DIY Stonehenge
Old Noaa Sun position calculator
New Noaa Sun position calculator
by Dennis Randall
Introductory Astronomy: Stonehenge
Goal: In this lab we will design Stonehenge-like monuments for
different latitudes on Earth, thereby understanding how the sun appears
to move throughout the year. These sheets also contain questions that should
be answered in the writeup. Materials: solar-motion demonstrator, scientific
calculator, ruler, protractor.
Today, Stonehenge is a broken stone ring 30 meters in diameter
made of hewn blocks that mass between 25 and 50 tons each. The blocks
were transported from Marlborough Downs, some 20 miles north of the Stonehenge
site. The ring is called the "sarsen ring" and over half of its component
blocks were quarried away sometime in the centuries between 2100 B.C. and
today. Archaeologists have partially reconstructed some 16 of them, and
6 are now re-capped with their lintels. There is also an inner, horeshoe-shaped
arrangement of 5 lintel-capped pairs called "trilithons". The whole arrangement
is surrounded by a low earthwork embankment 100m in diameter with only
one gap, to the northeast, in which direction lies another boulder known
as the "heel stone". (That's not the heel stone in the upper part of the
above picture, but one of four "station stones".)
The purpose of Stonehenge is astronomical. It is carefully aligned
so that, if one sits at the center, one has a clear view of the summer-solstice
sun rising over the heel stone. Such monuments are fairly common, such
as Nabta or Karnak in Egypt, Teotihuacan in Mexico, Moose Mountain in Saskatchewan,
Medicine Wheel in Wyoming, or scores of stone rings found in Britain
and western Europe.
Upon 20th century archaeological inquiry, it was discovered that the Stonehenge
just described was one of several versions constructed on the site. The first
(Stonehenge I) was built in 2400 B.C., and appears to have been by far the
most
practical. The Stonehenge we see today is Stonehenge III, and
seems to be more of a
monument to the earlier Stonehenges , a massive
commemoration (perhaps ceremonial) of the earlier site, perhaps like the
erection of a cathedral rather than a small, more practical church. One thing
is for sure: with its smaller ring diameter, Stonehenge III is less accurate
than its predecessors.
The basic Stonehenge plan is illustrated above, where north is
straight up, east is to the right. The outer sarcen ring surrounds the
inner 5 trilithons, which open up to the northeast. Lighter-grey colored
stones are toppled, broken, or missing. Darker stones have been restored
by archaeologists. FYI, more detailed maps of Stonehenge I and II, and
III are included at lab's end (note that north is slanted left in these additional
diagrams).
Procedure
Let us design a few Stonehenge-like plans for different places on
Earth. For this we will use two methods: (1) seat-of-the pants using
our solar motion demonstrators, and (2) using a calculator. Using a protractor,
we will sketch lines of sight for midsummer (summer solstice) sunrise
and sunset and midwinter (winter solstice) sunrise and sunset.
First, review the behavior of the sun during the year by filling in the
following table.
Celestial Sphere Coordinates of the Sun
| Date |
Name |
Right Ascension (hours) |
Declination (degrees north or south) |
| March 21 |
Spring Equinox |
|
|
|
Summer Solstice |
|
|
|
Autumn Equinox |
|
|
| Dec. 21 |
|
|
|
We will use the earthbound coordinate system of
altitude and
azimuth. Altitude measure the angle of an object in degrees
above the horizon. So an object on the horizon has an altitude of 0 degrees,
and an object straight overhead at the zenith has an altitude of
90 degrees. Azimuth is usually measured starting at North and increasing
toward the East, so that an object due East has azimuth 90 degreees,
and object due south has an azimuth of 180 degrees, and an object due
west has an azimuth of 270 degrees.
Write some azimuths around the green portion of your solar motion demonstrator.
Fill in the following table using your solar motion demonstrator tool.
Each tick represents 10 degrees. Try to estimate the azimuths to the nearest
degree. The Keck telescope is located on the big island of Hawaii.
Sunrise/set azimuths using solar motion device
| Location |
Latitude |
Az. of summer sol. sunrise |
Az. of winter sol. sunrise |
Az. of summer sol. sunset |
Az. of winter sol. sunset |
| Equator |
0.0 |
|
|
|
|
| Pullman |
46.8 |
|
|
|
|
| Stonehenge |
51.2 |
|
|
|
|
| Anchorage |
60.5 |
|
|
|
|
Next, upack your calculator and try the following formula.
sin D = sin o / cos L
Where
- D is the maximum deviation from due east (for example, the sunrise
azimuths will be 90 degrees plus and minus this number for summer and
winter, respectively),
- o is the tilt of the Earth's axis away from the ecliptic, 23.5
degrees, and where
- L is the latitude of the observatory.
When you have computed sin
D, just hit the inverse-sin button
to get the answer.
Refined azimuths using trig. formula
| Location |
Latitude |
D (from formula) |
Az. of summer sol. sunrise (90-D) |
Az. of winter sol. sunrise (90+D) |
Az. of summer sol. sunset (270+D) |
Az. of winter sol. sunset (270-D) |
| Equator |
0.0 |
|
|
|
|
|
| Pullman |
46.8 |
|
|
|
|
|
| Stonehenge |
51.2 |
|
|
|
|
|
| Anchorage |
60.5 |
|
|
|
|
The formula assumes a perfectly flat horizon.
Q1: How do the numbers
in the second table compare with the numbers in the first? (Approximately,
by how many degrees do the two estimates differ, on average?)
Next, using a ruler and protractor, sketch in lines of sight for the
following observatory plans for each of 4 phenomena listed in the above tables.
The first one, for the equator, is done for you, as a model.
