Sun Finder
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Introduction
There are several ways to figure out where the Sun will rise or set on any day of the year. Our Orthographic Projections section is one way. This is done with a pair of compasses, a straight edge, protractor and pencil and paper. Even if you do not plan to use this technique, we encourage you to go through this section, as it will give you a good feel for what is happening between where you are on the Earth and the Sun throughout the year
Thanks to Sig's nephew, Fred VandenBergh, we can now offer you another way to figure out where the Sun will rise on any day of the year at any latitude and any angle of elevation to the horizon. This is useful not only at prehistoric sacred sites to figure out if outlying stones or notches on the horizon have an astronomical orientation, but also in the construction of new sites, to orient them to Sun rises or sets on any day of the year. One of the best aspects of this program is that it is done in JavaScript, so you may download this program to your laptop, and use it out in the field without a connection to the Internet!
To begin with, you will need some tools and information:
I. Latitude and Longitude  Where On Earth Are You? You will need to know this for several reasons  it will allow you to figure out Magnetic Deviation, and you will also need it when you come to figure out where the Sun will rise or set at your location.
a. A good topographic map (Ordnance Survey Map in the UK) of your area will give you these,
b. If you own an iPhone, I use an iTunes App called $0.99. Also, $0.99  in addition to latitude and longitude, it gives the azimuth of the Sun, its angle of elevation to the horizon (above or below), temperature, and other useful info. (I am using my iPhone more and more for outdoor astronomy and archaeoastronomy.)
c. If you are on a computer, one way to get your latitude is to go to iTouchMap.com.
These sites will give you the Latitude and Longitude for the town you are in. This should be accurate enough for most purposes  though the topographic map will be even more accurate. A Global Positioning System (GPS) is another way to find Latitude and Longitude in the field. It uses satellites to locate you very accurately on the surface of the Earth. Also, Google Earth is an easy way to find it. You can have a free download of this useful program at < http://earth.google.com/>.
II. A Compass  You will need a compass to determine the Azimuth (number of degrees from true North in a clockwise direction) you are shooting. To begin with, any compass will do, but as with all tools and operations here, the more accurate, the better. Orienteering compasses are not what you want. They are useful to begin with, but they really are not accurate enough. Sig uses a Suunto Tandem (page 11). Check out their KB20 Vista, and their KB14/360RD, and their Twin – A compact compass and clinometer combination. Silva offers several different less expensive options, the 54LU Combi has a see through lens that gives remarkably accurate azmuth readings, and the Ranger 24 uses a mirror for accuracy, and comes with a clinometer  to measure the angle of elevation to the horizon. See Silva's Swedish web site (see Precision Instruments).
Given a level horizon, on either Equinox, the sun will rise due East, and (North of the Equator) the Summer Solstice Sun will rise North of there and the Winter Solstice Sun will rise in to the South, the exact azimuth depends on your latitude.
With the Sun Finder on the next page, you can find out azimuths for sun rises and sets. There are 360 degrees in a circle. If your azimuth is less that 180°, it could be a sun rise point. If it is over 180°, it could be a sun set point.
III. Magnetic Deviation  At 99% of the places on Earth, your magnetic compass will not point true North. This is due to something called Magnetic Deviation. This deviation (also called magnetic declination, magnetic variation, or compass variation) is the angle between the north compass (magnetic) heading and the heading to true (geographic) north. True north can be determined with a compass reading plus/minus (as appropriate) the location’s magnetic deviation. Geodetic Maps can show you this deviation, but be aware, it changes significantly over time (the map should tell you how much per year)!
There are several web sites that can give this deviation as of today. One is Ricardo's GeoOrbit Quick Look. It is a visual chart/map of these deviations all over the Earth. Like the Sunfinder program itself, we recommend that you download a copy of these maps, so you can refer to them for magnetic deviation when you are in the field with your lap top computer. Another place to visit is the National Geophysical Data Center World Data Center/Geomagnetism in Colorado USA. This is more accurate, and figures out the deviation at your particular Latitude and Longitude mathematically. The Longitude and Latitude are in degrees and minutes. For the National Geophysical Data Center web site, you will need to convert the minutes, of which there are 60 in a degree into a decimal. (Example: 3° 30'. 30/60 = .5, so 3.5) The answer is  the first number at the top column on the left. Declination is measured positive east and negative west (i.e. D 6 means 6 degrees west of north). If your Magnetic Deviation is a positive number, add it to your magnetic compass reading. If it is a negative number, subtract it from your magnetic reading.
