English 233: Introduction to Western Humanities - Baroque & Enlightenment

Developments in astronomy & physics: 1543-1687

Nicholas Copernicus (1473-1543)  

See the biographical sketch of Copernicus at the Rice University "Galileo Project," or the one at the History of Mathematics site at St. Andrews University (UK), or the one by J.C. Evans of the Physics & Astronomy Department at George Mason University, or this one by Dalibor Paar, part of his site at the University of Zagreb devoted to famous physicists and astronomers.

1543: De revolutionibus orbium coelestium [On the Revolutions of the Heavenly Bodies.  In this work (published at the end of his life) Copernicus proposes the heliocentric hypothesis.  What are the features of this hypothesis, and what is Copernicus's rationale for recommending them?

(1)  Copernicus's heliocentric model is a simpler model than the (geocentric) Ptolemaic model for accounting for the appearances

Remember:  a theoretical model is a complex of hypotheses.  Hypotheses are tools -- like hammers, saws, levers, except that hypotheses are intellectual rather than physical constructions.  A tool is something used to accomplish a task -- drive a nail, saw a brick, lift a stone.  Tools are better or worse to the degree that they accomplish their proper task(s), and do this with least effort.  If a hammer drives the nail, is cheaper, lasts longer, and is easier to wield than some other hammer, then it is better, and deserves to take the place of the less efficient hammer in our toolbox.  Now the task that hypotheses are resorted to to accomplish is to explain some state of affairs -- for example, some pattern of appearances.  So if Hypothesis B can explain all of the appearances that Hypothesis A can, and can explain some of them more simply than Hypothesis A can, and without introducing complexities that Hypothesis A does not incorporate, then Hypothesis B is better at explaining the appearances than Hypothesis A.  The principle that, in explanation, entities should not be multiplied unnecessarily, had been formulated in the 14th Century by the philosopher William of Ockam, and is today known as "Ockham's Razor."

We could say that Copernicus had become unsatisfied with the Ptolemaic theory because it struck him as bad intellectual engineering -- an intellectual equivalent of what in our century has come to be known as a "Rube Goldberg invention" -- a unnecessarily complicated way of accomplishing something that can be done far more economically.

Yet Copernicus himself was motivated by an even deeper consideration.  Since he thought of astronomical hypothesis as an attempt to describe, indirectly, the the actual positions of the heavenly bodies in objective space -- an aspect of real nature of the cosmos --, he came to the conclusion that Ptolemaic astronomy had ironically ended up attributing to God Himselfa creation that was a kind of "Rube Goldberg invention,"which would be inconsistent with God's nature.  It struck Copernicus as unseemly to imagine that a perfect creator would construct a creation with the senseless complexity the cosmos would have if it were really to look like astronomers working within the Ptolemaic scheme were increasingly driven to imagine it, in order to account for the actual data. 

Within the overall geocentric scheme, these complications were of course rational as hypotheses, in the sense of rationally required in order to account for the data (the basic rationale of any scientific hypothesis as such).  But if the cosmos actually were to be the sort of super-elaborate contraption such a (developed) hypothesis would say that it is, then it would seem to be irrational from the point of view of the creator.  Note that Copernicus was driven to these reflections because he was working under a teleological assumption:  for him, it was not just that behind the appearances were actual motions in real space, and that behind these motions were physical mechanisms that kept these bodies on these particular paths, but that behind the cosmos as a whole was a Creator, and one whose basic properties (omnisicience, omnipotence, omnibenevolence) had long been known through perfectionist monotheistic theology.  Since Copernicus was working in Western Europe during the 16th Century, astronomy was for him itself subsumed within the traditional Christian picture of history.  In the Biblical book of Genesis, God Himself had, through Moses, provided human beings a report of how the world had come into being, in time.  And since God always acted in accordance with a rational Providence, His ways must always, ultimately, make sense.  Within this framework of assumptions, the laws of nature were thus to be understood as expressions of God's will.  Hence, for Copernicus, the astronomical laws postulated by astronomers were under a double obligation of rationality, one "downwards" and one "upwards."  On the one hand, the rules imagined to explain the phenomena of the heavens had to rationally require the phenomena to be the way they were actually observed to be.  On the other hand, what they could be was broadly constrained by some conception of what a rational Creator might choose.

If we look closely we can detect that these two demands for rationality are logically distinct. 

