0.49
S5 2010-09-21-06:29 am 5461.06181 5462.63125 -1.57 89.17 0.40
S6 2015-09-23-06:31tc am 7289.06319 7288.84792 0.22 90.12 0.49
S7 2015-09-24-06:32tc am 7290.06389 7288.84792 1.22 90.63 0.53
S8 2015-09-25-06:33tc am 7291.06458 7288.84792 2.22 91.14 0.56

(Sunrise near summer solstice has been observed only once three days after solstice on June 24, 2011.)

A summary of the equinox observations is this picture with the distances to the astronomical equinox in days indicated (negative is before):


Depending on the location from where the sunrise is observed, the rocks in the foreground (at a distance of about 280 meters) may be used to indicate the location of the sunrise at a desired date.


 

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Timetable of Events

(primary shadow interactions only)

The following is a kind of timetable of the interaction of the shadow with the markers to be observed each year in relation to the astronomical equinox and the solar quarter days.
Observation have been made only on the dates marked in light red. For the coming years the dates of the events have been estimated from the data base of the observations available. They are good ± 1 day.



Any verification of the dates of the events that have not been observed and documented so far would be extremely welcome!

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last update 2022-09-07  
by Helmut Steinle