1. Upon Whose Shoulders We Stand: A History of Astronomy Up to 200 A.D.
Dick Mallot
3/17/2005
The astronomers that I admire the most are the ancients. They were able to discern our universe with jus their eyes, smart thinking, newly developed mathematics.

2. Who were these “ancient astronomers?”
Where did “real” astronomy begin?
What did we know about astronomy years ago?
Who discovered some of our basic principles of astronomy—and how did they do it?
What tools did they use “back then”?
Why did they get into astronomy?
When were maps of the sky created?
When were constellations “invented”?
Most of what we now call ancient astronomy originates in Greece, Asia Minor (Turkey) and modern day Iraq

3. Why was astronomy important?
Calendars
Planting/Farming depended upon the knowledge of the seasons
Religion/ Astrology
Navigation
Timekeeping
Land Surveying

4. Datelines:
China
India
Greece
Egypt
Mexico

5. Timelines:
Most of us think of Astronomy really starting with Copernicus, Tycho Brahe, Galileo…..
But a lot of what we know today and take as fact was “known” and measured thousands of years ago.
This a short history of some of those early astronomers who reasoned and measured out a lot of the universe without sophisticated tools—but with sophisticated reasoning and mathematics.
And to paraphrase that golf commercial; “these guys were good!!”

6. Archaeoastronomy
The study of the astronomical sites which have left us with no written records or names of the people who set up the ruins that we study today.
It is understanding how these sites were used, and the determination of what these ancients knew by studying the geometry and alignments of the sites.
If you go back to pre-recorded history, you are in the realm of Archaeoastronomy…

7. Archaeoastronomy What are some of the famous archaeoastronomy sites?
Nabta: Megalithic Site – 1000 years before Stonehenge.
Circle of stones marking solstices and cardinal points more than 6000 years ago in Southern Egypt.
Stonehenge: BC to 2000 BC
Mesoamerican sites: BC to 1500 AD
Nazca Lines in Peru: 300 BC to 800 AD

8. Nabta

9. Stonehenge

10. Nazca Lines in Peru

11. History of Astronomical Science
Starts about 600 BC in Greece
Differs from Archaeoastronomy in that it is documented, written records of events. It is reasoned out (even if wrong) theories of how things work.
It is attributable to someone/some learning center.
It is experiential (in most cases) with data and observations.
Academy—Plato
Lyceum—Aristotle
Museum--Ptolomy

12. Who were some of the “stars”?
Thales of Miletus, Asia Minor
Pythagoras of Samos
Democritus of Abdera, Greece
Oenopides of Khios, Greece
Aristotle of Athens, Greece
Aristarchus of Samos
Eratosthenes of Cyrene, North Libya
Hipparchus of Rhodes
Ptolemy of Alexandria, Egypt

13. Thales: 624 to 547 BCE
Said to have predicted a solar eclipse in 585 BC
Greeks already knew about the 19 year cycle for lunar eclipses.
Measured height of the pyramids by understanding “similar triangle” theory: measure the shadow length at the time of day when your shadow is as long as your height.
Developed the early geometric theorems.

14. Pythagoras of Samos: 580 -500 BCE
Invented some of the math that was needed to get a scientific basis for astronomical calculations –Pythagorean theorem.
First to note that the morning and evening stars were both Venus.
Built on Anaximander, who postulated that planets and stars go around in perfect circles.
Still geocentric thinking at his time.
Founded the Society (of mathemeticians)
Pythagorean therom was known a 1000 years earlier but he was probably the first to prove it.
Not easy to separate what he did from his Society.

15. Democritus: BC
Developed the concept of the atom: all things were made of microscopic and indivisible, indestructible atomic particles.
He understood that the Milky Way was a large collection of stars and also thought that space was limitless.
Was his eyesight much better than others? Possible to have 20/10 or 20/5 telescopic vision.

16. Oenopides: 450 BC Popularized the 12 signs of the zodiac
Probably copied them the Assyrians in Mesopotamia
First to fix the angle of the ecliptic with the celestial equator—called it 24 degrees.
Fixed the year at 365 ¼ days.
Postulated the “Great Year”—the number of years when the motion of the Sun and the Moon exactly repeated their motions—59 years.
Oenopides' result leads to a lunar month of days which is remarkably close to the modern value of
They knew this but continued to make calendars that were clearly going to be off in just a few years….