On the one hand, the fact that A has been around longer than B, or believed by more people over the ages than B, or seems to be more directly in accordance with the statements about the behavior of nature in certain "authoritative" books -- including the Bible -- is irrelevant.  Since tools are judged in respect of their doing the jobs for which they are tools, and since a hypothesis is a tool whose job is to explain a particular state of affairs, then that hypothesis which best explains the record of appearances is to be taken as better corresponding to the real state of affairs in nature that lies behind the appearances nature presents to the observer.

On the other hand, it was in part because Copernicus took the the Bible seriously that he took seriously the idea that there might be something deeply wrong with an astronomical theory that was driven to depart so radically as the Ptolemaic tradition had from canons of simplicity in explanation.  There were in medieval Western Christianity two broadly antagonistic traditions on the question of how much man can know of God.  One held that the purposes of God, except for those He had chosen explicitly to reveal through Scripture or the Church, were largely inscrutable.  In the 16th Century, this tradition, shorn of dependence on the doctrines of the Church, fed into Protestantism, with its insistence on the radical natural corruption of the human faculties, and on the express Word of God in Scripture as the sole authority for knowing God's will in matters important to God.  The opposing tradition held that God's will could in important respects be known independently of Revelation, through the faculty of reason God installed in human nature per se.  It was this latter theological tradition that was open to the idea that Christian thinkers might be able to learn important things from non-Christian thinkers -- pagans, Jews, Muslims, Chinese -- so long as the teachings in question did not contradict the truths of the Christian religion as grounded in Scripture and Church tradition.  The most systematic exponent of this theological tradition was Thomas Aquinas (d. 1274), who undertook to forge a synthesis between the Christian doctrine and the philosopher of the ancient Greek philosopher Aristotle, whose works had recently become re-available to the West.  It was because Copernicus' mentality was shaped by this tradition that he was unable to reconcile himself to the "senseless" complexity of the world according to Ptolemaic astronomy.  Had he been comfortable with the idea that God's reason as applied to the work of the heavens was simply inscrutable to man, he might not have taken his own intellectual dissatisfactions with the Ptolemaic theory so seriously.  But then, had he believed passionately that outside of Scripture nothing worthwhile could be known by man of God, he would never have bothered to turn his intellectual talents to astronomical questions in the first place.

For Copernicus, as for Aquinas some two-and-a-half centuries before, Reason and Revelation, properly understood, are complementary avenues for knowledge of God's will.  Not everything testified to by one is testified to by the other, but neither does either contradict the other, provided that nothing be accepted on the basis of Reason that rationally contradicts anything Revelation makes necessary for Christians to believe.  (There was still a place for certain fundamental mysteries that were necessary to be affirmed merely by Faith on the basis of Revelation -- the creation out of nothing, the virgin birth, the resurrection -- but none of these argued the fundmental irrationality, from a human perspective, of the universe and history.)  It is therefore one of the ironies of history that, as the hypothesis put forward by Copernicus itself came to be modified and supplemented in the century-and-a-half after his death, educated Europeans would increasingly experience themselves as forced to choose between the Reason (operating on sense experience) and Faith (based on Scripture as interpreted by both Catholic tradition and early Protestant authorities). 

Correspondingly, by the end of the 17th Century, the two kinds of rationality -- that of strictly descriptive and physical explanation on the one hand, and that of teleology on the other -- will be regarded not merely as distinct but, in the practice of natural science, opposed:  the first will be considered the very essence of the enterprise, and the second completely out of place. 

How does the Copernican picture account differently but just as well for

  1. the apparent path of the sun across the sky on successive days?
  2. the apparent rotation of the constellations around the pole star every night?
  3. the fact that, after a year, for any moment on a given date, the same constellations show up in the same position in the sky (with respect to the horizons and the pole star) in which they appeared in the previous year, at that moment on that date?

How does the Copernican picture account differently, but via a simpler mechanism, for

(2)  In Copernicus's model circular orbits are retained.  Copernicus does so out of metaphysical considerations:  he holds a notion -- quite traditional -- that the universe is the product of an act of divine creation and that the Creator in question is "perfect."  Circles are a series of points at a constant ("unchanging") distance from fixed point.  The association among the concepts of  regularity, reliability, and faithfulness give rise then to the concept of "undefective."

An eventual irony:  the result of the Copernican proposal, in respect of accurately accounting for the record of appearances turned out to be only marginally better than what one could get with the Ptolemaic hypotheses.  Until Kepler dispensed with the idea of circular orbits in favor of elliptical ones, astronomers working within the framework of the heliocentric model proposed by Copernicus were constrained to introduce all sorts of complicated sub-hypotheses -- epicycles on deferents, equants, etc. -- to account for the appearances.

