One of the minor “problems” in making a Henge is that you want to mark the solstices AND the equinox. Getting a solstice is pretty easy. The Equinox is a bit more tricky.
To find the Solstice dates and alignments:
Pick a spot as your “center” and stick a pole in the ground “a ways away” (with a clear horizon) toward sunrise. Every day, watch for sunrise. If it is to the North of your pole (and you are headed into summer) move your pole north to match. One day, the sun will no longer be rising “to the North” of your pole. It will seem to halt ( that is the “stopped sun” or solstice). That is your Summer Solstice. The same thing happens as winter approaches, but to the South. The sun keeps rising lower on the horizon, further south, until one day it stops. At that point, you plant the pole and that is the Winter Solstice. Pretty easy, really. One center marker and a pole. (After the spot is found, you can plop down a stone with a pointy top instead). A similar thing is done for the setting sun for both soltices, so you end up with 4 stones. Summer and Winter solstices, rising and setting. (Those of you in the Southern Hemisphere need to reverse winter and summer, or north and south, but not both. Then again, you ought to be use to us doing things backwards up here ;-)
But what about the equinox?
You could sort of measure 1/2 way between the two and stick a pole in the ground. But that’s not very precise. Is there a better way? Well, yes. The Equinox happens when the sun rises on the celestial equator. The celestial equator matches the earth equator, but is projected out to the stars. Now we could just use whatever latitude we are at, and measure the elevation of the celestial equator using it. There is a nice ‘how to’ here:
They have you find the north pole star (a bit useless south of the equator) and then measure that elevation up from the horizon. But there is an easier way. They mention it. The celestial equator is at the horizon due east and due west. So if you can spot those, you have each end. For sunrise / set, that is all you really need.
From geometry, it is easy to see that angle p, the elevation of the celestial pole from the horizon, is equal to angle l, the latitude. This is very important in navigation, as it allowed ancient sailors to tell their latitude by measuring the elevation of the celestial pole (in the Northern Hemisphere, this is easy because Polaris, a bright star lies near enough on the pole.) So if you’re ever lost in the snaky swamps of some strange country, or get shipwrecked and you’re marooned on some desert island, you know how to find your latitude- the elevation of the celestial pole.
Note also that the celestial equator always intersects the horizon exactly at East and West, wherever you are. To find the celestial equator, find the pole first. Look 90° one way, then the other, these are East and West. Then turn round through 180° so you’re facing the opposite way. At this point (opposite the pole) the equator is at an elevation from the horizon of 90° – your latitude, and it runs from East, through this point, then down to meet the horizon again at West. It will help you if you learn where the celestial pole and equator are where you live. Now you can see how the stars appear to move: following the line of the celestial equator, rotating around the pole.
Now finding “due east” and “due west” to under 1 degree might be just a bit hard if you are in the middle of a stone age plain (or geometric plane) and don’t have a sextant, compass, etc. etc. So lets say you don’t have much more than a few sticks, rocks, and rope? Yeah, you can get “due east” roughly pretty easy, but how exact? (Remember, you don’t have a calendar either, unless you make it…)
Find the three stars of Orion’s Belt. Notice one of them is almost on that 0 degree celestial equator line? Mintaka.
Declination −00° 17′ 57″
You can be under one degree just by watching for the rising of the belt of Orion and picking the star closet to the bow. For even more precision, put your pole in the ground with the point just a bit ‘above’ the top edge of the star.
So now you have an exactly due east point where that star rises. When the middle of the sun rises directly over that pole point, you have the equinox. (A similar point can be marked at the setting for due west). To save your eyes and not be staring right at the rising / setting sun, look for when the pole point shadow aligns with the enter of your circle; your observing point.
And that, IMHO, is why Orion was so important to the old Druids and the makers of Henges. Some even having 3 circles in the layout of Orion’s Belt. It lets you find with quite good precision where east and west are; by watching it through the night, it marks the entire arc of the celestial equator; and by finding when the sun rises at the same point, it gives the equinox dates.
So with just that knowing, a couple of sticks, stones, and a bit of rope ( to swing an arc and mark the outer circle of your eventual ‘stone ring’ of your henge); you too can make a basic stone circle with the solstices and equinox points accurately marked, and with precise east / west and north / south lines marked.
North South can be marked via a perpendicular to the East West line. Measure one radius from your central observing point with your rope to either the East or West marker. Use that to measure 6 equal chords around your ring. Those are 60 degrees of arc each on your perimeter circle. Take the segment running east west on each side – the north and south sides – and bisect them. Run a line between those bisected points on each line. That’s due North South. There are other ways to do it too, but I like this one as all it takes is the rope… Alternatively, you can just take the rope and have a chunk a bit over one radius long; then swing one arc from the East point and another from the West point. They will cross at two points. The line between those two is North South. But that doesn’t mark your 60 degree points on your celestial circle rose…
(Bisecting each of those chord lines gives a line to the circle that marks the 30 degree points. A cord between each of them, bisected, gives the 15 degree marks. Celestial objects move through 15 degrees of arc in 1 hour; so you also get a rough clock; along with a fairly decent compass.)