17. Aristotle: BC
Did his best work on classifying plants and animals
Took a qualitative approach to science
Did not use mathematics in his studies
Earth, air, fire and water were the elements
Earth is immobile
Stars and planets use the Pythagoras’ circular spheres model
Re-discovered in the late Middle Ages, and used to impede observational science.
Studied in the Acadamy with Plato, but left and founded his own Lyceum—differences with Plato.

18. Aristarchus of Samos: 310-230 BC
Believed in a heliocentric universe
Estimated the distance of the moon and sun
Utilized excellent mathematical principles but lacked the tools to get the observational data correct.
All of his written records destroyed in the fire of the library in Alexandria.
The diagram shows an argument used by Aristarchus. He knew that the moon shines by reflected sunlight, so he argued, if one measured the angle between the moon and sun when the moon is exactly half illuminated then one could compute the ratio of their distances. Aristarchus estimated that the angle at the time of half illumination was 87 so the ratio of the distances is sin 3 . Of course, we have translated this into modern notation for Aristarchus did not use degrees nor had trigonometry been invented so he did not have the sine function at his disposal. However this is in effect the calculation he made, correct in principle yet almost impossibly difficult to observe in practice since determining the moment at which half illumination of the moon occurs can only be very inaccurately found.
Aristarchus was then faced with calculating an approximation for what is in our notation sin 3 . He obtained the inequality
1/18 > sin 3 > 1/20
and deduced that the sun was between 18 to 20 times as far away as the moon. In fact at the moment of half illumination the angle between the moon and the sun is actually ' and the sun is actually about 400 times further away than the moon.
Rather strangely Aristarchus uses values for the angle subtended by the sun and moon to be 2 . This figure is quite inaccurate as it is four times too large. He correctly uses the evidence of eclipses to state that the sun and moon subtend the same angle. However, Archimedes quotes a value of 1/2 for the angle subtended by the sun and attributes this figure to Aristarchus. We can only assume that Aristarchus wrote On the Sizes and Distances of the Sun and Moon early in his career, then later on he adopted his hypothesis of a sun centred universe and computed a much more accurate value of the angle subtended by the sun. One has to assume Aristarchus was able to develop instruments to make accurate astronomical measurements later in his career.

19. Aristarchus Mathematical Genius
The diagram shows an argument used by Aristarchus. He knew that the moon shines by reflected sunlight, so he argued, if one measured the angle between the moon and sun when the moon is exactly half illuminated then one could compute the ratio of their distances. Aristarchus estimated that the angle at the time of half illumination was 87 so the ratio of the distances is sin 3 . Of course, we have translated this into modern notation for Aristarchus did not use degrees nor had trigonometry been invented so he did not have the sine function at his disposal. However this is in effect the calculation he made, correct in principle yet almost impossibly difficult to observe in practice since determining the moment at which half illumination of the moon occurs can only be very inaccurately found.
Aristarchus was then faced with calculating an approximation for what is in our notation sin 3 . He obtained the inequality
1/18 > sin 3 > 1/20
and deduced that the sun was between 18 to 20 times as far away as the moon. In fact at the moment of half illumination the angle between the moon and the sun is actually ' and the sun is actually about 400 times further away than the moon.
Rather strangely Aristarchus uses values for the angle subtended by the sun and moon to be 2 . This figure is quite inaccurate as it is four times too large. He correctly uses the evidence of eclipses to state that the sun and moon subtend the same angle. However, Archimedes quotes a value of 1/2 for the angle subtended by the sun and attributes this figure to Aristarchus. We can only assume that Aristarchus wrote On the Sizes and Distances of the Sun and Moon early in his career, then later on he adopted his hypothesis of a sun centred universe and computed a much more accurate value of the angle subtended by the sun. One has to assume Aristarchus was able to develop instruments to make accurate astronomical measurements later in his career.

20. Aristarchus: Measuring the Sun’s Size
Determined that the moon and Sun had approximately the same apparent diameter, thus the sun must be 19 times bigger.
Rather strangely Aristarchus uses values for the angle subtended by the sun and moon to be 2 . This figure is quite inaccurate as it is four times too large. He correctly uses the evidence of eclipses to state that the sun and moon subtend the same angle. However, Archimedes quotes a value of 1/2 for the angle subtended by the sun and attributes this figure to Aristarchus. We can only assume that Aristarchus wrote On the Sizes and Distances of the Sun and Moon early in his career, then later on he adopted his hypothesis of a sun centred universe and computed a much more accurate value of the angle subtended by the sun. One has to assume Aristarchus was able to develop instruments to make accurate astronomical measurements later in his career.

