5. The Science of Astronomy

Hypatia's Astronomy

Welcome to the Observatory of Alexandria. Here, on the southern shores of the Mediterranean, at the delta of the Nile, I teach astronomy and mathematics at the University. This year, 400 AD, I have been appointed director of the Observatory of Alexandria--a fine observatory where famous astronomers Aristarchus, Eratosthenes and Ptolemy made observations of the heavens. We also have a large and important library here in Alexandria a scholars come from all over the Roman Empire to study here.

I have been invited to tell you about Greek and Roman astronomy so I am going to show your the sorts of things that I discuss with my students at the University of Alexandria.

I would like to start before the Greek Empire. For thousands of years people watched the Sun rise and set, the Moon move in cycles with the Sun. From the very beginning people noticed the same patterns of stars rise and set. These cycles became the rhythm of life on Earth. Stories and myths developed around these familiar objects in the sky and the patterns in the sky, star constellations, were given names. Among the people of the Babylonian civilization that grew up in the fertile valleys of the Tigris and the Euphrates rivers, were early astronomers who began to measure the cycles of the heavens. They noticed that the Moon changed phases with a cycle of about 30 days. They counted about 360 days between the times when a favorite bright star, such as Sirius the dog star, first appeared at twilight on the eastern horizon. This gave astronomers the power to predict the timing of important events for this agricultural community such as the annual flooding of rivers. They were also able to predict the occurrence of eclipses--awesome and mysterious events that made people afraid. Thus, by counting the days between celestial events they measured the cycles of the heavens and developed a calendar.

The Babylonians developed a cosmology --a view of the universe--based on the cycles of the heavens. But their view was limited--they did not really develop a sense of what these cycles meant--they fitted them into their mythology. For example, they believed the Earth was flat and that when the Sun set from the western sky it was carried in a boat along a canal around to the north by night, to rise again in the east at the break of the day.

Now let's move to the Greek Empire when there were two important developments: (1) the development of philosophy and mathematics, (2) the development of means of making measurements. In particular, I would like to mention a famous Greek mathematician, Pythagoras who lived around 500 BC. You probably are familiar with Pythagoras' famous theorem:

This development of geometry allowed the early Greeks to make measurements of the stars. Thus, they were able to measure the location of a star using just a plumb-bob and a measuring stick. They were able to quantify the angle above the horizon when a star is at its highest point in the sky--when it crosses the meridian. They also measured the day of the year when the star is first visible at twilight. Thus, the Greek astronomers established a cosmology based on measurement rather than mythology.

These two tools of measurement and mathematics led to the development of the scientific method--building a model of the heavens and an understanding of the construction of the universe that is based on developing a theory of how the objects move in the sky. This led to prediction of what where an object should be at a specific time and allowed the testing of a hypothesis by measurement, observations which either confirming the hypothesis or negating the hypothesis and forcing a modification of the theory if the measurements did not match up. Thus, the Greeks developed a philosophy based on rational argument rather than mythology.

For example, Aristotle, who lived in about 350 BC, made a hypothesis that the Moon is a sphere. He could construct a model of the Sun-Earth- Moon system using a candle for the Sun and a ball for the Moon. He showed that the observed phases of the Moon could only be replicated using a ball for the Moon rather than a plate or disk.

Aristarchus, who lived here in Alexandria in ~250 BC, further explored the Earth-Sun-Moon system. He used eclipses to estimate the relative sizes and distances of the Earth, Moon and Sun. First he looked at the Earth's shadow on the Moon during a lunar eclipse. The gentle curve of the Earth's shadow on the Moon indicated that the Earth is larger than the Moon, over twice the size. On the other hand, the Moon's shadow on the Earth had to be small, Aristarchus argued, because solar eclipses were rare events and observed in some parts of the extensive Greek Empire but not other areas. Solar eclipses also suggested to Aristarchus that the Earth had to be much bigger than the Moon. After all, the Sun and Moon have the same angular size (half a degree). If the Sun is much farther away than the Moon then the Sun has to be much larger.

But how far away is the Sun? Aristarchus developed an ingenious way of measuring the distance.

From his measurements of the fraction of a lunar month between times when the Moon appeared to be cut exactly in half, he estimated that the Sun was 20 times farther from Earth than the Moon. Aristarchus went a step farther. He conjectured--if the Sun is much farther away than the Moon and therefore much bigger than the Moon, and even than the Earth, then perhaps the Sun must be the center of the universe. The problem with Aristarchus' reasoning is that the Earth does not appear to be moving--the stars to not appear to change position (there is no parallax). Without evidence of parallax it is hard to image the Earth to be moving. So how can the Sun rather than the Earth be the center of the universe?

