Return to Archeoastronomy Index Page

Academic Setting:

Highland High School is the most ethnically and culturally diverse public high school in New Mexico. Our student population includes Anglos, Hispanics, African-Americans, Native Americans, Vietnamese, Chinese, Cambodians, Indians (east) and Arabs. Next year Catholic Relief Services plans to relocate a number of Bosnian families in the Highland district. Indeed the Highland school district seems to be quite popular with new immigrant communities. Highland High School also has a relatively large Native-American student population.

The objective of this unit is to provide an historical and cultural context for the study of physics. I would like the students to understand that the modern worldview has evolved from and is linked to the beginnings of civilization, and in particular, to the ancient’s study of astronomy.

This Curriculum Unit is intended for a Physics I class. Physics students at Highland are usually high achievers, with very good academic skills. The students who take Physics also reflect the ethnic diversity of the school. For the coming school year, we have 80 students enrolled in three sections of physics.

Introduction

Being an amateur historian, I like to put the development of science and math in a historical and cultural context. It appears to me that the development of a system of astronomy is one of the first things that a civilization produces. Astronomy is integral to the development of culture. When I discuss the earliest developments of math and science with my students, I usually take examples from the ancient civilizations of Babylon and Egypt. The development of math and astronomy appear to be closely linked to the development of organized agriculture and the need to plan planting and harvesting (astronomy), and to tax agricultural production (math). Astronomy is the first discipline to develop a really rigorous system of observation and data recording, followed shortly by the keeping of records of land ownership and taxation. Astronomy is also closely linked to a civilization's religious and cultural development. Thus in my classes, I like to talk about why a civilization would develop a system of mathematics or find patterns in the heavens and how these developments relate to our current civilization and culture.

Pueblo culture is an important and interesting part of New Mexico's culture and history. Also, Highland High School has a relatively large Native-American student population. The first civilizations of Babylon and Egypt are both temporally and spatially distant from my students, while Pueblos surround Albuquerque. The Pueblo culture is something we can witness today. As it happens, however, I know a lot more about the ancient Near East than I do about Pueblo culture. I would like to be able to share with my students facts about the development of astronomy by our own native cultures. Math and science come alive when we can see how and why they were developed, and better yet if we can go and look at nearby examples.

In this curriculum unit I will discuss the approach to astronomy of a number of ancient or traditional cultures and where possible relate those approaches to the modern world and how we do science now. I will also discuss some of the key cultural differences, and emphasize how our cultural context influences (if not dominates) our view of physical reality.

Cultural Background:

Astronomy and the Beginning of Civilization

Observational astronomy is considered to be the oldest science. Ancient astronomers used the motions of the Sun, Moon, stars, and planets to provide them with the first clocks and calendars. By observing the yearly motions of objects in the sky, they were able to determine when to plant and harvest their crops and when to prepare for the cold weather and the coming of spring. While our reasons for observing the sky have changed over the centuries, our awe of its wonders remains as strong. Many cultures throughout history have contributed to our knowledge of the universe.

Early civilizations along the Tigris and Euphrates rivers and along the Nile river, as well as the Anasazi watched the stars for religious and agricultural purposes. According to Will Durant, science, like civilization, in general began with agriculture. Geometry began as the measurement of the soil. Predictions of planting and the harvest, the cycle of the seasons and the development of a calendar may have evolved into astronomy. New civilizations seem to have stargazing linked to the development of organized agriculture.

In some civilizations, like ancient Egypt, and Babylon, astronomers began to incorporate mathematics into their observations; the Anasazi however did not. In the seventeenth century BC, the Mesopotamian (hereafter referred to as Babylonians) accurately observed Venus, the Moon, planets, eclipses, solstices and equinoxes; the Greeks contributed modeling, geometry, and logic; the Egyptians, observations; the empire of Islam, instrumentation, constellations patterns, and star names. Astronomy, initially a tool of religion and agriculture also became the basis for scientific observation, data collection and a good bit of the mathematics of geometry and trigonometry.

Much of the ancient culture is with us today. For the traditional people of the modern Pueblos, the astronomy of the Anasazi is still an integral element of their cultural and spiritual lives.