21. Eratosthenes of Cyrene: 276-197 BC
Developed a map of the world
Developed a way to find the prime numbers
Estimated the circumference of the earth.
Measured the tilt of the earth
Suggested that a leap day be added to the calendar every fourth year.

22. Eratosthenes Measurements
Working in Syene and Alexandria, which Eratosthenes assumed were on the same meridian, he estimated the distance between the cities to be about 5,000 stades (a stade is believed to be about 559 feet - approximately one-tenth of a mile). At summer solstice, at noon, the Sun cast no shadow in Syene, but in Alexandria a shadow was visible. Using a gnomon (a vertical stick), Eratosthenes measured the shadow's angle to be about one-fiftieth of a circle.
Calculated earth radius at 4212 miles vs the 3963
Calculated moon radius at 1478 vs miles
NOT BAD for 220 BCE!!!

23. Hipparchus: 190 – 120 BC
Introduced the idea of 360 degrees in a circle.
Calculated the length of a year within 6.5 minutes.
Calculated the moon’s distance at between 59 and 67 earth radii…correct answer: 60
Discovered precession—and calculated it at 46 seconds per year (vs. the actual of degrees per year.
Develop a star catalogue of 850 stars used later by Ptolemy.
Developed the currently used magnitude scale of 1-6
Discovered the first nova.
Measured distance to moon using a “parallax” method
Used different views of a solar eclipse
Small angle formula
Distance ~240,000 miles
His catalogue of 850 stars visible to the naked eye and map of the skies was so accurate that the famous modern astronomer Edmond Halley, nearly 2,000 years later, was able to compare his own map to Hipparchus', and figure out that stars have their own motions ... they change positions slowly over the centuries

24. Hipparchus: Distance to the moon
About a century after Eratosthenes had calculated the radius of the Earth, the Greek astronomer Hipparchus calculated the distance to the Moon based on the radius of the Earth. In this case, the method is, firstly, to establish two points on the Earth's surface from which the Moon is visible at the same time: at one point (we can call it point A), the Moon is on the horizon; at the other point (B), the Moon is directly overhead. The distance between A and B is known. A triangle is inscribed with one side extending from the center of the Earth to A, the second side extending from A to the center of the Moon, and the third side extending from the center of the Moon through B tothe center of the Earth. This triangle forms a right angle at A. By using such a triangle, Hipparchus was able to calculate a ratio between the distance to the Moon and the radius of the Earth. He calculated that the distance to the Moon was 59 times the radius of the Earth, and this ratio is extremely close to present-day measurements.

25. Hipparchus: Distance to the Sun
                                                                                                                                                
The Greek astronomer Aristarchus, a predecessor of Hipparchus, had already attempted to calculate the distance between the Earth and the Sun as a ratio of the distance between the Earth and the Moon. His method was to envisage a right triangle between the Sun, the Earth and the Moon when the Moon was in its first quarter. His calculations indicated that the distance from the Earth to the Sun was 19 times that from the Earth to the Moon. The correct figure is now known to be 400 times, but bearing in mind that before Aristarchus the Sun was believed to be three times more distant than the Moon, his figure may be regarded as a more accurate estimate.

26. Claudius Ptolemy: AD
Developed the most sophisticated model of concentric circles (epicycles) to demonstrate star and planetary motions
He followed a geocentric model
His Almagest had most of Aristotle’s ideas in it, with a geocentric approach.
Because it survived long periods of upheaval and wars, and was “the” astronomy manual until the time of Columbus.

27. So, what was known back then….and then lost?
The earth is round
Circumference/diameter of the earth/distance to the moon
The solar system is heliocentric.
An estimate of the distance to the sun (while wrong, much further than commonly thought)
Precession of the equinoxes
Length of the year to a high precision

28. The Story does not end here…
Most of what was known was lost again after this “high” period of astronomy in Greece, Turkey and Egypt.
Romans were not much interested in astronomy or astrology.
Arabs conquered many of these countries starting in the 7th century, and preserved a lot of the work done by the ancients, refined it, and passed it back to the western world at the end of the Middle Ages..
Thus it became the foundation of the work and ideas that became prevalent in the 15th and 16th centuries.