(3)  As a Renaissance neo-platonist, Copernicus proposes that these circular orbits be conceived as focused upon a more suitable central body than the earth -- on the sun, as an emblem of divine perfections.  The sun is

vs. the earth (the pit of the sublunary realm) as a compendium of defects

A cosmos so structured would make nature itself communicate a fundamental spiritual truth that God (as conceived in the Christian picture) wants to convey to his favorite creature, man:  all bodies in the creation circle around, are illuminated, warmed and controlled by the sun, just as all creatures should focus their attention on and obey God, whose intelligence, love and power are responsible for their very existence.

Notice that this is a teleological explanation of the structure that in turn is functioning as a descriptive explanation of the data.  That is, it is an explanation in terms of the purpose that the made object (here the cosmos, understood as a decipherable emblem) was designed to serve.  For more on the importance of teleology in Copernicus' outlook, go here and above.

(*)  To summarize:  if effects reflect their causes, the Creation will reflect its Creator.  Now since (Copernicus assumes) God is perfect, his engineering will be elegant.  The cosmos, then, will not be overly elaborate for the purpose it was designed to accomplish, and the purpose it was designed for would be one which a perfect being would adopt.  Any theory of nature that has the structure of nature being simpler and more more intelligible in light of God's known purposes will be more likely to be true than any theory of nature that has the structure of nature being pointlessly complicated  -- so long, of course, as it can (rationally) account for the appearances (that the world presents to our senses)

.Tycho Brahe (1546-1601). 

See the biographical sketch of Brahe at the Rice University "Galileo Project."

(1)  Brahe carried out new systematic observations with the best naked-eye equipment so far available.  Result:  more plentiful & precise data.

Result:  the apparent planetary movements described with new accuracy.

Result:  any proposed model for explaining astronomical appearances would have to be able to do so within narrower degrees of "slack" for possible observational error.  The demands on any theory of the cosmos were henceforth more stringent.

(2)  Brahe noticed a striking new category of phenomenon -- stellae novae ("new stars").  These were new in the sense not that they were stars they someone noticed for the first time, but in the sense that they exhibited the characteristics heretofore regarded as exclusively the properties of stars and characteristics heretofore regarded as impossible for stars (specifically, coming into being, before the eyes -- i.e., "novelty").  Several of these strange objects appeared in Brahe's lifetime, and he took careful measurements of them.  (The first -- and most spectacular -- appeared in 1572-4 in Cassiopeia (across the pole from the Big Dipper.  Two more appeared by 1601.)

[Caution:  In the astronomy of our day, these "novae" are dubbed "supernovae," and interpreted through a conceptual scenario concerning the life-history of stars that does not enter upon the stage of human thought until the 20th Century.  According to the current picture, over a long history of atomic fusion, a star eventually exhausts the energy reserves that enable it to maintain its size against the forces of gravity by which all particles making up its mass attracts all others. The result is that a sufficiently old star suddenly collapses, and the rising pressure causes its heat energy to rise catastrophically, so that the star explodes, broadcasting huge emissions of electromagnetic energy in a various ranges, including that of visible light.  This tremendous burst of energy is short (in astronomical terms), subsiding within a couple of (terrestrial) years, though energy from the dispersed gas continues to radiate for centuries, and can be picked up by sophisticated instruments.  If you are acquainted with this theoretical framework, you want to set it aside for the purposes of understanding the problems novae presented to 16th-century thinkers.]

These phenomena seemed to be stars.

Yet they exhibited qualities inconsistent with the nature of stars (as these were conceived in the Aristotelian-Ptolemaic and original Copernican pictures).

(3)  Moreover, several comets appeared during Brahe's observing career at Oraniborg (1577, 1580, 1585, 1590, 1593, 1596).    Careful tracking via parallax  of their positions revealed that they passed successively through the orbits of the planets.  That is:  they could not be assumed to be sublunary phenomena.

From the standpoint of the assumptions built into the Aristotelian-Ptolemaic theory of the cosmos, here is another striking anomaly (contradiction, strangeness):  why no evident effect on the celestial spheres, which were supposed (literally "hypothesized") to be not merely transparent (to let the light of more remote bodies be visible to observers on earth) but also rigid (so that their revolutions would compel the planets to follow the regulations supposed to be taking place in real space that would result in the regular paths the observational record exhibited over time for their appearances in the night sky).  So:  how can it be that these comets are going where they do and yet the planets are continuing on their accustomed observed paths?  Why haven't the crystalline spheres been smashed, and the planets gone haywire?