Mesopotamia and Egypt

Religion was an important aspect of astronomy for the Babylonians. They believed that the motion of the heavens could predict the future. The Babylonians thought of each planet as a god, and every movement of the sun, moon and stars foretold some earthly event. The Babylonians began charting the stars around 2000 BC. Their priest-astronomers plotted the motion of the sun and moon and could predict their eclipses and conjunctions. They divided the ecliptic into the twelve signs of the Zodiac, and developed a calendric system to fix the dates of the equinoxes and solstices. To manage this, they observed and recorded astronomical data for centuries. The Babylonians gave us the 360-degree circle, the sixty-minute degree and the sixty-second minute. These probably result from their sexagesimal counting system (and I have no idea why they used a base 60 number system). They even solved quadratic equations. They gave us the year of twelve lunar months and from time to time added a thirteenth month to keep time in kilter. They also divided the day into twelve hours.

The Egyptians were less skilled at astronomy than the Babylonians. But they were good enough to predict solstices and equinoxes. Most importantly they could use astronomy to predict the flooding of the Nile. The Egyptians were more agriculturally oriented than the Babylonians in their Astronomy. (Our Oriental Heritage, Will Durant, Simon and Schuster, New York, 1954). The Babylonians possibly knew already that the rotation of the stellar constellations was subject to change, but Hipparchus was, in the 2nd century BC, the first astronomer who gave a description of this phenomenon

The Greeks

Greeks were odd by ancient standards. They often studied things just because they were curious. They were also unusually eager to share their wisdom with anyone who would listen. So for the Greeks the religious aspects of astronomy were much less important than for other cultures.

Three prominent figures in Greek astronomy are Hipparchus, Ptolemy and Aristotle. Little is known of Hipparchus's life, but he is known to have worked in Nicaea, Rhodes and Alexandria. He worked on trigonometry. He introduced the division of a circle into 360 degrees into Greece and produced a table of chords, an early example of trig tables. He also gave methods for solving spherical triangles and advocated the use of latitude and longitude for position on the Earth. Hipparchus calculated the length of the year to within 6.5 minutes and discovered the precession of the equinoxes. Hipparchus's value of 46" for the annual precession is good compared with the modern value of 50.26" and much better than the 36" Ptolemy was to obtain nearly 300 years later. His star catalog, containing about 850 stars, lists magnitude with a six-point scale similar to that used today. His star catalogue, completed in 129 BC, was used by Ptolemy and its quality was such that it was even used by Halley.

Ptolemy (AKA Claudius Ptolemaeus) lived in Alexandria (in Egypt) from approx. 87 -150 AD. Very little is known about his personal life. He was an astronomer, mathematician and geographer. He codified the Greek geocentric view of the universe, and rationalized the apparent motions of the planets, as they were known in his time. Ptolemy synthesized and extended Hipparchus's system of epicycles and eccentric circles to explain his geocentric theory of the solar system. He believed the planets and sun to orbit the Earth in the order Mercury, Venus, Sun, Mars, Jupiter, and Saturn.

This system became known as the Ptolemaic system. It predicts the positions of the planets accurately enough for naked-eye observations. This is described in the book Mathematical Syntaxis (widely called the Almagest), a thirteen book mathematical treatment of the phenomena of astronomy. It contains a myriad of information ranging from earth conceptions to sun, moon, and star movement as well as eclipses and a breakdown on the length of months. The Almagest also included a star catalog containing 48 constellations, using the names we still use today.

In addition to his well-known works in astronomy, Ptolemy made very important contributions in geography and cartography. Ptolemy, of course, knew that the Earth is a sphere. Ptolemy's map of earth is the first known projection of the sphere onto a plane. His

Geography remained the principal work on the subject until the time of Columbus. But he had Asia extending much too far east, which may have been a factor in Columbus's decision to sail west for the Indies.

The Ptolemaic explanation of the motions of the planets remained the accepted wisdom until the Polish scholar Copernicus proposed a heliocentric view in 1543. It should be noted, too, that Ptolemy's system is actually more accurate than is Copernicus's. The heliocentric formulation does not improve on Ptolemy's until Kepler's Laws are also added to take into account that the planetary orbits are elliptical.

