IAL 4: The History of Astronomy to Newton

Don't Panic


  1. Why the History of Astronomy to Newton?
  2. Introduction
  3. Prehistoric Astronomy
  4. Babylonian Astronomy: Reading Only
  5. Ancient Greek Astronomy to Aristotle: Reading Only
  6. Aristotle: Reading Only
  7. Mathematical Ancient Greek Astronomy
  8. Ptolemy
  9. Aristarchos
  10. The Middle Ages: Ptolemy to Copernicus: 13 Centuries of Wheel Spinning: Reading Only
  11. Nicolaus Copernicus (1473--1543) and Heliocentrism
  12. Tycho Brahe (1546--1601)
  13. Johannes Kepler (1571--1630)
  14. Galileo Galilei (1564--1642)
    1. The Galileo Affair: The Sequence of Events Leading to Galileo's Trial and Condemnation by the Roman Inquisition
  15. Isaac Newton (1643--1727)
  16. Epilogue
  17. An Essay on the Three Epochs of the History of Astronomy: Not a Required Reading

  1. Why the History of Astronomy to Newton?

  2. Why cover the history of astronomy to Isaac Newton (1643--1727)?

    The short answer is that it is traditional in intro astro textbooks to do so.

    Going back to back to Stonehenge is very traditional: see the figure below (local link / general link: sullivan_stonehenge_003_remains.html).

    But why is the
    history of astronomy to Newton traditional?

    There are two rationales:

    1. The Classic Example of the Scientific Method in Action:

      One of the general learning outcomes of an introductory astronomy is to learn something about how science is done. One aspect of learning how science is done is to see scientific method in action: a cycle of theory and observation/experiment leading to progress in understanding nature: see the figure below (local link / general link: sci_method.html).

      history of astronomy to Newton is the grand classical example of the scientific method in action.

      However, the history of astronomy to Newton is NOT a typical exmple of the scientific method in action.

      The history stretches over millennia and most of the participants were unaware of the roles they were playing in the scientific method---the scientific method was first explictily expressed in the 17th century as illustrated by the quote from Robert Hooke (1635--1703) in the figure above (local link / general link: sci_method.html).

      In some cases, the participants in the history of astronomy to Newton may have thought that they were establishing truth for all time at least insofar as human reason could reach.

      In some cases, they may have thought that truth was beyond human capabilities, and all that could be done is give a satisfying-to-reason explanation of how things could be: i.e., a rational myth.

      A modern perspective is that final truth may beyond human capabilities, but there may be no limit it seems to how much we can improve our understanding.

      Note that others earlier in the 17th century before Robert Hooke's (1635--1703) statement exemplified the scientific method in their work: outstandingly Galileo (1564--1642) and Johannes Kepler (1571--1630).

      Before 17th century, the scientific method was certainly practiced sometimes (e.g., Archimedes (c.287--c.212 BCE)), but it was NOT recognized as a prime rule of science.

      Certainly, effective recognition of the scientific method was a key ingredient in Scientific Revolution of the 17th century, and so a key ingredient in the modern history (c.1500--present) since then.

        Note that the trial-and-error method practiced by everyone always is distinct from scientific method since it is NOT a search for general theories, but a search for solutions to limited problems. There is NO sharp line between the two methods, but there is a definite fuzzy one.

      By the by, Robert Hooke (1635--1703) discovered the super-important Hooke's law which is illustrated in the figure below (local link / general link: harmonic_oscillator.html).

    2. Cosmology: A Vital Human Concern:

      First note that the nature and meaning of everything just is an intrinsic vital human concern.

      Now cosmology (the science of the universe as whole) is NOT the science of everything of course, but it is the science of the largest scale of everything, and so attracts special interest---like elephants and whales---but more so since we are in universe and sustained by it.

      It also seems reasonable that the largest scale will be vital for "meaning of", NOT just "nature of". See pondering the universe in the figure below (local link / general link: infinity_eternity.html).

      cosmologists usually do NOT address "meaning of", but it seems to hover NOT far away from their expessed concerns. And it seems reasonable that if we ever fully understood universe on the largest scales, that understanding would have implications for "meaning of"---but it's hard to say what those implications will be.