(4)  Tycho was unable to accept either the Ptolemaic or the Copernican picture.  As an compromise he proposed a theoretical model (now known as the "Tychonic model").  In it, a stationary earth orbited by moon & sun, w/ the 5 planets orbiting the sun.

This model dispenses with crystalline spheres (an untenable feature of the Ptolemaic model).

It exhibits Brahe's willingness to leave open the question of physical mechanism in favor of first getting right the question of spatial location (second-order description)

But it avoids the necessity (under the Copernican model) of postulating the sphere of the fixed stars at an "inconceivable" distance

Tycho's unwillingness to entertain this possibility is a symptom of limiting assumptions of the day:  what was a "conceivable" size for the universe as a whole.

Johannes Kepler (1571-1630)  

See the biographical sketch of Kepler at the Rice University "Galileo Project."

Kepler's alternate descriptive (geometric) hypotheses provide better fit to the improved data (Tycho's) concerning apparent motions.  (For a more succinct summary of the ideas whose significance is spelled out below, check here.  For a more detailed treatment, with useful graphics -- some even animated -- look here.  [The writer is a bit condescending to Ptolemy, but the page is very helpful.]  If your browser has Shockwave, you should definitely experiment with Raman's orbit simulator.  It will do wonders for giving you an intuitive feel for what Kepler was imagining in his head on the basis of 11 years of pen-and-pencil calculations!)

1609: On the Motion of Mars

substitution of elliptical for circular orbits in Copernicus' model. This dispenses, in favor of empiricism, with the supposition that, God being perfect, He must have used spheres [resulting in circular motion] as his fundamental building blocks, since spheres are "perfect."  Yet it does not dispense with the assumption that nature is rule-governed, and that behind the regularities in appearances must lie deeper laws, whose essence is to be captured in the language of mathematics:  a circle is, after all, just a special case of the more general figure that is an ellipse, just as a square is a special case of a rectangle.

Kepler's First Law:  The orbit of each planet is an ellipse, of which the center of the sun is one of the foci.

hypothesis of non-uniform motion.  The planets travel faster when closer to the sun, slower at greater distances.  Yet this change is still completely regular -- i.e., rule-bound, describable in mathematical terms.  (At a higher level something remains constant after all.  The law specifies what this is.)

Kepler's Second LawThe radius vector of each planet (the line joining its center with the center of the sun) sweeps through equal areas of the ellipse in equal times).

1619: Harmonice mundi [The Harmonies of the World]

regular (mathematically formulable) relationship between the relative position in space of the planets' orbits with respect to the sun and the relative time it takes to complete their journeys around the sun.

Kepler's Third Law:  The square of the period of each planet is proportional to the cube of its mean distance from the sun.

Galileo Galilei (1564-1642)  

See the biographical overview of Galileo (loaded with links to specific topics) at the Institute and Museum of the History of Science of Florence, Italy

Galileo's contributions to science are quite rich.  Here we are primarily focusing on his confirmation of Copernican model by way of

new data (via telescope)

powerful arguments

1610: The Starry Messenger (based on telescopic observations of 160910)

(1)  The surface of the moon turns out to be irregular, not smooth:  mountains, valleys, plains.

But, on earth, mountains, valleys and plains are known to be the products of temporal processes.   If such processes are at work on the moon, what are we to make of the Aristotelian division (taken over by later medieval Christian astronomers) between the sublunary and superlunary realms:  it appears that "superlunary" [= "celestial] realm is as subject to "temporal process" (in the sense of change in structure) as the sublunary (specifically mutable) world is.  For the then-current version of Christianity -- which had integrated itself into the Aristotelian picture by interpreting the realm of mutability as the portion of the cosmos affected by the Fall of Man -- this raised a variety of disturbing questions.

(2)  Milky Way turns out to be composed of a vast collection of stars, most of which had been hitherto invisible..

This observation raises teleological questions (i.e., with respect to Divine Providence):

If God's purpose in creating the cosmos anthropocentrically (focused on the redemption of a fallen humanity), what could be the divine purpose in creating heavenly bodies that were not detectable by human beings?  More specifically, recall the Creation story in Genesis, where the stars are placed in the sky in order to provide light.  What would then be the point in creating invisible stars?

[Can you think of an answer to this challenge?]