In addition to formalizing the law of formal logic, Aristotle chiefly contributed a flawed theory of the universe that posited a geocentric universe, where all celestial motion was circular. The Church viewed the theories of Aristotle as though they were divinely inspired. Galileo, Copernicus and Kepler finally put an end to the Aristotelian View of the universe.

The Mayans

The Maya were quite accomplished astronomers. They seemed to use astronomy more for religious purposes than for agriculture. Their primary interest, in contrast to "western" astronomers, were Zenial Passages when the Sun crossed over the Maya latitudes. On an annual basis the sun travels to its summer solstice point, or the latitude of 23-1/3 degrees north. Most of the Maya cities were located south of this latitude, meaning that they could observe the sun directly overhead during the time that the sun was passing over their latitude. This happened twice a year, evenly spaced around the day of solstice. The Maya could easily determine these dates, because at local noon, they cast no shadow. Zenial passage observations are possible only in the Tropics and were quite unknown to the Spanish conquistadors who descended upon the Yucatan peninsula in the 16th century.

The Maya had a god to represent this position of the Sun called the Diving God. The Maya evidently thought quite a bit about the Sun and they watched it trace out a path along the ecliptic. They followed it year round, presumably following its path along the horizon. At Chichen Itza, during sunset a sun serpent rises up the side of the stairway of the pyramid called El Castillo on the day of spring and Autumn Equinox. It tells us that the Maya noted not only the extremes of the Sun at the Solstices, but also the Equinoxes when the Sun appeared to rise due East or due west. In addition to the Zenial Passages mentioned earlier, ecliptic observations must have been a major portion of Maya solar observing.

The Maya had a lunar component to their calendric inscriptions. After giving the pertinent information on the date according to the Maya calendar the typical Maya inscriptions contain a lunar reckoning. The lunar count was counted as 29 or 30 days, alternating. The lunar synodic period is close to 29.5 days, so by alternating their count between these two numbers the moon was carefully meshed into the calendric sequence as well. Their lunar knowledge was impressive for they also made eclipse predictions. An almanac for predicting them is contained in the Dresden Codex.

The Maya Kings timed their accession rituals in tune with the stars and the Milky Way. They celebrated a feast called k'atun approximately every twenty years. At the end of the 20-year k'atun period, Maya rulers regularly erected a stela, called a stone tree, to commemorate the event. On stone stela they depicted themselves at the time of these ceremonies dressed in costumes that contained the symbols that were associated with the World Tree. By wearing the costume elements of the World Tree the Maya ruler linked himself to the sky, the gods and that essential ingredient, life. In addition, it has been found that when the k'atun ending coincided with certain planetary positions the Maya went to war to obtain captives for sacrifice.

Anasazi and Pueblos

Indian tribes in what becomes the southwestern United States paid close attention to the sun, moon and stars. These elements were seen as powerful religious figures, and most tribes paid homage to them. The Anasazi, who are thought to be the ancestors of the modern Pueblo tribes, left numerous sites of astronomical/religious significance in the areas of Chaco Canyon and Mesa Verde. The Anasazi paid especially close attention to the winter and summer solstices.

Anasazi, and later the Pueblos’ prayers and ceremonies were dedicated to the sun in order to keep the world in harmony. The changes of the season were mostly determined by sun watching. The single most powerful and highly respected symbol in Pueblo life is the sun. According to Ray A. Williamson, "The Sun and its power dominates the Southwest."

Most of Pueblo astronomy can be linked directly to the sun. Extensive observations of the sun led to the development of an advanced sun-based religion among the Pueblo cultures. Each pueblo consists of a tight organizational structure headed by a priesthood, which controls the social, political and religious aspects of daily life. The primary function of the priesthood in Pueblo society is to perform ceremonials for the good of the people by keeping them in harmony with nature. The purposes of the ceremonials are to control the weather and the movements of the sun, and to promote fertility in all living things. In addition, a common outlook exists between the Pueblos, which probably resulted as a response to how successful their crops were.

