6. TWO REVOLUTIONS: THE BEGINNINGS OF
SCIENTIFIC ASTRONOMY

A. INTRODUCTION

• Sky phenomena and motions were important to most human cultures

• Astronomical time cycles were recognized and studied by many cultures

• Tracking astronomical cycles encouraged development of certain technologies:
  • Systematic, persistent observations
    
  • Multi-generational methods of record-keeping (often no traces left)
    
  • Skilled design of observing "instruments"---e.g. special alignments in buildings
    
  • Basic types of geometry and counting/arithmetic
    

B. GREEK ASTRONOMY (ca. 500 BC - 200 AD)

A Mathematical Perspective

With the Greeks, there is a major shift of emphasis from collecting/recording information to the interpretation of the physical nature of astronomical phenomena, ultimately with few religious/mythological trappings.
In earlier (and many later) cultures, cosmologies were mythological or supernatural. They had a strong "projective" tendency: human characteristics, inflated to supernatural proportions, were imposed outwards on the cosmos. Direct, persistent, supernatural control of sky phenomena was assumed.
The Greeks had enormous impact, both because they were remarkably innovative and they left a large, coherent body of written records. They developed the Western versions of: literature, history, philosophy, logic, mathematics, & science. Not bad work. First (recorded) scientific interpretation of astronomy
Flourished 500 BC - 200 AD; but Greek science was rediscovered during the Renaissance & was therefore influential until 1500 AD. ===> a span of 2000 years!
Greek geometry (e.g. Euclid) is, of course, still the foundation of modern mathematics and is taught to millions of people (however reluctant) each year.

Early discoveries in mathematics (e.g. the Pythagorean theorem, irrational numbers, plane geometry) became the basis of their scientific approach. Pythagoras: "all things are numbers."

Extract from Aristarchus' study of the distances to the Moon and Sun

Astronomical Accomplishments

• The spherical shape of the Earth. Evidence:
  Curvature of ocean horizon seen from good vantage points
  Different stars visible from different latitudes
  Length of day changes at different latitudes
  Circular shape of Earth's shadow on Moon during lunar eclipses
  Shadow lengths at different latitudes at same time of day (Eratosthenes, see below)

• The spherical shape of the Moon and the origin of lunar phases (see Study Guide 5)
  
• The origin of eclipses (see Study Guide 5)
  
• The existence of precession of the equinoxes (Hipparchus, see Study Guide 5).

• They measured, using simple geometric arguments:
  • The approximate distance to the Moon & Sun (Aristarchus, see extract above)

  • The diameter of Earth to an accuracy of about 150 miles (Eratosthenes, ca. 200 BC). Eratosthenes' method uses simple measurement of shadow lengths at noon at different latitudes on a given day. It then applies the geometric concept of the congruence of triangles, as shown in the diagram below. If the Earth had been flat, the shadow lengths at the two latitudes would have been the same.

  • Eratosthenes estimated the diameter of the Earth to be 8050 miles; the true value is 7900 miles. An astonishing feat, particularly if you consider that most "educated" people today, 2200 years later, would have trouble figuring out how to do this (or how to explain eclipses or the phases of the Moon).
    

Scientific Cosmology

• The Greeks developed the first scientific cosmological models

• Greek models were intended to be consistent with their large and accurate collection of observations of the Sun, Moon, planets, and stars.

• They treated the Sun, Moon, planets, stars as inanimate physical objects, not living beings with supernatural volition and powers.

• Influenced by the philosophical idealism of Plato & Aristotle, they attempted to deduce the character of nature from abstract postulates (like mathematical axioms), with little appeal to empirical tests and with explicit dismissal of experiments.
  • On philosophical grounds, they favored a highly symmetrical (spherical), perfect universe.

  • They attached special, but arbitrary, characteristics to basic building blocks: "earth," "air," "water," "ether," etc. A primitive but nonetheless recognizable version of the modern atomic interpretation.

  • Although a revolutionary improvement over supernatural interpretations, this reliance on deduction instead of empirical investigations ultimately misled Greek astronomers.
    "Aristotle maintained that women have fewer teeth than men; although he was twice married, it never occurred to him to verify this statement by examining his wives' mouths."
                                          --- Bertrand Russell

  
• The first attempts at serious cosmological models placed Earth at the center of the universe (geocentric) and introduced the notion of "crystalline spheres" concentric with Earth, each carrying a celestial object and revolving uniformly on an axis. Click on thumbnail at right for larger view.