It also reinforces speculation concerning the size (and boundedness) of the universe

Recall that 16th-century followers of Copernicus were already imagining that the stars might not all lie on a single sphere that constituted the outer boundary of the cosmos, but rather that the universe might be of indefinite size.  (Cf. the diagram of the Copernican system in the version of Thomas Digges, Figure 15.3 on p. 384 of WH.)

(3)  Telescopic observation also forced Galileo to the conclusion that Jupiter has 4 satellites.  (Subsequent investigations over the centuries has led to the discovery of several more.)

Hence there is no single center of orbits in the cosmos.

But acknowledging this took away one of the strongest apparent arguments in favor of the traditional picture against that of Copernicus.  Copernicus's system has satellites orbiting around both the sun (i.e., Mercury, Venus, Earth, Mars, Jupiter and Saturn) and a satellite orbiting around one of these (the moon going around Earth). 

But henceforth, any picture would have to accommodate the idea of at least two centers of rotation.  If a physical theory could not explain how this could happen, that was no longer an argument against the idea that such a thing could be happening, but rather an argument that such a theory was wrong, since it failed to do what, as a theory, it was invented to do:  account for appearances.  If Jupiter could have 4 satellites and still orbit the sun (as the Ptolemaic theory would in any case now have to be updated to allow), then why couldn't the Earth orbit the sun with one?

Letters on Sunspots (dated December 1612, but published in 1613).

(4)  As phenomena "sunspots" are dark spots on the sun that, over time, pass across the disk, disappear over the edge and eventually reappear on the other side, but eventually pass away altogether; others emerge after a while and display the same pattern of appearance. 

To Galileo, this suggested that perhaps the sun, by its rotation, might somehow impart motion to its satellites.  This idea thus seemed to lend support to the Copernican hypothesis

The speculation here was neo-platonic, and ruled out under Newton's (later) physics.  But at the time, it was plausible and (in a certain sense) in the right direction (though not for a reason Galileo was in a position to appreciate).  The fact that the sun is by far the hugest mass in the solar system does indeed, under the Law of Gravitation, mean that the other bodies in the system (the planets, etc.) are put into elliptical orbits around the sun, but the same Law of Gravitation says that the force gravity exerts between the planets and the sun (and, indeed, among all the planets themselves) is reciprocal, not just one-way (as Galileo's hypothesis imagined) -- and in any case, has nothing to do with the rotation of the sun.

(5)  The phases of Venus, though first discovered 1610, were first announced to the public in the Letters on Sunspots).

This was one of the strongest arguments in favor of "Copernicans" as distinct from the Ptolemaic.  The fact that Venus showed a smaller full disc when it appeared near the sun just before dawn and just after dusk at certain seasons but showed a crescent (but "taller," implying an actual larger disk) at others invited the interpretation that it showed a full disk when it was farthest away from the earth, and on the other side of the sun, and a larger but crescent shape when it was closer to the earth, and between it and the sun.

(6)  The "ovoid" shape of Saturn had been discovered about the same time.

Galileo thought that he had discovered evidence of two "stationary" satellites associated with the planet.  (His telescope was not powerful enough to resolve the smudge into a clear image of a planet with rings.  This was not done until 1656 -- some 14 years after Galileo's death -- when Christiaan Huygens brought to bear a far more magnifying instrument.)  He rejected the suggestion of a correspondent that the planet itself might be ovoid.  Yet when he observed the planet again just before he sent the Letters on Sunspots to the publisher, he discovered, to his surprise, that he could not detect the effect.  Instead of simply removing his earlier report from the manuscript, he added a passage in which he reported his failure to repeat it, and confessed he had no idea how to explain the difference.  This was an expression of his deep convictions about the necessity for honesty in the face of empirical evidence.

(7)  diurnal & monthly librations of the moon (wobbling from side to side)

1623: Saggiatore... [The Assayer]: a reply to an attack on him regarding the nature of comets and

(8)  an exposition of new scientific method (vs. scholasticism in natural philosophy).

Science is advanced not by compiling quotations from books published by authorities, but by rational argument on the basis of evidence readable through the senses from the Book of Nature, which is open to inspection by everyone all the time.  Observations are thus constantly able to be tested by others, and reasoning upon them is likewise subject to critique in terms of the laws of logic which inhere in the human mind.

(9)  In this work, too, he lays out a distinction between "primary" (i.e., measurable) qualities (shape, weight, motion) and "secondary" qualities (e.g., smell) of matter:  "The Book of Nature is written in mathematical characters."  This is one of the classic steps in the development of the mechanical picture of the universe.