Since the Sun is such an important factor for the health of the pueblo and for the individual, Pueblo astronomy is different from astronomy in the traditional sense; it focuses more on the daytime sky, rather than the stars and other features of the night sky. The Pueblo people have put much emphasis on the sun for practical purposes. Solar calendrical devices were made to indicate proper times for ceremonials and other important events. In particular, the solstices were regarded as special occasions and many of the calendrical markers were geared to indicate precisely when a solstice would occur. At Hovenweep Castle, an ancient Anasazi ruin, a room acts as a solar calendar. Several "ports" or holes cut into the walls of this room align with the rays of the sun at particular times and indicate the summer and winter solstices and the spring and fall equinoxes. Other ruins have indicated similar findings. Of course, planting and harvesting are tied to the equinoxes.

At Chaco Canyon, the Casa Rinconada site appears to have astronomical functions. The Anasazi built Casa Rinconada in nearly a perfect circle. The four main supporting posts in the ancient kiva were located in the corners, which also indicate the four cardinal directions: northwest, southwest, southeast, and northeast. The portholes found in the ruins were likely used for predicting the equinoxes.

Relevance to Modern Science

So what is the relevance of ancient or traditional astronomy to modern science? Although astronomy predates the scientific method, the methodology of the ancient astronomers sets the groundwork. The scientific method entails observation, hypothesis, and the testing of that hypothesis to determine if it is an accurate predictor. The ancients observed the motion of the sun and moon and stars. They noticed that eclipses occurred from time to time. They looked for patterns in the motion of the celestial bodies. They developed hypotheses about when the next eclipse would occur. They tested those predications and eventually developed an accurate methodology for eclipse prediction. To do such predictions, the ancient Chinese and Babylonians developed the idea of systematic observation and data records.

The regular and predictable nature of the motion of sun and moon becomes the basis for measuring the passage of time. Perhaps it is the basis for the pre-relativity concept of the passage of time as regular, constant and immutable. I have heard arguments that the way Native Americans view the nature of space and time is more in tune with Einstein's view of an integrated space-time. This is a big divergence in the view of nature from the ancient civilizations of Asia and the Anasazi/Pueblo tradition.

In Babylon and Egypt and later in Greece the astronomer/priests developed geometry and the rudiments of algebra to help them with their celestial calculations. The early mathematics also facilitated property records and taxation. The Native Americans of the Southwest did not develop a system of math; they also appear to have had a less hierarchiacal social structure with less emphasis on ownership of property and no record of taxation.

Further, in order to do predictive astronomy, one needs a frame of reference for observations and measurements. Ancient people thought that the Earth was the center of the universe. Ptolemy developed a complete (or as complete as one can be without a telescope) and accurate model of celestial motions, with the Earth at the center of the universe. The heliocentric model gained acceptance in the 17th century. As we began to grasp the size of the universe, it was no longer clear that we could find its center. In the 17th and 18th century, with the development of the laws of motion and the mathematical tools to describe them, one could do calculations from any frame of reference.

Astronomical Background

What can we all observe in the sky without the aid of instruments- the sun, the moon and the stars (some of them anyway)? After observing the sun rise daily for a number of years, even the most casual primitive observer might notice a pattern. Seeing a pattern in day following night, our observer might begin to look for patterns elsewhere. Pretty soon early civilizations find that agricultural cycles can be tied to the motions of the sun and moon. So a cottage industry of sun and moon gazing springs up in conjunction with developing civilizations increasing dependence on a successful agricultural system. The dawn of astronomy, perhaps the dawn of all science.

Some basic things the early astronomical observer will note are the seasons, the phases of the moon, the variable length of the day as follows:

The Earth is in an elliptical orbit around our Sun. In Earth's case, its orbit is nearly circular, so that the difference between Earth's farthest point from the Sun and its closest point is very small. Earth's orbit defines a two-dimensional plane which we call the ecliptic . It takes roughly 365 days for the Earth to go around the Sun once. The time it takes for the Earth to go around the Sun one full time is what we call a year. The combined effect of the Earth's orbital motion and the tilt of its rotation axis result in the seasons

As the Earth travels around the Sun, it remains tipped over in the same direction, towards the star Polaris. This means that sometimes the northern half of the Earth is pointing towards the Sun (summer ), and sometimes it is pointing away (winter). These points in the Earth's orbit are called solstices. When the northern hemisphere is tilted towards the Sun, the southern hemisphere is tilted away. This is why people in places north of the equator have the opposite season of people south of the equator.

