University of California, San Diego
Physics 7 - Introduction to Astronomy

H. E. Smith   Winter 2007

Physics 7 Lecture Summary #2

Astronomy is among the oldest of the sciences. When Stoneage humans turned to an agrarian way of life and began to settle into communities, their interest must naturally have turned to the "heavens":

  1. The seasons became important; during different times of the year, different stellar patterns appear in the sky. In the spring, Virgo and her accompanying constellations signalled the time to prepare the earth, to plant crops, and to be wary of floods. In the fall, Orion rises to indicate time to harvest and to prepare for winter.
  2. The approximate equivalence of the human menstrual cycle and the 30 day orbital period of the moon which produces lunar phases led to the belief that the heavens, and the moon in particular, were related to fertility.
  3. To early humans facing an uncertain and changeable future, the constancy of the heavens must have suggested perfection and certainly led to deification in many cultures.
  4. We may expect that eclipses would have been especially frightening to early humans. After predicting the seasons, eclipse prediction may have been one of the earliest astronomical activities.

Stonhenge constructed between 3100-2000 BCE on England's Salisbury Plain may have been a Stoneage astronomical site (observatory is too strong a word), at least in part. Certainly the alignment of the "heelstone" with the rising Sun on Midsummer's Day (June 21, the Summer Solstice) represents a true astronomical alignment, and many other Megalithic sites have similar alignments. In Stonehenge Decoded, astronomer Gerald Hawkins argued that there exist a large number of astronomical alignments, though further study suggests that many of these are fortuitous.

Cosmologist Fred Hoyle has suggested that Stonehenge may have been used to keep track of the solar-lunar eclipse cycle. Far outside the still partially standing ring of Sarsen Stones is a ring of 56 holes, known as the Aubry holes. Hoyle has suggested that movement of a marking stone by 3 positions each time the Sun rose over the heelstone (or by one position three times yearly) would complete a circle in 18.67 years -- approximately the period for the "nodes", the intercepts of the lunar and solar paths in the sky, to complete a cycle. Certainly ritual use of Stonehenge would have been more important that its astronomical functions and much of this interpretation must remain speculation. We may be certain, however, that Stonehenge was indeed constructed by Stoneage humans without the assistance of alien astronauts as suggested in some pseudo-scientific books. Visit the Complete Stonehenge

Eastern observers, notably the Chinese, kept careful track of events in the skies, particularly the appearance of "guest stars" -- comets, novae and other transients. Chinese records of the guest star that we now call Comet Halley can be traced back to 240 BCE and possibly as early as 1059 BCE. One of the most important Chinese records is of a guest star that was bright enough to be seen during the daytime for nearly a month in the constellation that we call Taurus in July 1054. We believe this to be the supernova explosion that gave rise to the Crab Nebula and our knowledge of the date of the explosion itself is a very important key in understanding the deaths of massive stars. This event was also chronicled by the Anasazi in Chaco Canyon and by Native Americans elsewhere, but is curiously absent from European records in the Middle Ages.

As the above suggests, Archaeoastronomy is an active and exciting field of research.

Western scientific history begins with the ancient Greek civilization about 600 BCE.

The Ionian region of Asia Minor appears to have been a site of particular philosophical/scientific/mathematical activity for several centuries.

We will review the progress of science by highlighting a few key natural philosophers, scientists and mathematicians. As Isaac Newton said,"If I have seen further, it is by standing on the shoulders of Giants."

Pythagoras of Samos (~580-500 BCE)

Most famous for his theorem, little is known of his actual work. He founded a school (some would call it a cult) of natural philosophy and mysticism that attracted many followers. The Pythagoreans lived by a strict regimen including vegetarianism, silence for the first 5 years of membership, and anonymity with respect to personal accomplishments (so that it is difficult to know what to ascribe to Pythagoras as opposed to his followers). The Pythagorean Theorem was actually known to the early Babylonians but it may be that Pythagoras was the first to prove it. The Pythagoreans recognized the existence of irrational numbers and were interested in the relationship between music and mathematics.