      The upshot so far is that cosmology is itself a vital human concern.

      Given that, the history of how we got to where we are today in cosmology starting from mythological cosmology becomes its own vital human concern---an aspect of cultural history.

      The history is always seen as a big part. It is NOT outmoded.

      Now the history of astronomy to Newton is essentially the history of cosmology to Newton. At every stage, the astronomers were studying the universe as they perceived it. In fact until circa 1600, they mostly studied Solar System. The Solar System was just most of cosmology as it was understood until circa 1600.

      So we study the history of astronomy to Newton in order to study the history of cosmology to Newton (see the figure below: local link / general link: newton_principia.html).

      But why stop in particular with the age of

      We have enough astronomy lore now to understand the history of cosmology to Newton.

      One needs to learn more astronomy lore to carry that history further.

      It is also true that the period from prehistory to Newton (i.e., circa 1700 when Newton's work was essentially done) is a unity in the history of cosmology as yours truly argues at length below in the section An Essay on the Three Epochs of the History of Astronomy: Not a Required Reading.

      After Newton is another distinct epoch in the history of cosmology in the opinion of yours truly.

      Also astronomy becomes distinctly more than just cosmology after Newton. Various fields of astronomy become subjects in themselves. So the history of astronomy after Newton CANNOT be said to be essentially just the history of cosmology.

      The era in the history of cosmology from Newton (circa 1700) to circa 1900 and current era starting circa 1900 that leads to today's cosmology are covered briefly in IAL 26: The Discovery of Galaxies and IAL 30: Cosmology---after we have learnt enough modern astronomy to understand the history of those eras.

    3. On With It:

      Now having rationales---at least rationalizations---let's get on with it---the history of astronomy to Newton.

    4. General References:

      Some useful general references for the history of astronomy and the history of science in general are:

      1. H. Floris Cohen (1946--), How Modern Science Came into the World: Four Civilizations, One 17th-Century Breakthrough, 2011: See also H. Floris Cohen (1946--).
      2. F.M. Cornford, Principium Sapientiae, 1952: See also F.M. Cornford (1874--1943).
      3. David Furley (1922--2010), The Greek Cosmologists, 1987: See also David Furley (1922--2010).
      4. Marie Boas Hall (1919--2009), The Scientific Renaissance 1450--1630, 1994: See also Marie Boas Hall (1919--2009).
      5. Hesiod (fl. c.700 BCE), Theogony, circa 700 BCE: See also Hesiod (fl. c.700 BCE).
      6. Otto E. Neugebauer (1899--1990), The Exact Sciences in Antiquity, 1969: See also Otto E. Neugebauer (1899--1990).
      7. John North (1934--2008), The Norton History of Astronomy and Cosmology, 1994: See also John North (1934--2008).
      8. Bertrand Russell (1872--1970), A History of Western Philosophy, 1945: Not a well received book and now badly out of date, but sort of the great philosophy novel. See also Bertrand Russell (1872--1970).
      9. Stephen Toulmin (1922--2009) & June Goodfield (1927--) The Discovery of Time, 1965: See also Stephen Toulmin (1922--1990) and June Goodfield (1927--).
      10. Wikipedia.
      11. And lots of others.

  3. Introduction

  4. First, we should remark that the history of astronomy to Newton given here is the short version, and therefore necessarily simplified. But it's plenty long enough.

    Second, yours truly is knowledgeable about the subject, but NOT a great expert. Yours truly has NOT done relentless checking of aspects---caveat lector.

    Third, it is mainly the history of astronomy in the cultural region western Eurasia---and counting North Africa as part of western Eurasia as culturally it is---for two reasons:

    1. Your truly is only knowledgeable about the history of astronomy in this region.

    2. It's true to say that this region was pretty much always the leader in astronomy at least overall over any millennium and that modern astronomy largely developed out the astronomy of this region.

      Other astronomical traditions (e.g., Chinese astronomy, Indian astronomy, Mayan astronomy) have their interest in the general history of science and the history of culture, but just arn't as interesting qua astronomy in the opinion of yours truly.