Halfway in between the solstices, the Earth is neither tilted directly towards nor directly away from the Sun. At these times, called the equinoxes, both hemispheres receive equal amounts of sunlight. Equinoxes mark the seasons of autumn and spring and are a transition between the two more extreme seasons, summer and winter.

The Moon has an elliptical orbit which is nearly circular. Its average distance from the Earth is 384,400 km. The combination of the Moon's size and its distance from the Earth causes the Moon to appear the same size in the sky as the Sun, which is one reason we can have total solar eclipses. It takes the Moon 27.322 days to go around the Earth once. The changing position of the Moon with respect to the Sun leads to lunar phases . The same side of the moon always faces the Earth. It takes the Moon the same amount of time to rotate around once as it does for the Moon to go around the Earth once. Therefore, Earth-bound observers can never see the 'far-side' of the Moon

c. 30000 BC Bone carving interpreted as record of lunar phase cycle (France)

c. 7000 BC Rock paintings interpreted as tally of lunar-month days (Spain)

4000 BC Evidence of specific labeled constellations (Euphrates Valley)

2800 BC Beginning of Stonehenge construction (England)

2608 BC Observatory built (China)

2500--2000 BC Equinoxes and solstices determined, gnomon invented, observations of Pleiades, comets, solar eclipses (China)

2000--1501 BC Geometry used as basis for astronomical measurement signs of the zodiac known (Babylonia)

1750 BC Temple Wood observatory built (Scotland)

1500 BC Oldest known sundial (Egypt)

165 BC Spot on Sun reported (China)

140 BC Construction of armillary sphere (China)

129 BC Hipparchus catalogued 1080 stars divided into 6 magnitudes positions were given in latitude longitude as referred to the ecliptic

500 AD Written commentary on astrolabe (Egypt)

850 AD Astrolabe perfected by Arabs

1600--1609 AD Telescopes invented perfected (Netherlands), Galileo constructs a telescope, Kepler's laws of planetary motions, and Simon Marius observes Jupiter's moons

1610 AD Galileo observes Jupiter's moons, Harriott discovers sunspots,
Peresc discovers Orion Nebula

1665 AD Cassini determines rotations of Jupiter Mars Venus

1666--1668 AD Newton measures the Moon's orbit; constructs reflecting telescope

1705 AD Halley predicts return (1758) of comet seen in 1682

1750 AD Expedition to Cape of Good Hope to determine solar lunar parallax

1781 AD Herschel discovers Uranus

1800 AD Herschel discovers existence of infrared solar rays

1846 AD Adams/Leverrier discover Neptune

1930 AD Tombaugh discovers Pluto

1989 AD Magellan and Galileo spacecraft launched

1990 AD Hubble Space Telescope placed in orbit

1992 AD Mars Observer launched

Vocabulary

Altitude- the angle of elevation from the horizontal plane to a point above the horizon. Altitudes range from 0 (on the horizon) to 90 (straight up).

Annular eclipse - a solar eclipse in which a ring of sunlight can be seen around the edge of the moon.

Ascending lunar node - the intersection of the moon's orbital plane and the ecliptic where the latitude coordinate is increasing.

Autumnal equinox - one of the two points on the celestial sphere where the ecliptic intersects with the celestial equator.

Azimuth- the angular measure from a particular point on the horizon to another point also on the horizon. Traditionally the starting point of the azimuth is the northern most point on the horizon. Azimuth angles are then measured positively from the north (0°) through (90°), south (180°) and west (270°).

Central eclipse- a solar eclipse in which the axis of the moon's shadow cone crosses the surface of the earth.

Descending node- the intersection of the moon's orbital plane and the ecliptic where the latitude coordinate is decreasing.

Ecliptic- the sun's apparent annual path or orbit as seen from the earth. Against the background stars, the sun appears to traverse the ecliptic in the course of one year. From the point of view of the sun, the ecliptic is the path of the earth about the sun. The word ecliptic is also used to define the plane that contains the orbit of the earth about the sun.

