- Hits: 10557
Major and Minor Standstills of the Moon
The Metonic Cycle
While the monthly path of the Moon causes it to swing high and low in the sky, successive Fullmoons - the time when we notice the Moon most - are always opposite the Sun. Thus, as the Sun moves higher in the sky to the North in the Summer, successive Fullmoons rise further to the South and their paths are lower in the sky. In the approach to Winter it is just the opposite. The Sun moves lower, and it is the turn of the Fullmoons to ride high in the Winter sky.
If the Moon is New or Full when it Crosses the Ecliptic, as in the illustration above, there will be an Eclipse. But as you can see in the illustration below, most of the time, this is not the case.
Our ancient forefathers and mothers were interested in eclipse prediction. One piece of evidence we have is their interest in what is called the Major and Minor Standstills of the Moon. The Moon deviates from the ecliptic by as much as 5 degrees 08 minutes (5.1°), thus making a total deviation from the ecliptic of 11.2°. It takes 18.67 years for the Moon to go from one extreme to the other and back again. This 18.67 year cycle is called the Metonic Cycle after Meton, the Greek who supposedly identified it. The Fullmoons' rises and sets mirror the Sun's throughout the year. The Fullmoon closest to the Winter Solstice rises around the point where the Summer Solstice Sun rises - and vice-versa, the Fullmoon nearest the Summer Solstice rises around the point on the horizon where the Winter Solstice Sun rises. We will see evidence shortly that the Neolithic people of Britain were well aware of the major standstills of the Moon and more than a millennium before the Greeks.
The reason why these major and minor standstills are important is for the prediction of Eclipses. It takes 9.3 years for the Moon to go from the ecliptic out to one of the extremes, and back to the ecliptic. While an inexact Eclipse can occur at other stages of the cycle, the stage where Eclipses are most exact occurs when the Moon is half-way between extremes of declination, when it is on the ecliptic. If, at the time of the Summer Solstice, the Fullmoon rises where the Winter Solstice Sun rises, there's going to be an Eclipse.
As with all previous exercises, at this point connect the minor standstills and the major standstills across the meridian with two parallel lines. Determine half their length, mark this on the latitude line, and connect the two to create the paths of the various major and minor standstills. Bring these lines down to the horizon. Measure the distance where these paths Cross the level horizon from C, transfer them down to C', and draw the four parallel transfer lines.
The major standstill is as far outside the Solstice rise/declination as possible. The minor standstill is as far inside the Solstice Sun's path (ecliptic) as the Moon deviates.
Connect the various major and minor standstill rises and sets by drawing lines that Cross through C'. Note how the major standstill Moonrises and Moonsets are in opposition to each other, as are the minor standstills.
At the 51st latitude, what is the azimuth to the rising point of the Southern major standstill of the Moon?
While all of the azimuths of the major and minor standstills of the Moon can be easily determined with a circular protractor, we are interested here in the rising point of the Southern major standstill of the Moon. By using our circular protractor:
The azimuth of the Southern major standstill of the Moon is 141°.
There is a very interesting thing that happens when you compare the azimuth of the Summer Solstice Sunrise with the azimuth of the Southern major standstill of the Moon at the 51st latitude.
The major axis of Stonehenge is oriented towards the Summer Solstice Sunrise. The four Station Stones create a rectangle whose longer side is a tangent to the major Trilithon Circle. The longer axis of the rectangle is perpendicular to the major axis, and is aligned with the rising point of the Southern major standstill of the Moon.
As you can see from the animated .gif above, the azimuth of the Summer Solstice Sunrise at the 51st latitude is 51° (an interesting coincidence of 51s), and the azimuth of the rising point of the Southern major standstill of the Moon is 141° - exactly at right angles to each other (90°). This is one of the special characteristics of the location of Stonehenge.
You now have the tools to locate the quarter and Cross-Quarter Days and the major and minor standstills of the Moon, all at any angle of elevation to the horizon, at any latitude. It is our goal to have a cgi script that will give the rising and setting points of the Sun for any point on Earth, on any day of the year, at any latitude between the polar circles.
The 51st latitude is only place on Earth above the Equator where the furthest North that the Sun rises is exactly 90o from the furthest South that the Moon rises! This shows clearly that the builders of Stonehenge I, in about 2750 BCE, knew about this 19.67 year cycle of the Moon several thousand years before Meton 'discovered' it.
Write comment (0 Comments)
It is essential to know about the lunar standstills in order to begin to predict eclipses.
Quarter & Cross-Quarter Days >>
- Hits: 9811
The simplest way to measure the angle of elevation to the horizon is with your D-shaped protractor.
Notice the tiny hole in the center.
Put a piece of thread through the hole and and tie a weight on it so that it will hang somewhat below the sweeping arc of the D.