      We will be unabashedly western-Eurasia-ocentric.

    Of course, we also got our muse from ancient Hellas: see the figure below (local link / general link: muse_astronomy.html).

    And now on with the show:

    1. Astronomy, the Oldest:

      Astronomy is often cited as the oldest, empirical, exact science.

      One can quibble, but there really is no other candidate for oldest empirical exact science if one regards mathematics as an abstract science that is only applied in the physical world.

      How old is astronomy as an empirical, exact science?

      In very simple ways, probably way back in the Paleolithic (2.6 Myr ago to circa 8000 BCE) when humankind first developed a sufficiently sophisticated language---but exactly when that was we do NOT know (see Wikipedia: Origin of language). See the Paleolithic (2.6 Myr ago to circa 8000 BCE) (i.e., the good old days) illustrated in the figure below (local link / general link: pleistocene_mammoth.html).

      In fact, it seems very likely that the
      days of the lunar month were counted as far back as people did counting and those counts would have been kept track of by some means in many Paleolithic societies for calendrical reasons. For more pondering on astronomy as the oldest empirical exact science, see the figure below (local link / general link: sapien_neanderthal.html).

      lunar month and lunar phases are illustrated in the animation in the figure below (local link / general link: moon_lunar_phases_animation_2b.html).

      To conclude, plausibly exact
      astronomy---in a very modest sense---goes back tens of thousands of years.

    2. Why Astronomy?

      There were calendrical reasons, but these need only very modest input from astronomy:

      However, even from its earliest days, some observers were probably interested in astronomy for its own sake. They wanted to know where things in the sky were and when they would appear.

      astronomy for astronomy's sake was probably NOT important for most early people.

      There is NO reason to doubt that prehistoric and early historic (i.e., literate) peoples saw celestial phenomena as signs from gods---particularly rare phenomena that were unpredictable (or seemingly so) like comets, eclipses, and bolides (much brighter than usual meteors). The rare phenomena were usually probably thought of as being signs aimed at all and/or at rulers portending great disasters (meaning something like destroying stars).

      But, of course, prehistoric and early historic peoples mostly just saw the sky as part of everyday life---it's just there, part of the background.

      Yours truly has NEVER heard of anyone directly worshiping celestial phenomena, but rather they regarded these phenomena as established by the gods or taking place in the realm of the gods.

        It has to be emphasized that early religions usually had NO definite formulation of theology NOR fixed dogma. So it was perfectly possible, for example, for an adherent to believe the Moon in the sky was the Moon god and at the same time believe the Moon god was person who you could talk to.

        The idea of making a systematic theology of their beliefs probably seldom occurred to them.

        In most cases, their gods were anthropomorphic gods at least psychologically if NOT always in form.

        Anubis straddles the line in form as shown in the figure below (local link / general link: anubis.html).

      The ancient
      Babylonians for example certainly took a keen religious interest in astronomy and believed the Heavens were under the power of their gods and that particular astro-bodies were manifestations of particular gods.

      However, they did NOT regard those particular astro-bodies as being the only manifestations of those particular gods.

      They seemed to have principally thought their gods were manifested by divine images maintained in temples (see Op-???; Wikipedia: Babylonian religion: Importance of idols).

        Their religious observances were certainly centered on the temples, NOT on the celestial phenomena.

      On the other hand, Medieval Christianity certainly had a TENDENCY, reinforced by Aristotelianism, to regard the observed Heavens as part of the theological Heaven---the realm of God and angels. But this concept was NEVER seen as an article of faith.

      Dante Alighieri (1265--1321) gives the famous retelling of the concept that the observed Heavens were the theological Heaven in his Divine Comedy. See the figure below (local link / general link: dante_beatrice.html).

      But it must be emphasized that
      Dante was consciously writing an allegory and referred to aspects of his story as "the fable"???.

      See more Divine Comedy. in the figure below (local link / general link: dante_divine_comedy.html).

      In any case, Medieval Christianity did NOT include sky worship.

      To conclude, it seems that early peoples probably did NOT worship the sky in any direct sense.