Equinox - either of the two days when the periods of daylight and darkness are of equal length. The one in March is vernal equinox and the one in the fall is called the autumnal equinox.

Gregorian Calendar a reformation of the Julian Calendar which changed the way intercalary days (leap years) were calculated. For example: the year 2000 is a leap year, but 1900 and 2100 are not. Similarly, 1996 is a leap year, but 1997 is not. This reform approximates the tropical year to within about one day in 2500 years.

Horizontal coordinates these use azimuth and altitude to measure a location in the sky. They are referred to the plane of the observer's horizon.

Julian Calendar Day- A day in the calendar created by Julius Caesar. That calendar was a solar calendar that had twelve months each of a fixed length. An intercalary day, or leap year, was added every fourth year, so the average solar year was 365.25 days. This calendar was instituted in 46 BC and was replaced by the Gregorian Calendar in 1582.

Latitude - angular measure on the celestial sphere measured north or south of the ecliptic along the great circle that includes the poles.

Latitude- angular distance on the earth measured north or south of the equator along a great circle that includes the poles.

Longitude- an angular measure on the celestial sphere along the ecliptic starting from the vernal equinox (0°) and continuing positively to the east.

Longitude- angular distance measured along the earth's equator starting from Greenwich, England and continuing positive to the east.

Node- the intersection of a great circle on the celestial sphere with a plane that contains the origin results in two points called nodes. For example, the moon's orbit intersects the ecliptic plane at the ascending node and the descending node.

Season - one of the four divisions of the astronomical solar year, either solstice or equinox.

Solar eclipse- the partial or total apparent darkening of the sun when the moon come between it and the earth. The Sun appears in the sky either partially or totally covered by the Moon.

Solstice the day when the sun's longitude is either 90° (summer solstice) or 270° (winter solstice). At those times noontime Sun is either highest in the sky (summer solstice) or lowest in the sky (winter solstice).

Synodic month- the time from one full moon to the next (29.530588 days).

Presentation of the Unit

This unit will be presented at the beginning of the term. Highland is on a block schedule; each class session is 85 minutes long. I anticipate presentation, along with the demonstrations to take about three class sessions. On the first day we will discuss the motion of sun and moon. Lecture and discussion will last about an hour followed by the "Revolution and Rotation" activity described below.

 

On the second day we will discuss the astronomy of the four cultures discussed in the cultural background. We will do the demonstration " the Lunar Month" described below.

 

On the third day we will discuss the relevance of the work done by the ancients to our world. We will do the " Day on Earth" activity.

 

The demonstrations of rotational motion will be used to present the most difficult concepts of the unit. The motions of spinning bodies orbiting other moving bodies should be the most challenging portion of the unit.

 

Unit Objectives:

Students will: 1) become familiar with the motion of the earth relative to the sun and the rotation of the moon relative to the earth, 2) understand the cultural origins of the science of astronomy, 3) gain an appreciation of how the past is relevant to the present, 4) gain an understanding of how one’s culture affects one’s understanding of the world.

Outcome/Evaluation:

 

The degree to which students achieve the unit objectives may be measured in a number of ways. Since we will not be focusing on computational methods or physical theories, the traditional problem and short answer based physics test format is not appropriate. A long essay or an essay test which addresses the key ideas and concepts of the unit is the most obvious method of assessment. A group project where students collaborate to prepare a presentation to the class of new, but related, material is also a reasonable method of assessment.

The first time the unit is presented, student understanding of the unit will be evaluated by an essay test. I will try the group presentation the next time and determine which works better for my classes. A term paper is also required for the course, and topics presented in this unit may be used as the subject of the required paper.

Demonstrations:

Rotation and Revolution: The Moon

Have a student stand in front of the class facing the back of the room. Have him slowly turn counterclockwise a full 360 degrees. Have him describe what he sees as he turns: the back of the room, the left side (as viewed from the front of the room), the front, the right side, and then the back again). Explain that the student has just rotated once and as the student turned he saw, in turn, all sides of the room. This is rotation.