Pythagoras developments in astronomy built upon those of Anaximander from whom, apparently, came the idea of perfect circular motion. The Pythagoreans believed that the planets were attached to crystalline spheres, one for each planet, which produced the Music of the Spheres. These spheres were centered on the Earth, which was itself in motion. Pythagoras is also credited with recognizing that the "morning star" and "evening star" are both the planet Venus.

Aristotle (384-322 BCE)

Aristotle was a student of Plato, founding his own school of Natural Philosophy, the Lyceum, in Athens about 335 BCE. Aristotle's philosophy involved the qualitative study of all natural phenomena, pursued without the aid of mathematics which was deemed to be too "perfect" for application on an imperfect terrestrial sphere. In Aristotelian cosmology, the "imperfect" Earth was situated at the center of the Universe (Solar System). It was composed of the four elements: earth, air, water, and fire, each of which sought its natural place in the Universe (e.g. earthen bodies fall to Earth, rain falls from the sky, travelling through rivulets, to streams, to rivers and finally to the sea). Aristotle adopted Pythagoras' model of concentric spheres for the planets, but deduced that the Earth must be immobile. Aristotle's Natural Philosophy was embodied in the writings of St. Thomas Aquinas and became the foundation of Church doctrine and University instruction in medieval times.

Aristarchus of Samos (~310-230 BCE)

Aristarchus concluded that the Solar System must be heliocentric following his geometrical estimates of the relative sizes and distances of the Earth, Moon and Sun. His geometrical methods were perfectly correct, but the required observations of the exact time of first and third quarter moon and the duration of lunar eclipse were beyond the instrumental capabilities of his era. He calculated that the Sun is about twenty times farther away than the moon, about 20 times larger than the moon and ten times bigger than the Earth. Unfortunately, all of Aristarchus work was lost in the great fire in Alexandria which destroyed the magnificent library and its records of Greek science and culture. A lunar crater bears his name in recognition of his accomplishments.

Eratosthenes of Cyrene (276-197 BCE)

Eratosthenes was a mathematician and geographer. He developed a map of the world, a method for finding prime numbers called Eratosthenes' Sieve, and estimated the circumference of the Earth. His method involved determining the direction to the Sun in Alexandria at noon on the summer solstice and comparing this with the fact that the Sun is overhead in Syene(Aswan), about 500 miles away. Here are the results of a worldwide high school recreation of Eratosthenes' experiment along with pictures of how to do the experiment yourself.

Claudius Ptolemy (~85-165AD)

Ptolemy, Alexandrian (Greek) mathematician, geographer, and astronomer, developed the most sophisticated mathematical model of the motions of the Solar System based upon the geocentric (Earth-centered) model and the principle of perfect circular motion. His model was quite complex in order to follow the details of planetary motions, requiring circles (epicycles) upon off centered circular orbits. His major astronomical work is known as The Almagest. Here's how epicycles work to produce retrograde motion.

Ptolemy's Geography remained the principal work in that field until the time of Columbus.

Copernicus Heliocentric Solar System vs. Ptolemy's Geocentric Model
Both models employed perfect circular motion with epicycles, equants ...

Nikolas Kopernig (Copernicus, 1473-1543)

Copernicus studied mathematics and astronomy in Cracow and Italy, but spent his life as a physician, attorney and church administrator. By Copernicus' time, the Ptolemaic model could no longer reproduce the observed planetary positions. Copernicus developed a heliocentric model of the Solar System which retained the notion of perfect circular motion, but placed the Sun at the center and established the proper order of the planets outward from the Sun. Copernicus model, a mathematical tour de force (not bad for an amateur), was published in De Revolutionibus Orbium Celestium in 1543, the year of his death.

Tyge (Tycho) Brahe (1546-1601)

Danish astronomer Tycho Brahe is chiefly remembered for his meticulous observations, made with instruments of his own design before the advent of the telescope. His early observations were carried out on the island of Hven (now Swedish) where he built a pair of observatories, Uraniborg and later Stjerneborg. In 1572 he observed a supernova and in 1577 a comet; his parallax measures demonstrated that these objects were beyond the moon and his measures of the brightness of the supernova showed that it was clearly variable. Tyco's measurements of planetary positions were at variance with the ptolemaic model and he developed his own Solar System model in which the Sun orbits the Earth, but the remaining planets orbit the Sun. Tycho's abrasive nature ultimately led him into disfavor. He moved to the court of Rudolph II in Prague in 1599 where he would pass along his observations to Johannes Kepler. These became the basis for Kepler's Laws of Planetary Motion.