Now you can mark the seasons, know the major celebration days, and make a good solar calendar. I’m fond of using 12 months of exactly 30 days each, with an Holiday on each of Summer Solstice, Winter Solstice and both Equinox days. Then an added holiday, for a total of a two day
party Holy Day on the Winter Solstice. To that, we add a “Leap Holy Day” every few years according to one of two methods. The modern one, using “Jackson’s Leap” formula; or the ancient one. Watching Sirius rising. When it rises one day off cycle, that year you add the extra Holiday… er, Holy Day ;-)
In a comment on another posting about calendars:
Wayne Jackson posted a simple and accurate method of calculating Leap Years. I present it here just as he posted it:
22 December 2011 at 4:49 am
E.M., I went back to my old machine and there were additional terms. Since the current tropical year is ~365.2421897 days then an equation as
365 + 1/4 – 1/128 + 1/262144 – 1/524288 = 365.2421894
365 + 1/(2^2) – 1/(2^7) + 1/(2^18) – 1/(2^19)
gets you to where the next one day correction needed to the calendar would be about 3.44 million years in the future. Thought you might get a kick out of that… a near perfect binary calendar.
(and sure, you can use it freely, it’s yours
So that formula would be used to calculate “leap years”.
Egyptian Sirius Leap
For primitive conditions, we would use the Egyptian Calendar method. They would watch for Sirius to rise on the proper day. Eventually it becomes a day late. That year, you add another leap day. In practical terms, the Egyptians had figured out when to do this, and had their own “Leap Year” intervals figured.
The adjustments needed to make a complete year, i.e. the difference between 365.25636 days and the 360 (30 x 12) days, were made as follows:
The difference of 5.25 days comes at the end of the Egyptian year, by adding 5 days every year and an additional day every 4 years. The Ancient Egyptian Year currently begins (in 2003) on 11 September. The 5/6 extra days begin on 6 September.
The difference of 0.00636 day (365.25636 – 365¼ days) for each year requires adding another day every (1/0.00636) 157¼ years, which the Egyptians continued to do until our present times. This is accomplished by adding an extra day every 157, 314, 471, and 629 year cycles.
As you can see, the Egyptian Calendar is a bit complex. They also have only 3 seasons of 4 months each, so the only bit I’m picking up is the sync to a celestial timer. They also had a couple of different calendars, with one for agriculture that stayed in sync with Sirius, and an administrative calendar that tended to change with the Pharaoh. (But an in depth look at the complexities of old Egyptian calendars is not for this posting.)
Now, Smith’s Calendar starts on the Winter Solstice of 2012. (And not on the new Pharaoh date ;-) Then next leap year will be 2016, and every 4 years after until out of sync. So in 2169, 2326, 2483, and 2641. In addition, we watch the date when Sirius has a “Heliacal Rising”. This is at August 7th at my latitude presently. So it ought to stay on August 7th. (It will be a bit different at other latitudes, so each latitude needs to figure their own rising date and keep in sync accordingly.) The Heliacal rising is when the star just gets above the horizon and is visible, then the sun rises and snuffs it. So when it is not visible, you have not reached that day yet. When it is first visible then “snuff”, that’s the day. Later, when you see it for a long time… you are too late. So, if you miss a leap, and find that the Heliacal rising of Sirius is on the wrong day, toss in a leap year to get back in sync.
(In reality, you could use any of several rising dates, or even the equinox or solstice dates. In fact, the Solstice dates would be the easiest. Any time the actual standstill comes ‘a day late’, you just add a holiday to that solstice… Personally, I’d do it on the Summer Solstice since we already have a Winter Solstice double-day… In the original Smith’s Calendar, I had all leap years add the day to the Summer Solstice, and that is my preference; but folks are used to the big winter parties, so “as you like it” ;-) Stuck in the rough somewhere, I would just do the ‘leap years’ via a summer solstice sync day.)
Back To The Basic Henge
That is the basic Henge function for Solar use. In another posting I’ll add the parts for the lunar calendar, how to keep the two in sync / oriented, and how to predict likely eclipse dates. Oh, and the weather cycling bit too… but that’s pretty easy once you have a lunar calendar.
The nice thing about this method of Henge Making is that it does not depend on your latitude. It also takes nearly no materials or tools. Celestial alignments are used to lay out the stones. (That is, it is function based). When we eventually add standing stones, the henge will look similar too, but not exactly the same as, Stonehenge. But it will function correctly at whatever latitude it is built.