Now have another student stand in front of the class, facing the back of the room, toward the class. Have the first student move in a circle, counterclockwise, around the second student, always facing the back of the room. The first student starts out in back of the second student, then to their right, then in front, then to their left, and then back in back of them. This is revolution.

Now ask the students whether or not the first student rotated while revolving around the second student: No, they always faced the back of the room. Now, have the first student revolve around the second student, but this time always facing the second student. As they move around the second student, have them describe what part of the room they are seeing: first the back, then the left side, then the front, then the back again --- they rotated once as they revolved around the second student!

The Lunar Month

We can now discuss the Moon as it goes around the Earth. Since we always see the same side of the Moon, this implies that the Moon rotates once as it revolves around the Earth Student 1 = Sun. student 2 = Earth, student 3 =Moon. Have student 3 revolve and rotate around student 2 once (2 motionless). This is how long it takes for the Moon to go once around the Earth, 27 1/3 days. However, in reality, the Earth is revolving around the Sun. In 27 1/3 day, it has one nearly 1/12 of the way around the Sun. Have student 2 demonstrate this by having them move a little counterclockwise around student 1, the Sun.

Now, bring back student 3. Line up the students Sun, Earth, and Moon (1, 2, and 3) with the Moon student 3) facing the Sun and the back of the room. As seen from the Earth, this is full Moon. Now, as student 3 rotates and revolves around the Earth, have the Earth revolve slowly around the Sun. Have the Moon revolve and rotate once, so they are facing the back of the room again --- as can be seen in Figure 1, the three students are no longer in a straight line, it is not full Moon. The Moon must continue to revolve and rotate about 1/12 of an orbit until the Sun, Earth, and Moon are aligned again. This is defined as one month, the time from full Moon to full Moon, 29 1/2 days.

Have student 2 rotate once counterclockwise, begin facing the Sun and rotate until they are facing the Sun again --- they have rotated once. For the Earth this is 23 hours 56 min 4 sec. Now have student 2 do the same thing, but have them revolve slowly around the Sun at the same time.

In order for them to end up facing the Sun again, they have to rotate a little bit more than once. Therefore, the time from noon to noon, when the Sun is overhead (24 hours or one day), is slightly more than the time it takes the Earth to rotate on its axis. This is why we see different stars at different times of the year. The stars are like seeing different parts of the room as we rotate on our axis and revolve around the Sun.

Bibliography

                    Our Oriental Heritage, Will Durant, Simon and Schuster, New York, 1954

Internet Resources

http://www.astro.uva.nl/home2.html

http://seds.lpl.arizona.edu/nineplanets/psc/theman.html

http://idt.net/~craigi19/archaeoastronomy/DEFINED.HTM

http://ethel.as.arizona.edu/~collins/astro/subjects/observation3.html

http://www.ukans.edu/history/index/europe/ancient_rome/E/Gazetteer

Suggested Reading

Star Names: Their Lore and Meaning, by Richard Hinckley Allen. ISBN 0-486-21079-0. 1963, Dover Publications.

Native American Astronomy edited by Anthony F. Aveni. ISBN 0-292-75511-2. 1977, University of Texas Press

Archaeoastronomy in Pre-Columbian America, edited by Anthony F. Aveni. ISBN 0-292-70310-4. 1975, University of Texas Press.

Astronomy of the Ancients, edited by Kenneth Brecher and Michael Feirtag. ISBN 0-262-52070-2. 1981, MIT Press.

When Stars Came Down To Earth, by Von Del Chamberlain. ISBN 0-97919-098-1. 1982, Ballena Press.

Echoes of Ancient Skies: The Astronomy of Lost Civilizations, by E.C. Krupp. ISBN 0-452-00679-1. 1983, Harper & Row Publishers..

In Search of Ancient Astronomies, edited by Ed Krupp. ISBN 0-07-035556-8, 1978, McGraw-Hill Publishers. Star Tales, by Gretchen Will Mayo. ISBN 0-8027-6672-2. 1987, Walker & Co., New York.

Living The Sky: The Cosmos of the American Indian, by Ray A. Williamson. ISBN 0-395-35414-5. 1984, Houghton Mifflin Co. Boston.