Galileo Galilei (1564-1642)

There is an exquisite WebSite, The Galileo Project about Galileo and his world put together by Rice University's History department; many of the following links are to pages on this site. Another excellent site at Lawrence Livermore Laboratory is The Art of Renaissance Science.

Galileo was the first "modern scientist". He argued that mathematics, rather than being abstract perfection, is the true language of science. He performed many revolutionary experiments in mechanics and other fields of physics. Among his accomplishments in mechanics are:

Using telescopes of his own design and manufacture, Galileo also made many discoveries in astronomy: Galileo's observations suggested that the heavens were as "imperfect" as the Earth; that other objects in the Solar System have satellites which orbit around them, and that Venus passes through a full range of phases. These observations led him to the conclusion that the Copernican Model of the Solar System is preferable to the Ptolemaic Model. Galileo published his views in Italian in Dialogues Concerning the Two Chief World Systems in 1632. They were in direct contradiction to the world-view taught by the Catholic Church, and he was called before the Italian inquisition in 1633. Galileo was forced to disavow his work, and was sentenced to house arrest for the remainder of of his life.

I highly recommend a tour of the Museum of the History of Science in Florence if you can tear yourself away from the Renaissance Art; here is a tour of the Museum which has an extensive collection of Galilean exhibits including the famous middle finger. Here is their biography of Florence' greatest scientist.

Also highly recommended is a new book about Galileo and his daughter Sister Maria Celeste. Galileo's Daughter by science journalist Dava Sobel, which sheds important new light on Galileo and his beliefs, his family relationships, and the position of women in Renaissance Society.

Johannes Kepler (1571-1630)

Kepler came to Prague to work with Tycho Brahe and his observational data. Kepler was a mathematician and mystic, interested primarily in numerical relationships among objects in the Universe. Using Tycho's unprecedentedly accurate observations he made highly precise calculations of planetary orbits. Although he could come very close to matching Brahe's data with perfect circlular orbits, his faith in the data led him to continue his calculations until he matched Tycho's accuracy. Kepler developed three mathematical rules for the orbits of the planets:
  1. The orbits of the planets are ellipses with the Sun at one focus.
  2. The planets sweep out equal areas during equal times of the orbit.
  3. The square of the orbital period is proportional to the cube of the planet's distance from the Sun. (If you measure the period in Earth years and the distance in Astronomical Units (A.U.),(1 A.U.= the average distance of the Earth from the Sun), then Period2 = Distance3.)

Here's a page with some nice animations of Kepler's Rules, and here is another way to play with them.

Obviously Kepler's Rules require that the Sun be the center of the Solar System, in contradiction with the Aristotilean ideal. The first rule eliminates the circular motion which had been fashionable for 2 millennia. The second replaces the idea that planets move at uniform speed around their orbits,with the empirical observation that the planets move more rapidly when they are close to the Sun and more slowly when they are farther away. The third rule is a harbinger of the Law of Gravitation which would be developed by Newton in the latter part of the 17th century.

Isaac Newton (1642-1727)

Certainly the greatest classical Physicist, Newton developed the science of mechanics as we know it. His first development was his Laws of Motion. In order to perform mechanical calculations and to understand Gravity, Newton invented a mathematical tool that he called "fluctions" now known as calculus. At the urging of Edmund Halley, Newton published his Laws of Motion and analysis of Gravity in the Principia Mathematica, probably the greatest physics text ever written, in 1687. Halley, of course, wanted to use Newton's theories to analyze orbits, particularly that of the comet of 1682 which now bears his name. More about Newton's Laws in the next tutorial.

Other selected pioneers and milestones in the advance of Astronomy:

Basic Forces & Light  Introduction  Physics 7 Lectures  Physics 7 Home  

Conducted by Gene Smith, CASS/UCSD.
Comments? You may send email to

Prof. H. E. (Gene) Smith
CASS   0424   UCSD
9500 Gilman Drive
La Jolla, CA    92093-0424

Last updated: 16 April 1999