In addtition to magnetic deviation, be aware that a number of sacred sites in the British Isles have magnetic anomalies that pull the needle of your compass away from Magnetic North. At Carn Angli in Wales (just West of the Prescelli Mountains), there is a space about the size of a brick where you can stick your compass in, and the needle turns 180°! In the Grampian region of northeast Scotland, there are a number of recumbent stone rings that also exhibit these anomalies as well, though not necessarily as strongly as Carn Ingli. The point here is that where ever you are, you need to check that this isn't happening where you are needing to take a compass reading. Find Magnetic North, then move to a number of different places on your site to see if the needle continues to point to the same point on the horizon. If it doesn't, you need to wait 'till dark locate Polaris also known as the North Star to find True North. Then you can figure out the azimuth you seek from that.
IV. Clinometer  measures the angle of elevation to the horizon  The Sun doesn't rise vertically. North of the Equator, it rises at an angle to the South  and vice versa in the Southern Hemisphere. If you have a level horizon, you have no problem. It is at the azimuth you have measured. But most horizons are not level. You will need a tool to measure this angle. The most simple one is as D shaped protractor, some fishing line or thread, and a weight. Suunto makes combination compasses and clinometers like the Tandem, and their Twin. In the United States, Forestry Suppliers Inc., PO Box 8397, Jackson, Mississippi 39204 (Phone: 8006475368) sell a number of different clinometers by Brunton, Suunto and others. When you get to their home page, type in their Search window.
Two Limitations  We have not included the capability to do latitudes south of the Equator, and we have not yet built in the capability to do dates before the time of Christ (BCE). We intend to rectify these two deficiencies in the near future, but we wanted to get this Sunfinder up because we trust that it will be useful to many. If you have any suggestions or other observations, please contact Sig Lonegren.
You will find the Sunfinder on the next page. To download it to your lap top, so you can take it into the field, go to the next page, then go to on your menu line, and click on . Save it as a . When it is on your computer, just double click on the icon, and enjoy!
Sunfinder Calculator >>
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Here are the formulae that we are using in our JavaScript Sunfinder:
Fred VandenBergh has written the JavaScript for the Sunfinder based on
Alexander Thom's Declination equation (I understand that Thom did not create this formula, but his book is where I found it.):
inv sin D = (sin L * sin H) + (cos L * cos H * cos Az)
where
D = declination
L = latitude
H = horizon height (degrees)
AZ = Azimuth can be more practically expressed as;
D = asin ((sin L * sin H) + (cos L * cos H * cos AZ))
This finds the declination for a given azimuth and elevation in degrees Today, the Sun's declination at equinox = 0 deg. At solstice = 23.45 degs.
from Thom, Alexander, 1967. Megalithic Sites in Britain. London: Oxford University Press. p. 17.
Chuck Pettis' Azimuth equation:
AZ = acos ((sin D  (sin L * sin H) / (cos L * cos H))
Byron Dix's equation to calculate sun's declination for any day of the year:
D = 23.45 sin (360/365.25 * t)
where t = number of days from vernal equinox (NB vernal equinox date is variable!) WITH EQUINOX AS DAY 1 or we can reverse that to show the days past equinox for a given declination between +/ 23.45 (sun's in this case) : t = (inv sin (D/23.45))/(360/365.25) or t = (asin(D/23.45))/(360/365.25).
Grahame Gardner writes:
radians = 360/Pi 2 x deg. degrees = 2 Pi R/360
To find solar declination (D) for a particular day (t):
D/23.45 = sin (0.985 * t)
(the 0.985 is 360/365.25 from Bryon's equations)
asin (D/23.45) = 0.985 * t
therefore: (asin (D/23.45)/0.985) = t in other words, t = asin(D/23.45)/0.985 so, do:
D/23.45
find the asin (inv. sin) of that result, divide it by 0.985 and that should be our desired result.