• Aristarchus (ca. 250 BC) proposed a heliocentric (sun-centered) cosmos, based on his realization that Sun was probably larger than Earth, but this was not favored.

The Ultimate Greek Cosmological Model

• Developed by Ptolemy, ca. 130 AD

• The model is geocentric, with the Earth sitting stationary at the center of a spherical universe.

• The Earth is fundamentally distinct from the planets. It occupies a special location and has special properties. Objects fall downward toward the Earth not because its gravity attracts them (as in our modern view) but because they tend to move to the center of the universe.

• The terrestrial region is regarded as corrupted and changeable, but at larger distances from Earth the universe becomes ideal, perfect, unchanging.

• All celestial objects move in (perfect) uniform, circular celestial motions around Earth

• Earth does not spin on its axis; rather, the universe revolves about Earth once a day.

• But in the real solar system, the Earth moves and the planetary motions are not perfectly circular, therefore:
  • Ptolemy had to include a number of complicated geometric features in order to reproduce the observed planetary motions.

  • Viewed from Earth, the planets all appear to undergo occasional "retrograde motion"---a brief, loop-like reversal in their general eastward motion with respect to the stars. This is readily visible in the computer planetarium simulations. For an example, click here.

  • To reproduce such motions, Ptolemy's model used "epicycles" (wheels moving on wheels). See the illustration below. The epicycles were purely geometrical constructs, without any presumed physical reality to them.

  • Here is an animation showing how epicycles generate retrograde motion.

• Ptolomy's complex model was a success it that it allowed accurate predictions of the locations of the planets for several centuries into the future. But because of its inherent flaws, errors accumulated over time.
  

  
  

• Here is an animation of a Ptolemy-like model.

The Virtues of Greek Cosmology

Ptolemy's work is often treated dismissively because it "got the solar system wrong" and was discarded by the "Copernican Revolution." However, it is important to appreciate how enormous a step forward this was over all the other modes of thinking at the time and, in fact, over any other framework for understanding the universe for the next 1300 years(!)
Science is a cumulative and pan-cultural enterprise. It discards wrong ideas that are found to be empirically unsupported but retains useful ones. Statistically, most important scientific ideas have been wrong. Wrong ideas are just as important as "right" ideas if they are credible and establish empirical tests that push the envelope of scientific understanding forward.
Despite their many errors and misconceptions, the Greeks laid the groundwork for all later science. Many features of the cosmology of the Greeks propagated through to modern science, including these:
• They attempted to incorporate all of the extant reliable data.

• They insisted that theoretical models reproduce the observations.

• They regarded the planets, Moon, and Sun as inanimate, physical objects moving through space without supernatural interference. This was a tremendous break with the interpretations of almost all other cultures of the time.

• Their models were based on mathematics. All later science likewise used mathematics (of an ever-increasing sophistication). The modern view is that although all things may not BE numbers (as the Pythagoreans claimed), all things can be measured by numbers.

• The models emphasized geometrical symmetry. In modern science, symmetry emerged as a central concept in simplifying mathematical descriptions of nature. In the 20th century, symmetry was found to be the key to understanding subatomic particles, crystalline solids, DNA molecules, and a wealth of other phenomena.

Ptolemy's model reproduced the angular motions of the planets on the sky reasonably well. Despite flaws, this is a scientific model which makes predictions that can be tested: e.g. concerning the brightnesses of the planets and their distances from the Earth as they move around their complex orbits. Although the Greeks apparently did not test the models this way, later observers like Tycho could easily do so.

C. DARK INTERLUDE AND RENAISSANCE

D. COPERNICUS (d. 1543)

Relative Motion

Copernicus introduces the concept of relative motion: namely that apparent motions in the sky could be produced by motions of the Earth as well as by motions of the cosmic bodies and that it was difficult to tell these cases apart.

Earth as a Planet

• Copernicus recognizes Earth to be a spinning, orbiting planet.

• Identifying Earth as a planet was a much greater leap than might be supposed. Remember that Copernicus did not have access to telescopes, so he could not know that the planets were spherical or not self-luminous (like the Earth). Until the time of Galileo, no one saw the planets as anything other than glowing points of light.

• A wrenching change in perspective: Earth is now merely one among the (six) known planets. It has been "dethroned" from its privileged situation at the center of the universe and has lost the special properties associated with that location attributed to it by Aristotle and the Greek philosophers. The Sun becomes the most important object in the solar system.
  • Removing the Earth from its imagined special cosmic location was the first step toward the modern theory of gravity, in which objects exert an attractive force on one another. However, it would be another 120 years before Newton was able to formulate that.

