ASTR 1210 (O'Connell) Study Guide

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 simple observing "instruments"---e.g. special alignments in buildings
    
  • Basic types of geometry and counting/arithmetic
    

B. Greek Astronomy (ca. 600 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, or supernatural 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. These elements were discarded by the Greeks.

The Greeks had enormous impact, both because they were remarkably innovative and because they left a large, coherent body of written records. They developed the Western versions of: mathematics, science, literature, history, philosophy, and logic. Not bad work. First (recorded) scientific interpretation of astronomy
They flourished 600 BC - 200 AD, an 800 year period during which their best thinkers persistently grappled with the nature of the universe. But Greek science and philosophy was rediscovered during the Renaissance and became the basis of European thinking until about 1600 AD, so Greek scientific ideas were influential over a span of 2000 years!
Greek geometry (e.g. Euclid) is, of course, still the foundation of mathematics and is taught to millions of people (however reluctant) each year.

In fact, early discoveries (ca. 525 BC) in mathematics by Pythagoras and his followers (e.g. the Pythagorean theorem, irrational numbers, plane geometry) became the basis of not only the Greek approach to science but also to philosophy. Pythagoras: "all things are numbers." Writers such as Arthur Koestler and Bertrand Russell argue that Pythagoras was the single greatest influence ever on the human intellect (even when he was wrong).

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 philosopher/scientist Thales of Miletus was the first to predict a solar eclipse, in 585 BC.

• The existence of precession of the equinoxes (Hipparchus, see Study Guide 5).

• The approximate distance to the Moon & Sun (Aristarchus, ca. 250 BC, 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 amazing 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 explored a wide variety of interpretations of the physical universe. Early on (ca. 400 BC), the atomists, followers of Democritus, arrived at an astonishingly modern interpretation in which all matter is composed of indivisible particles called "atoms," which interact according to natural laws; gods or other supernatural influences were assumed to be unimportant in controlling nature. The universe was thought to be filled with worlds like Earth, many of them inhabited by similar lifeforms. The atomists influenced a number of thinkers, through the time of the Roman poet Lucretius (ca. 50 BC), but they were overshadowed by the philosophy of Plato and Aristotle.

• 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.

  • Drawing on the atomist interpretation of matter, they attached special, but arbitrary, characteristics to basic building blocks: "earth," "air," "water," "ether," etc.

  • 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 a larger view.

• Aristarchus (ca. 250 BC) proposed instead a heliocentric (sun-centered) cosmos, based on his realization that the 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 a spherical Earth sitting stationary at the center of a spherical universe.

• In this picture, 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 motions around Earth

• Earth does not spin on its axis; rather, the universe revolves about Earth once a day.
  Note that as long as you do not admit it is possible for the Earth to spin on its axis, the observed diurnal motion of the sky requires that the Earth be at the center of the Universe.

• But in the real solar system, the Earth moves and the planetary motions are not perfectly circular, therefore:
  • Ptolemy had to add 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 was readily visible in the computer planetarium simulations. For an example, click here.

  • To reproduce such motions, Ptolemy's model used "epicycles" (a compound system of 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 unsupported empircally but retains useful ones. Statistically, most scientific ideas have been wrong. Wrong ideas are just as important as "right" ideas if they are credible in their time and establish empirical tests that push the envelope of scientific understanding outward.
Despite their many 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. Symmetry was found to be the conceptual 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. The Copernican Revolution

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.

• For instance, the apparent revolution of the sky around the Earth once a day, which was traditionally interpreted as a rotating universe surrounding a central, stationary Earth, could equally well be produced by a spinning Earth in a stationary universe. But in that case, the Earth would not have to reside at the center of the universe---it could be anywhere, and we would still see the same relative motions.

Earth as a Planet

• Copernicus recognizes Earth to be a planet with two independent kinds of motion. It spins on its rotational axis once a day, and it orbits the Sun once a year.

• 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). The brightness of Jupiter and Saturn, which were most distant from the Sun in his picture, might even have argued that planets were self-luminous. Until the time of Galileo (1609, 66 years after Copernicus died), no one saw the planets as anything other than glowing points of light.
  The recognition that Earth was a planet also eliminated the distinction that the Greeks had assumed between the physical properties of the Earth and those of the celestial realm. It was now possible that matter had universally common properties, just as the Atomists like Democritus had proposed (and we know to be true today).

• A wrenching change in perspective: Earth is now merely one among the (six) known planets. It has been "dethroned" from its special situation at the center of the universe and has lost the unique 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. Aristotle believed that objects fell Earthward because it was at the center of attraction. But if the Earth is not at the center of the universe, then some other influence must be attracting matter to it. Newton (120 years later) realized that each object with mass exerts an attractive force (gravity) on all other objects with mass.

  • The extent to which conditions on the other planets 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.

The Origin of Retrograde Motion

• In C's interpretation, the planets, including Earth, 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 naturally 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:
  
• But C's system still assumed uniform circular motions for objects and still required epicycles (because planetary orbits aren't pure circles)
  Here is an animation of C's model.

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.

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

• Three examples of simplification in the Copernican picture: the epicycles responsible for the retrograde motion of the planets were eliminated; the alignment of the centers of the epicycles for Mercury and Venus with the Sun was explained without arbitrary assumptions; and the fact that the relative sizes of the retrograde loops of the planets decreased with distance from the Earth had a natural, not arbitrary, explanation.

• But Copernicus had no conclusive observational evidence of Earth's motion: either its 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).

Copernicus' Heliocentric Model

• Copernicus 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 and this Java animation. For more discussion of astronomical parallax, click here.

  • 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 telescopically 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 Ptolemy's model, the universe must rotate around the Earth once a day. It therefore cannot be very large. But in Copernicus' 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 "Copernican Principle"

Copernicus' system had profound philosophical, religious, and scientific implications because it removes the Earth (and 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.

Bennett textbook: Ch. 3.2
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.

Bennett textbook: Ch. 3.3 (Copernicus, Tycho, Kepler, Galileo)
Study Guide 7
Puzzlah for Wednesday, Feb. 13:
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!

• Greek Astronomy (MacTutor)
  
• More detailed notes on Greek science from Mike Fowler, UVa Physics.
  
• Biography of Aristarchus
  
• Aristarchos of Samos, The Ancient Copernicus by Sir Thomas Little
  
• Lucretius and De Rerum Natura (Stanford Encyclopedia of Philosophy)
  
• More information on the Ptolemaic model
  
• Ptolemy Almagest Web Calculator
  
• 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

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Last modified February 2013 by rwo

Text copyright © 1998-2013 Robert W. O'Connell. All rights reserved. Picture of sunset at Sounion by Bobesh. Eratosthenes' method drawing based on original at IUCAAP. Epicycle and parallax drawings by Nick Strobel. Retrograde motion animation from ASTR 161, UTenn at Knoxville. These notes are intended for the private, noncommercial use of students enrolled in Astronomy 1210 at the University of Virginia.