Notice that when the flat edge of the D is held perfectly horizontal, the thread cuts the arc at 90°.
Sight along the flat edge of the D and align it with the point on the horizon that you wish to measure the angle of.
You need a second person here. Have them read the number of degrees away from 90 that the thread cuts the arc.
A note on accuracy. Obviously this is a very crude way to measure this angle of elevation to the horizon. There are many tools that can do this more accurately. I use a Suunto Clinometer.
The Sun doesn't rise straight up.
If the horizon is elevated the Sun will rise further to the South of where our calculations have shown us.
The animation at the top of this page shows a level horizon. If the horizon had been elevated the Sun would have set further South.
But how can we measure this?
Let's try this problem:
At what azimuth does the Equinox Sun rise at the 40th latitude given an angle of elevation to the horizon of 10°?
When the horizon is elevated, the Equinox Sun rises at a different place on the horizon - South of due East.
First let's make this at a latitude of 40°. This line comes into the United States just above Los Angeles and Denver, goes through Indianapolis, Indiana and Philadelphia, Pennsylvania. The 40th latitude enters Europe between Madrid and Toledo in Spain and heads Eastward through Southern Italy, the ancient city of Troy, the Caspian Sea, Beijing in China and out into the Pacific through Northern Japan.
Let's look for where the Equinox Sun rises at the 40th latitude with an elevation to the horizon of 10°. You would begin by drawing the 40° latitude.
There follows a quick review of the orthographic process for deriving the path of the Sun on the Equinoxes and the two Solstices.
The rising azimuth of the Equinox Sun, when there is an angle of elevation to the horizon of 10°, can be determined by raising the level horizon we have been working with up until now by 10°.
Measure 10° on the Meridian (red arc) up from the horizon to the North and same on the South, then connect the two points.
We are looking for the point where the Equinox Sun Crosses the elevated horizon E2. With your pair of compasses put your point where the horizon Crosses the zenith C1, and measure out to point E2. Go down to the lower circle and mark that out from C' at E2'
In rare cases - like a shot taken on top of a high mountain – there's a negative angle of elevation to the horizon. In this case extend the red arc of the meridian below the level of the horizon N-C-S, and continue as above. You might have to extend the actual paths of the Sun below the horizon.
This elevated equinoctal line Crosses the circular horizon at E3. Given a level horizon, on the Equinox the Sun will rise due East anywhere on Earth. Notice that the azimuth of the Sun with an elevated horizon is shunted towards the South. Likewise, with an elevated horizon, the Equinox setting Sun will also be shunted towards the South.
Notice that due East is 90°, but with the 10° elevation to the horizon the Sun rises at an azimuth 8.5° further South.
You can now find the quarter and Cross-quarter solar alignments for any place on Earth (within the Arctic and Antarctic Circles). In Section 4, we include information about how to determine major and minor standstills of the Moon.
Before long, it is our intent to have a page where you can enter your latitude, azimuth and angle of elevation to the horizon, and you will be able to find out what day of the year the Sun would rise in that particular direction. You will also be able to see the orthographic projection from which the specific day(s) were derived. This projection can be saved for later use.
This will be a useful tool not only if you want to check out an alignment at a sacred site, but also if you want to build a new sacred site locked into the astronomy of that place.
- Hits: 14812
Why did our foremothers and forefathers know so much about astronomy? First of all, unlike ourselves, they lived in it. Anyone who has lived outdoors for a while begins to develop a different relationship with nature and the sky. Living in houses and especially in cities, where the ambient light and the tall buildings block out the heavens, we have forgotten the natural flow of the cosmos. Outdoors, if you get up at first light and go to bed when it gets dark, you notice the Sun as it rises and sets each day. In the Northern hemisphere, over the months you see the Sunrise moving along the Eastern horizon from the North-East at Summer Solstice (the longest day of the year), to the South-East at the Winter Solstice. Likewise, at Sunset, you would see the Sunset also moves along the Western horizon over the year as well.
This is a copy of a Druidic Cross that was given to me by the Welsh Druid Ray Kerley when I lived in Glastonbury, England in the mid-eighties. It was Ray's family's druidic Cross.
From an astronomical point of view, the four arms represent:
The four Quarter Days of the yearly cycle
Winter Solstice - around December 21st (on the cross above: at 6:00 o'clock)
Spring Equinox - around March 21st (at 9:00 o'clock).
Summer Solstice - around June 21st (at 12:00 o'clock)
Autumn Equinox - around September 21st (at 3:00 o'clock)
But the Celts (pronounced "Kelts"), the people of Iron Age Northern Europe were interested in the days half way between these Quarter Days. These Cross-Quarter Days were the major feast days of the Celts. They are represented by the four black balls at the points where the two arms Cross on the Cross shown above.