(1624-)1632: Dialogo sopra i due massimi sistemi del mundo, tolemaico e copernicanico [Dialogue Concerning the Two Chief World Systems, the Ptolemaic and the Copernican].

(10)  In this Galileo systematically lays out the (convincing) arguments for the Copernican picture and against the Aristotelian-Ptolemaic picture, and the arguments (not compelling) against the Copernican picture and favoring the Aristotelian-Ptolemaic picture.

Publication precipitates his being called before the Inquisition (1633):  under threat of torture, he is forced to publicly recant the Copernican hypothesis as contrary to the Catholic Faith and put under house arrest for the rest of his life.

For the issues at stake in this trial, we'll be looking at Jacob Brownowski's video program The Starry Messenger (from the TV series The Ascent of Man).  Consult Study Guide 1 (to be worked through before our showing) and Study Guide 2 (to be worked through immediately afterwards).

1638: Dialogue Concerning Two New Sciences

(11)  presents the results of his experiments in mechanics:  acceleration of falling bodies proportional to time

His descriptions of the behavior of falling bodies here on earth and Kepler's descriptive hypotheses about the shape and variable speed of planetary orbits in his modified Copernican picture (of the heavens) will eventually be simultaneously explained by Newton's physics.

Isaac Newton (1642-1727)  

See the biographical sketch of Newton by Richard Westfald at the Isaac Newton Institute for Mathematical Sciences at Cambridge University.  Somewhat more detailed is the entry for Newton in the Mathematical MacTutor's Math History Archive.  Either one of these would be quite sufficient for our purposes. 

[Still not satisfied?  You must be ready for the 18-page biography (with diagrams and formulae) by W.W. Rouse Ball's Short Account of the History of Mathematics (4th Edition, 1908)!  There is also interesting material included in some lecture notes on Newton from a course in the Great Books program at Malaspina College in British Columbia, Canada.  The Isaac Newton Homepage at the University of Kentucky is a rich resource.  The brief essay there on "Newton's Life and Times" does something the others doesn't:  it compares and contrasts the approaches of some prominent scholarly biographers of Newton.  If you want to get wind of what some of the outstanding historical controversies have been, here's a good place to start.  These resources take us beyond what you need to focus on for the purposes of our course.]

1687: Philosophiae Naturalis Principia Mathematica [The Mathematical Principles of Natural Philosophy; famous as simply "The Principia"]

Newton manages to explain the solar system described by Kepler in terms of physical principles that simultaneously explain Galileo's description of the behavior of terrestrial projectiles:  erasure of the cosmic division between the "sublunary" and "superlunary" realms -- universe now completely subject to uniform body of natural laws.  He does this without recourse to question-begging assumptions about the metaphysical nature of forces, restricting himself instead to a mathematical description of how these forces operate, with no need to imagine how or why any factor beyond the universe itself (notably God) might have caused things to be just so.  (For more on this important aspect of Newton's achievement see "Teleology and Science" in general and from this point in particular.)

Newton's First Law of Motion: A body remains in a state of rest or of uniform motion in a straight line unless it is acted upon by an external force. [INERTIA]

Newton's Second Law of Motion: A change in momentum is proportional to the force causing the change and takes place in the direction in which the force is acting, or the increase or decrease in velocity is proportional to the force. [CONTRIBUTION OF FORCE TO MOTION]

Newton's Third Law of Motion: To every action there is always an equal and opposite (or "contrary") reaction; i.e., when one body exerts a force on a second, the second exerts an equal and opposite force on the first. [RECIPROCITY OF FORCE]

The Law of Gravity: For any two material bodies, each exerts a force upon the other that is proportional to their combined mass and inversely proportional to the square of the distance between them.  [Note that this is not to be confused with any of the "three laws of motion," but spells out the special way of operation of one particular force that these general rules apply to.]

[1704: Opticks]

  Go to Reading List #3.

  Go back to the outline of the logical structure of explanation in "natural philosophy" (what we now call natural science).

  Go to the discussion of the main points of difference between the Copernican and Ptolemaic schemes of descriptive explanation for astronomical observations.

  Go forward to remarks on the impact of the victory of the new picture.

  Go to the Home Page of the course.

  Suggestions are welcome.  Please send your comments to lyman@ksu.edu .

      Contents copyright 1997 by Lyman A. Baker

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      This page last updated 08 April 1999.