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.