Samhain - around November 1st, the Celtic New Year (The black ball at 4:30 o'clock - between Autumn Equinox and Winter Solstice)
Imbolc - around February 1st, the quickening (The seed planted at Samhain moves for the first time (the black ball is at 8:30)
Beltane - around May Day, May 1st, the Cross-quarter day of fertility (The crops are up, let's work for their fertility (the black ball is at 10:30)
Lughnasad (Lammas/Loaf-Mass) - around August 1st, the first harvest of the grain (ground into the first loaf of bread of the season for Loaf Mass/Lammas (the black ball is at 2:30)
In looking at orientations, in addition to those of the Quarter Days, some sacred sites on both sides of the Big Pond are oriented towards these Cross-Quarter Days.
Here's an example from Northern Vermont, USA. The picture was taken inside an underground stone chamber.
Cross Quarter Day - Imbolc - Sunset Rodwin Chamber, Northern Vermont, USA.
Notice the Sun is headed towards the notch in the horizon.
The Cross-Quarter Days
The Quarter Days of the year (the Solstices & Equinoxes) can be defined with extreme accuracy - to the nearest nano-second if necessary. The Cross-Quarter Days are somewhat more movable.
The Druidic Cross to the left indicates the Quarter Days with the four arms of the Cross. The Cross-Quarter Days were symbolized by the four much smaller dots in the crotches of the Cross. This would make it seem that they are evenly spaced around the eight-point year. They are in time - but not in space.
Calculating the Cross-Quarter Days
Go to the point on your Orthographic Projection of 51° and locate the declinations of the Summer and Winter Solstice Sun at noon (shown in gray in the illustration).
In half the number of days between the Spring Equinox and the Summer Solstice, at Beltane, around May 1st, the Sun has moved approximately 71% of the distance between these two points on the horizon. 71% of the 23.5° declination of the Summer Solstice Sun would put the Beltane (and Lughnasad) Sun at a declination of +16.6°, and the Samhain and Imbolc Suns at a declination of -16.6°
With your circular protractor, measure 16.6° above and below the declination of the Equinox Sun. Connect the two points, and mark the intersection with the Equinox Sun's path (E2). Put the point of your compass on E2. Your pencil should hit both the +16.6° and the -16.6°.
Without moving apart the arms of your pair of compasses, put the point of your compass on C and swing an arc through the latitude line, finding points B/L2 and I/s2.
Extend a line from BL1 through BL2 to the point where it breaks the level horizon N-C-S at B/L3. Extend a line from I/s1 through I/s2 to the point where it breaks the level horizon N-C-S at I/s3.
Connect B/L3 and B/L' with a straight (transfer line). Do the same with I/s3 and I/s3.
Now, just as we did with the Solstice Sun, let's move into the next dimension:- what does this look like from above? Put the point of your pair of compasses on C, and make short arcs through B/L3 and I/s3.
Without moving the arms of your compass, put the point on C', and make arcs that break the lower N-C'-S line at B/L' and at I/s'.
Draw lines B/L-I/s and I/s-B/L. They should intersect at C'. When viewed from C' this will give you the Cross-quarter day Sunrises and Sunsets at a latitude of 51o.
These are the azimuths of the four Cross-quarter day Sunrises and Sunsets at a latitude of 51°, given a level horizon. You would measure these angles (taken in a clockwise direction from North) using as large a circular protractor as possible.
Up until now, we have been assuming that there is a level horizon. This fixes the Sun in two dimensions. In reallity, the horizon is usually elevated, which adds a third dimension.
- Hits: 14192
The Sun's Movement Along the Horizon
Except for the times around the Solstices (Sun standstill), each day, the Sun rises and sets in a slightly different place along the horizon. The above animated picture shows the movement of the Sun over one year at a lake near Sig's home when he lived in Greensboro, Vermont. On each of the Eight Days, Sig went out, stood in the same place on a cement dock and took essentially the same picture each time. He used the same camera and wide-angle lens, and framed the picture with two tall cedars on the left horizon and the tip of the dock in the lower left.
Notice that the Sun doesn't travel an even pace along the horizon throughout the year. It's analogous to the travel of a pendulum. At both extremes, it actually stops. These are the Solstices. The Sun/pendulum stands still. Then it falls and begins to gain speed. In half of the days between any Solstice and Equinox, the Sun only travels 30% of the distance along the horizon.
The pendulum continues to gain speed, and by the Equinox (when the pendulum is directly below your hand), the Sun is travelling its own diameter each morning along a level horizon! Then the pendulum goes upward mirroring its downward swing only slowing down until it reaches the next standstill.
Now we're ready to ask the question, where will the Sun come up anywhere on Earth on any day of the year with any angle of elevation to the horizon?
Solstices & Equinoxes
Orthographic projection is one way to figure out where the Sun will come up at any latitude. While it probably is possible to follow the steps presented here just in your mind… PLEASE DO NOT YIELD TO THIS TEMPTATION!