Refraction and Parallax
We do not account for refraction – the degree to which the apparent position of a celestial body (in this case the Sun) is distorted by the redirection of its light as it passes through the Earth‚s atmosphere  since it has little effect on the azimuth. Since we're talking about sunrise and sunset times, the refraction is going to be pretty much constant since we are theoretically always looking through the same density of atmosphere. The horizontal refraction of the sun at 90 degs. of zenith (i.e. rising or setting) is 35 minutes of arc, which is just over half a degree of displacement; therefore sunrise will occur slightly earlier and sunset slightly later. For example, at the equator on the equinoxes, the sun will appear to rise about four and a half minutes earlier, and set four and a half minutes later. This refraction will be increased slightly if the observer is at altitude and the horizon is a great distance away. Refraction also accounts for why the sun appears slightly oval in shape when rising or setting.
Parallax is the apparent vertical displacement of a heavenly body due to the latitude of the observer. Since the true zenith distance of a star or planet is measured from the centre of the earth, the observed zenith distance will vary slightly according to the location of the observer. However because of its size, in the case of the sun the effect is minimal, at most about 8.8 seconds of arc, and again has little effect on the azimuth for our purposes. Corrections for Refraction and Parallax are really only important in navigation, when trying to locate your position on the earth by observing the heavens.
It is always my feeling that one should do this work as accurately as the tools available can allow. As we are not suggesting the use of theodolites or transits, we do not believe anyone using the best Suunto hand held compass can get to within half a degree of arc. So we have not included refraction or parallax in our calculations.
Calculating the Major and Minor Standstills of the Moon
The Moon deviates from the ecliptic by as much as 5 degrees 08 minutes (5.15 degrees), thus making a total deviation in declination of 11.2 degrees. 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 first identified it. The Full Moons' rises and sets mirror the Sun's throughout the year. The Full Moon closest to the Winter Solstice rises around the point where the Summer Solstice Sun rises  and viceversa, the Full Moon nearest the Summer Solstice rises around the point on the horizon where the Winter Solstice Sun rises. The Major Standstill is as far outside the Solstice rise/azimuth for that latitude as possible. The Minor Standstill is as far inside the Solstice Sun's path (ecliptic) as the Moon deviates.
Thus the Northern Major Standstill of the Moon, given a level horizon, will be at an declination of 5.15 degrees less than the declination for the Summer Solstice Sunrise for that latitude. The Northern Minor Standstill of the Moon, given a level horizon, will be at an declination of 5.15 degrees more than the declination for the Summer Solstice Sunrise for that latitude. And mirroring that, the Southern Major Standstill of the Moon, given a level horizon, will be at an declination of 5.15 degrees more than the declination for the Winter Solstice Sunrise for that latitude. The Southern Minor Standstill of the Moon, given a level horizon, will be at an declination of 5.15 degrees less than the declination for the Summer Solstice Sunrise for that latitude. The Major Standstill Moon sets work in the same ways. See the section on this in Orthographic Projection.
I wish to thank Fred VandenBergh, Grahame Gardner, Victor Rejis and Kevin Kilburn for their help in preparing these Sunfinder pages.
If you have enjoyed this section, for a different perspective on the movement of the Sun and Moon, please check out our MAG Orthographic Projections section.
Archaeoastrology >>
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AZIMUTH CALCULATOR 
DAY CALCULATOR 

Example: At what azimuth (degrees from True North) will the sun rise on the Summer Solstice at my home with a level horizon?  Example: I am in a new stone ring at 40 degrees north latitude, and there is a notch in the hills at an azimuth of 120 Degrees with an angle of elevation to the bottom of the notch of 4 degrees.  
On what day(s) of the year will the sun rise or set there?  
DISCUSSION
AZIMUTH CALCULATION
The answer is rounded to the nearest 1/100 of a degree.
DAY CALCULATION
Because of rounding errors and uncertainty with the date of the Solstices, the date(s) given are accurate to within a day on either side.*
*Because of the very small changes in azimuth around the Solstices, solstice azimi are accurate for several days on either side of the solstice.
If you want to download this script, it will work fine without having to be connected to the Internet, so you can take your laptop into the field and use this program there. In Internet Explorer, go to <Find> on the menu line. Go to <Save As>, and save as <Web Archive>. On your computer, double click on the <Sunfinder> icon, and it's ready to use. If you get answers that do not make sense, clear the script by reloading the page. Please let MidAtlantic Geomancy know how it worked for you.
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