Another measurement made by a Greek astronomer that you may have heard of was made by Eratosthenes around 200 AD, here in Alexandria (see page 88 of text book). Eratosthenes noted that in mid-summer the Sun shone directly down a well in the town of Syrene, about a 12 days journey south of Alexandria. On the same day, the Sun made a shadow here in Alexandria. The angle between the Sun's rays and a plumb-bob was about 7°. Using simple geometry, Eratosthenes was able to use this measurement to estimate the size of the Earth. He concluded that the Earth has about 40,000 km around. Thus, by ~200 BC we knew that the Earth was round and how big is was.

In around 130 BC there lived a man who is regarded as the first real astronomer--Hipparchus. Hipparchus made accurate measurements with precise instruments. He developed the astrolabe, made a catalog of about 850 stars and measured their relative magnitudes. He noted that the north star was not quite at the celestial pole and that the celestial pole wanders around in the sky. Thus, he discovered precession (see Figure 3.9). Hipparchus also made very careful measurements of the parallax of stars. Yet he was not able to measure a significant parallax and was forced to conclude that the Earth is stationary. Nevertheless, in order to fit the observations of the Sun, Hipparchus had to conclude that the Earth was displaced from the center of the Sun's circular orbit.

A great legacy of Greek and Roman astronomy has been the detailed textbook on astronomy written by Ptolemy in about 140 AD, again, here in Alexandria. Ptolemy compiled his knowledge of the heavens into 12 volumes, the Almagast. This included a large catalog of stars, mathematical descriptions of the motions of the Sun, Moons and planets. This allowed prediction of locations and timing of astronomical events that could be checked by observations. Perhaps Ptolemy is most famous for his description of the motion of the planets around the Earth. Each planet moves in a system of circles within circles.

So, what is the heritage of Greek and Roman astronomy? What is our cosmology at 400 AD.? Well, we know that the Earth is round and about 40,000 km around. We know that the Moon is round and about 2-4 times smaller. We know that the Sun is much bigger than the Moon, perhaps greater than 20 times larger and 20 times farther away. Where is the center of the universe? The Earth appears to be fixed relative to the stars. We can describe the motions of the Sun, Moon and planets accurately with a complex model of their motions? But is it reality?

The Greeks developed geometry and measurement which led to the scientific method and a cosmology based on rational argument rather than mythology. We have developed a complex mathematical description of the motions of celestial objects. But we still do not know of a physical principle that explains the lay-out of the universe.

The Geocentric View

In reality, scientific progress is not made in such a simple and straightforward manner--there are red-herrings, U-turns and blunders along the way. Let's look at where the Greeks had made progress and where they were stuck up the wrong alley.
 

(3) (a) What had the Greeks deduced about the Earth?  (b) What did they deduce about the Moon?  (c) What else had they found out about the lay-out of the Earth/Moon/Sun system?  (d) What was thought to be at the center of the universe?  (e) Did the Greeks believe that the Earth moved? Why or why not? (4) The second major issue is the retrograde motion of Mars. The modern accepted explanation for retrograde motion is that of the Earth overtaking Mars as both planets orbit the Sun. Looking at Figure 3.7, estimate over what sort of period of time do you need to observe Mars to see its retrograde motion? Seconds? Hours? Days? Months? Years?

Astrology and Pseudoscience

Astrology has its beginnings in Mesopotamia in the 3rd millennium BC. If you divide up the sky into constellations, you would see different constellations at night at different times of the year. The ancient Mesopotamians also realized that the Sun would appear in different constellations throughout the year, even though the constellations themselves would not be visible because it would be daytime when the Sun was up.

For more info on astrology, check out these web links: The Real Romance in the Stars, an article by biologist Richard Dawkins.  Horoscopes versus Telescopes: A Focus on Astrology, article from the Astronomical Society of the Pacific.  Astrology FAQ from sci.skeptic newsgroup.

The ancients posited that the Moon and the planets, whose motions also takes them through the zodiac, along with the Sun, can affect people's lives depending on which house they were in when they were born. However as science has uncovered more information about the universe, astrologers kept changing their interpretations of how astrology is suppose to "work." When it was revealed that the stars were extremely far away, and even the planets so far away that they would have minuscule physical effects on people on Earth, astrologers abandoned the idea of direct physical effects. They instead resorted to intangible forces that could not be detected, or talked about "synchronicities", or some idea of cosmic consciousness or direction that could be divined from the stars.