EVENTUALLY YOU MUST DO THIS WORK WITH A PAIR OF COMPASSES, A STRAIGHT-EDGE, A CIRCULAR PROTRACTOR, PENCIL AND PAPER!
This information is essential to any geomancer who wants to connect their site with the heavens. Orthographic Projection can show you where the Solstice, Equinox and Cross-quarter day Sunrises and Sunsets will take place anywhere on Earth. When this section is complete, you will be able to get this Sunrise and Sunset information for any day of the year at your latitude.
Let's start with the following question, using the latitude of Avebury (51.26°N), Stonehenge and Glastonbury (both 51.09°N):
Given a level horizon, at what azimuth (number of degrees from True North in a clockwise direction) does the Summer Solstice Sun rise at a latitude of 51°?
How to calculate
Imagine you are standing at point C, a sacred space on the 51st latitude (in England, Avebury, Stonehenge and Glastonbury are all at this latitude). You are looking South. In Fig.1, a line drawn over your head from true North to South is called the meridian.
As the figure is looking South, West comes out of the screen towards you, the reader. East is on the other side of the figure, or towards the back of the screen.
Draw the latitude (51 degrees) from North. The line should intersect the North/south line at C. (If you live South of the Equator, you need to do the mirror of this – have the person looking North, enter the latitude to the South, etc.)
Everywhere on Earth, the Equinox Sun rises due East and sets due West. At noon on that day, the Sun is exactly 90° to the latitude you are on.
At any given latitude, the declination of the Summer Solstice Sun is 23.5° higher in the sky than the Equinox Sun, and the declination of the Winter Solstice Sun is 23.5° below the declination of the Equinox Sun. Use a circular protractor to measure 23.5° degrees above and below the path of the Equinox Sun.
Draw a line SS-WS between the two points where the declination of Summer and Winter Solstice Suns intersect the meridian. This line intersects line CE at E1, and is perpendicular to the path of the Equinox Sun C-E1-E.
With your pair of compasses measure distance E1 to SS. This should equal E1-WS. Line SS-WS is perpendicular to line E-C. Line E-C is perpendicular to the line that represents the latitude you are on. Therefore, the latitude line is parallel to line WS-SS.
Putting the point of your pair of compasses at C, mark points SS2 and WS2 on the latitude line.
Connect WS and WS2 to intersect the horizon, N-C-S at WS3. WS3-WS marks the path of the Winter Solstice Sun.
Connect SS and SS2 and extend downwards to intersect the horizon, N-C-S at SS3. SS3-SS2-SS marks the path of the Summer Solstice Sun.
Now comes the magic, the shift from one dimension to another, from Two to Three. A vertical line drawn from point C through the observer breaks the meridian at the zenith. Also, extend this line downwards into the shift to the third dimension, where we will see how all this looks from directly above - from the point of the zenith.
Construct a perpendicular line at C'. Mark the left-hand end of this new line N and the right-hand end S. Line N-C-S is parallel to N-C'-S. Centered on C', create a circle that has the same radius as C-N. Viewed from above the human figure is standing at C'.
The Wisdom Wheel marks the Four Directions, and while this example is based on the Native American one, is honored by indiginous people all over the world.
Put the point of your compass at point C, with the other arm make a slash at WS3, the point where the Winter Solstice Sun breaks the horizon. Twisting your compass around on the point C, make another slash at point SS3, the point where the Summer Solstice Sun breaks the horizon. Go to point C' on the circle below without moving the arms, put your point on C' and mark points WS3' and SS3'. Connect WS3 and WS3' and extend to outside of lower circle. WS and WS mark the points on the horizon where the Winter Solstice Sun rises and sets.
Connect SS3 and SS3' and extend to outside of lower circle. SS and SS mark the points on the horizon where the Summer Solstice Sun rises and sets.
Draw a line WS - SS
Draw a line SS - WS
If you have done everything correctly these two lines should interersect at point C'.
Rotate the sheet you're working on 90° in a clockwise direction. This puts North at the top of the circle towards the top of the page. Measure the angle N-C'-SS. This shows that this is the answer to the original question:
Given a level horizon, at what azimuth (number of degrees from True North in a clockwise direction) does the Summer Solstice Sunrise at a latitude of 51°?
The answer is - at an azimuth of 51°
Also, given level horizons, at a latitude of 51°
- the Equinox Sun rises at an azimuth of 90°
- the Winter Solstice Sun rises at an azimuth of 129°
- the Winter Solstice Sun sets at an azimuth of 231°
- the Equinox Sun sets at an azimuth of 270°
- the Summer Solstice Sun sets at an azimuth of 309°.
Given this information, you should now be able to calculate the Summer and Winter Solstice Sunrises and Sunsets at your latitude. All of this assumes a level horizon.