Finally, note that, as in the figure below, if you look north, at the
celestial north pole (CNP), the altitude of the CNP above the horizon
is the same as the observer's latitude. (This checks for the equator, where
the CNP is right on the horizon, and for the north pole, where the CNP
is exactly overhead). Furthermore, the angle between the CNP and the celestial
equator must always be 90 degrees. So if the sun is on the celestial equator
then its noontime altitude can be found by adding all the angles: (Latitude)
+ (90) + (Sun Alt.) = (180).
Noontime sun altitudes
| Location |
Latitude |
Alt. of spring equinox noon sun |
Alt. of summer solstice noon sun |
Alt. of fall equinox noon sun |
Alt. of winter solstice noon sun |
| Equator |
0.0 |
|
|
|
|
| Pullman |
46.8 |
|
|
|
|
| Stonehenge |
51.2 |
|
|
|
|
| Anchorage |
60.5 |
|
|
|
|
The builders of Stonehenge originally found that the sun reached the same
spot on the horizon at midsummer by
patient observation over several
years. It must have been quite a discovery for these stone-age tribesmen!
In your writeup, tell how you could (
Q2) find north, (
Q3
) find your present latitude, and (
Q4) set up a (small) stonehenge
that would point to the rising and setting suns at the equinoxes and solstices.
You can use measurement devices like a protractor, string, astrolabe (a
protractor with a plumb-bob attached), and your solar-motion demonstrator,
but you have to be able to do the job in a few days or nights - you can't
wait years to see where the Sun actually goes.
Figure: The early Stonehenge. The illustration shows several
stages of construction at the site. The first of these, "Stonehenge I,"
is an earthwork ring about 100m in diameter and 2m high. Its completeness
was broken (as of about 2400 BC) by a single gap directed in the approximate
direction of an outlying marker called the Heel Stone. In this gap, excavation
has uncovered a grid of post holes: the remains, it seems, of an effort to
mark the northernmost excursion of the moon. Note that the Heel Stone lies
slightly away from a line drawn from the center of the earthwork ring to
the horizon point marking the midsumer (solstitial) sunrise; in 2400 BC the
Heel Stone was presumably more erect, and thus the alignment was more nearly
perfect. Stonehenge I also included a circle of chalk-filled holes now named
after John Aubrey. At some later time, Stonehenge II was added. It comprises
two mounds of earth, covering some of the chalk-filled holes, and also the
so-called station stones. As shown in the illustration, these additions to
the site mark out the corners of a rectangle whose sides and diagonal align
with various risings and settings of the sun and moon. In about 2100 BC,
Stonehenge III was constructed at the center of the site (shown by the circle
of dashes). Stonehenge III is the megalithic structure that draws our attention
to the site today. [From "The Great Copernicus Chase" by Owen Gingerich,
1992, Sky Publishing Corp.]
Age: 8 and up
Time: 1 to 2 hours
Type of Activity: Science
Materials needed:
- Center stake for reference point.
- 50 feet of rope.
- 20 to 30 marker stones or small stakes.
- A compass.
Here's a unique way to celebrate the solstice: Build your own
Stonehenge. As you might know, Stonehenge is one of the oldest (4,000+
years) and best known astronomical calendar sites in the world. You can
recreate it without going through the bother of lugging 25 to 50 ton
slabs of rock around the neighborhood. All you'll need is a bit of
ambition, and a location offering an unobstructed view of the eastern or
western horizon. Locations offering a 360� horizon view are ideal (and
rare).
What to do
The first thing you'll need to do
is create a viewing circle. Anchor a reference stake at the center point
of the circle and place your compass on top of it. Find due north and
place a marker at 50 feet north of the center. Repeat the process for
east, west and south. (The rope is used as a guide to insure that all
markers are equidistant from the center stake.) Again, using the rope as
a guide, place a small marker stone every few feet around the perimeter
of your circle. The center of the circle now becomes your fixed
reference point and the westward facing perimeter is where you'll be
placing the sunset markers.
The calendar can be started at any
time, but the solstice sunsets are the most fun. Mark the point of
sunset with a pole, stake or other (not easily moved) marker. Tag the
marker with the date of sunset.
Repeat the process every seven
days or so. Over the weeks and months you'll note that the sun appears
to "walk" faster at some times of the year than others. When you've
finished (in a year's time) you'll have a working astronomical calendar
and an excuse to invite friends and classmates over to the house to
check the date.
Non-construction alternatives
- Photo-op:
Take a snapshot of the western skyline and tape it to the wall by a
western facing window. With a felt tip marker draw an arrow on the photo
corresponding to the point of sunset and note the date. Repeat the
process.
- Window marks: (This takes two people.)
Standing at the same point in the room of a western facing window, have
the other person make a small mark on the glass where the sun sets. Note
the date and repeat the process on a weekly basis.
How it works
The principle behind an astronomical calendar is simple. The apparent
rising and setting horizon point of the sun changes with each passing
day. The different points correspond to different days of the year.
At minimum, an astronomical calendar only requires a fixed reference
point for viewing and another fixed reference point marking the position
of the rising and/or setting sun on the horizon.
In the
Northern Hemisphere, if you were to watch a time-lapse movie of a year's
worth of sunsets, you would notice that the sun appears to "walk" back
and forth across the western horizon. The winter solstice marks the
southern limit of the sun's journey and the summer solstice is the
northern boundary. Closer examination would reveal that, with the
exception of the two solstice extremes, every other point on the horizon
is crossed twice during the course of the year. Once on the southern
march and again on the northern return.
At the time of the
winter and summer solstices, (around December 22 and June 22) the sun is
directly overhead at either the Tropic of Cancer (summer) or the Tropic
of Capricorn (winter). In the Northern Hemisphere these dates mark the
beginnings of summer and winter and the days of the longest and shortest
hours of daylight.
