Archeoastronomy and World Cosmology
Astronomy 6, Spring 2008Pomona College
Short Assignment #2: Stonehenge and Time -- Due February 14, 2008
"In this world, time is a visible dimension. Just as one may look off in the distance and see houses, trees, and mountain peaks that are landmarks in space, so may one look out in another direction and see births, marraiges, deaths that are signposts in time, stretching off dimly into the far future. And just as one may choose whether to stay in one place or run to another, so one may choose his motion along the axis of time. Some people fear travelling far from a comfortable moment. They remain close to a temporal location, barely crawling past a familiar occasion. Others gallop recklessly into the future, without preparation for the rapid sequence of passing events.."
Excerpt from thought experiment "15 June 1905" from Einstein's Dreams, by Alan Lightman.
"And an astronomer said, Master, what of Time?
And he answered: You would measure time the measureless and the immeasurable... Of time you would make a stream upon whose bank you would sit and watch its flowing. Yet the timeless within you is aware of life's timelessness, And knows that yesterday is but today's memory and tomorrow is today's dream. And that which sings and contemplates in you is still dwelling in the bounds of the first moment which scattered the stars into space.."
Excerpt from "The Prophet", by Kahil Gibran.
"Imagine a world in which people live just one day... a man or woman sees one sunrise, one sunset. In this world, no one lives to witness the seasons. A person born in December in any European country never sees the hyacinth, the lily, the aster.. never sees the leaves of the maple turn red and gold, never hears the crickets or the warblers. A person born in December lives his life cold. Likewise a person born in July never feels a snowflake on her cheek, never sees the crystal on a frozen lake, never hears the squeak of boots in fresh snow. A person in July lives her life warm. The variety of seasons is learned about in books.."
Excerpt from thought experiment "3 June 1905" from Einstein's Dreams, by Alan Lightman.
You may find the equations below useful for this assignment.
Archeoastronomy Equations:I). a (Pole Star) = latitude
II). a (transit) = declination – latitude + 90
III). Sin () = cos (A) cos (latitude); A= Azimuth, = declination
Complete readings in Aveni and others as in syllabus
1). Time – How do ancient and modern notions of time differ? Using some of the quotes above as a starting point, discuss in a brief paragraph how our conception of time has evolved through time. Then try this experiment: Set aside one minute in a quiet place, and contemplate the minute of time, and compare the experience of this minute to other minutes you experience in a day or a year (“525,600 minutes…”)
2). Calendars! As you may remember, our year is 365.2422 days long, and the lunar month is 29.53059 days long.
a). Verify that the Metonic Cycle mentioned in class works, and determine how far off a lunar calendar will get using the Metonic Cycle of alternating 13 and 12 lunar months over 19 years. How many years will it take to accumulate 1 day of error? The facts below maybe useful for this problem:
19 tropical years = 6939.602 days
235 synodic months = 6939.688 days
b). The Julian Reform made the year 365.25 days long. Before this amazing innovation, the year was 365 days long. How many days off would this calendar be for the ancient people after 1000 years?
c). With the new (~500 year old) Gregorian reform, the year is now 365.2425 days long. There is an error of 0.0003 days per year. How far off will a new pope need to wait before declaring some extra leap days?
3). Design a “Stonehenge” or sundial for Claremont. Using the equation III above, calculate the azimuth positions for the sun at summer and winter solstice sunrise, and the extreme lunar azimuths. Then provide a labeled diagram of your monument, which will include labeled angles and cardinal directions. Please be creative, and include appropriate symbolism for Pomona. If you design a sun dial, try and sketch the gnomon, and its dimension, and indicate the location of different shadows for the gnomon at different times and dates. We actually are considering a new sundial for the front of our Physics Building, so your design could help us make campus more astronomically interesting!
You may find the following resources helpful if you are designing a sundial.
The analemma applet at :
The software “Shadows” for sun dial design at:
North American Sundial society – lots of pictures of sundials:
Essay Question – ( answer in a page or two):
4a). How do you consider Stonehenge? Is it your opinion that the eclipse prediction theory is credible? How about the solar and lunar alignments? How would you react to the quote by Jacquetta Hawkes: “Every Age has the Stonehenge it deserves – or desires”.