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.

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.

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.

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.

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.

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).

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.]