  • The extent to which conditions on the other planets may closely resemble those on Earth was not known to C. (without telescopes), but there was no evidence then that they were very different. A "multiplicity of worlds" therefore emerges, possibly inhabited worlds.

A Heliocentric Cosmology

• Copernicus hence develops the heliocentric model, with the Sun in the center of the universe surrounded by 6 orbiting planets: this simplifies the Ptolemaic model.

• C's arguments were based on mainly on: (a) simplicity; and (b) the recognition that motions of the planets in P's model (e.g. retrograde loops) were synchronized with the motion of the Sun, which implied the Sun was the key object.

• Two examples of simplification in C's picture: the epicycles responsible for the retrograde motion of the planets were eliminated (see below); and the alignment of the centers of the epicycles for Mercury and Venus with the Sun was explained without arbitrary assumptions.

• But C had no conclusive observational evidence of Earth's spin or revolution around Sun.
  • Such evidence became available only much later, with telescopes and other instruments which could measure, for instance, the "aberration of starlight" caused by the Earth's orbital motion around the Sun (Bradley, 1729) or the "coriolis effect" caused by its spin (best demonstrated by the Foucault pendulum--1851).

"Parallax" and the Size of the Universe

C was forced to assume that the stars were very distant in order that the "parallactic shift" would be too small to measure.
• The parallactic shift is a change in a nearby star's apparent location in the sky with respect to more distant stars caused by viewing them from different positions in Earth's orbit. See this illustration.

• The absence of stellar "parallax" implied an enormously larger universe than most astronomers were willing to accept at the time.

• The first measures of the parallactic shifts for nearby stars (about 1 arcsecond) were made by Bessel in 1838, almost 300 years after Copernicus' death. Using these shifts, stellar distances can be calculated by simple trigonometry. The nearest stars are at distances over 200,000 times the radius of the Earth's orbit. Even Copernicus himself would have been flabbergasted by the scale of our star system.

• In P's model, the universe must rotate around the Earth once a day. It therefore cannot be very large. But in C's model, this diurnal motion is caused by the Earth's spin. The universe is stationary. This permits it, in principle, to be infinite in extent.

The Origin of Retrograde Motion

• In C's model, the planets continuously move in the same direction (counterclockwise around Sun as seen from above Earth's north pole). Planets nearer the Sun move around faster. Retrograde motions are explained as the reflex of the Earth's orbital motion (i.e. the fact that we observe the other planets from a moving platform). For instance, Mars appears to move backwards in our sky as the Earth "catches up to and passes" it in its orbit. See the animation below:
  
• C's system still assumed uniform circular motions for objects and still required epicycles (since planetary orbits aren't pure circles)
  Here is an animation of C's model.

The Copernican Principle

Copernicus' system had profound philosophical, religious, & scientific implications because it removes the Earth (& by inference, the human race) from a privileged location. The idea that scientific arguments should assume that human beings have a typical, rather than special, perspective on the universe became known as the "Copernican Principle." So far, this assumption has been proven correct on three entirely different scales: our solar system, our galaxy, and the extragalactic universe.

Seeds text: 4.1 (Greek astronomy); 4.2 (Copernicus)
Study Guide 6
Optional references: Bertrand Russell, A History of Western Philosophy; Arthur Koestler, The Sleepwalkers; Timothy Ferris, Coming of Age in the Milky Way; J. L. E. Dreyer, A History of Astronomy from Thales to Kepler.

Seeds text: 4.2, 4.3, 4.4 (Tycho, Kepler, Galileo)
Study Guide 7
Puzzlah for Wednesday, 2/13/08:
You have two objects, A and B, both of which are the same shape. B weighs twice as much as A. You drop both simultaneously from a height of 3 feet. What happens?
1. A (the lighter object) hits the ground first.
2. B (the heavier object) hits the ground first.
3. They hit at the same time.

You should attempt your own experiments to determine the answer...don't just take the word of the readings!

• Early Greek Astronomy (to ca. 300 BC)
  
• Biography of Aristarchus
  
• Essay on Aristarchus
  
• More detailed notes on Greek science from Mike Fowler, UVa PHYS 109.
  
• Biography of Ptolemy
  
• More information on the Ptolemaic model
  
• Sailing the Wine-Dark Sea: Why the Greeks Matter new, popularized description of Greek culture, by Thomas Cahill
  
• The Antikythera Device (Weijgaert)
  
• The Antikythera Device (Coppens)

• More information on the Copernican system
  
• Manuscript copy of Copernicus' De revolutionibus