The "Mars Effect" There has been some talk about the so-called "Mars Effect" discovered by the French psychologist Michel Gauquelin. The claim is that the exact times when the best athletes are born are correlated with when Mars occupies a certain positions in the sky. The effect is small and there has been debate over whether the effect is real or due to subtle biases in how the data was selected (see for instance, Jan Willem Nienhuys' article). Other attempts to duplicate the Gauquelin study with different samples have had mixed results. However even if the Mars Effect, dubious now, turns out to have some basis in fact in the future, astrologers should not be rejoicing. The "sectors" that the sky is divided into which Gauquelin used to get his results are in no way related to any traditional astrological divisions of the sky. The Gauquelin work is thus in fact, evidence against the method that astrologers use.

If you ask two astrologers what exactly is the best way to create a horoscope, you will likely not get the same answer. Some astrologers use only the traditional five planets plus the Moon and the Sun. Others have added in planets that have been discovered since the ancients invented astrology. Still others even include asteroids and other minor Solar System bodies. (Of course there is disagreement about which asteroids to use: do you use all of the ones discovered or do you decide to cut it off at some minimum size? If the latter, how small of an asteroid should you go down to?) Some astrologers believe that using the traditional twelve zodiacal houses is accurate enough. Others believe you have to look at where the actual boundaries of the constellations are. Your average newspaper horoscope astrologer seems to think that just by knowing what time of the year you were born is enough to give an accurate prediction. Others think you need to be accurate down to the date. Still others think you need the precise minute and second that you were born. And still others think not only do you need to be accurate to within a minute, but you also need the precise geographic location on the Earth! What's amazing still is that with so many astrologers using so many different techniques, they will all claim to be successful in predicting your future!

Science and Pseudoscience: All serious studies of astrology have shown that the results from astrology either do not show the correlation it claims to, or the results can be attributed entirely to chance. Despite this lack of evidence, astrologers have not made any basic changes to their beliefs. This is one of the vital differences between science and pseudoscience. The scientific method requires that hypotheses about how the universe operates be subjected to rigorous tests and observations. If the observations and data suggest that the hypothesis is incorrect, the hypothesis has to be revised or thrown out altogether. As a hypothesis gains more and more backing in the form of new experiments and measurements that also support it, it gradually becomes a theory or a law. In this sense, a scientific theory is not "just a guess", but is something that has an enormous amount of evidence behind it. In addition, scientists do not treat theories or laws as the Ultimate Truth or Final Say on the matter. If there is experimental data or observations that invalidate a theory, the theory has to change. Theories are the best guesses we have of how the universe operates, and some of the greatest advances in science have occurred when a previous theory was shown to be inadequate in explaining empirical evidence.
 

(5) Some people reckon that if something "works" then it must be "true". What evidence would you need to be convinced that astrology "works"? For example, how many "events" in a month would have to be accurately predicted?

 

Ancient Astronomy

The objectives of the following assignments are (i) to have some fun exploring some interesting sites, (ii) to explore these sites with the goal of extracting specific information, (iii) to collect information and synthesize a coherent summary of your findings.
 

(6) Pick one of the following topics and use the web references and the textbook as sources of information. Write a page (~300 words) on the topic you choose. (a) Compare how two or more cultures viewed an astronomical object (the Sun, Moon, Milky Way, Venus, a constellation, etc.;). OR (b) Compare for two or more cultures the roles played by astronomy in the culture. You can find a lot of links to other sites (some of which are listed below) from  the University of Maryland Center for Archeoastronomy  As far as general archeoastronomy sites goes you might try this which has a cute animation! This page also gives you link to "The Stone Circle" - interesting information on stone circles in the UK and Ireland (but it may be slow to download). Mayan Mathematics and Calendar  Lords of the Earth Central America - this is a neat site, and you can find parts of the various Mayan Codices (the Dresden Codex for instance). It also has information on Aztec, Mixtecand, Inca (South America) and North Native American cultures.  Nepohualtzitzin, a Mesoamerican Abacus This site let's you play with an abacus. It has material on astronomical calculations of the precolombian cultures.  a site from Japan  South America (Chile)  North Native American  American Southwest  Earl y Greek Astronomy  Babylonian Planetary Theory

Model answers to the comprehension questions.