      But they were particularly conscious of signs from the gods.

      The behavior of birds and the entrails of sacrificial animals (i.e., haruspicy) were particularly popular regions to look for such signs at least in the Mediterranean region and Mideast.

      But celestial signs have always had particular resonance and there is a tradition that they were aimed primarily at royalty and rulers. Comets, in particular, were often considered ominous. See the great image of Comet Lovejoy in the figure below (local link / general link: comet_lovejoy.html).

    3. Astrology:

      With (horoscopic) astrology---invented by Babylonian astronomers---astro-divination became democratized: the stars at least partially determined everyone's character and at least influenced their activities. Astrology tended to become understood as a science based on regular cause/influence and effect/tendency and less as direct messages from the gods.

      See the consulting astrologer at work in the figure below (local link / general link: astrologer.html).

      How does
      astrology work?

      Most naked-eye celestial events are regular, but they come in a multitude of combinations. Thus, astrology could develop a vast realm of possible influences based on particular combinations for imaginative astrologers to work with.

      The influences are often easy to identify---Venus in your astrological sign is NOT hard to read---but giving the influences their exact weight is where the art of the astrologer was needed.

      Direct signs from the Heavens were still believed in, of course. Irregular events like comets were considered particularly ominous.

        It goes without saying that astrology is totally a pseudoscience nowadays and usually it was that in the past too.

        Some like Johannes Kepler (1571--1630) did try to make it scientific, but they failed because there is nothing to it.

        Of course, astrology still works. It usually gives you positive advice and positive advice is usually good, and so if you follow your horoscope, your day will usually be better.

        But the same is true if you follow your mother's advice.

      Astrology is still with us: it's only a click away to your horoscope.

      There have always been dissidents, of course:

      As well as Cicero (106--43 BCE), there was also Cassius (before 85--42 BCE) among the dissidents: see the figure below (local link / general link: brutus_james_mason.html).

      dissidents usually come to a sticky end:

  5. Prehistoric Astronomy

  6. As we suggested in the section Introduction, prehistoric astronomy as an empirical exact science may have started with very simple observations some of which may eventually recorded on paleolithic tally sticks (such as the Lebombo bone) tens of thousands of years ago.

    But the prehistoric astronomy that we know most about is simple alignment astronomy using the horizon as a natural measurement tool. We take this subject up in the subsections below.

    Note: Archaeoastronomy is the study of prehistoric and early-literate astronomy in its cultural role. In this lecture, we cross over the line into archaeoastronomy sometimes. An example of an object of archaeoastronomy is Newgrange (built c.3200 BCE): see the figure below (local link / general link: newgrange_1905.html). We discuss Newgrange (built c.3200 BCE) below in subsection Newgrange in Ireland.

    1. Horizons and Horizon Phenomena:

      Prehistoric peoples, and ancient historistoric peoples, were keenly aware of horizon phenomena (rising and settings of bright stars, etc.) because the horizon provides a natural measurement tool.

      We can consider one important example of a horizon phenomenon heliacal risings (of stars). Important to prehistoric peoples, and ancient historistoric peoples that is---us NOT so much.

      The heliacal risings of commonly recognized bright stars mark the times of solar year = 365.2421897 days (J2000). So you could tell whether it was January, February, March, etc. (by whatever name you used) by recognized heliacal risings But, of course, you could do that by weather too.

      Heliacal risings are explicated in the figure below (local link / general link: heliacal_rising.html).

      heliacal rising of Sirius is particularly noteworthy---see the figure below (local link / general link: hesiod.html).

    2. Alignment Astronomy:

      Elaborating on just casually observing horizon phenomena is alignment astronomy: finding the alignments for the rising and setting of astronomical objects.

      How did early peoples do alignment astronomy?

      They made observations using natural horizons or simple artificial horizons (e.g., sticks in the ground).

      The procedure is illustrated in the figure below (local link / general link: horizon_observation.html).

    3. Astronomical Monuments:

      Alignment astronomy is very easy to do---it's NOT rocket science.

      Simple artificial horizons are easy to build too---a few stakes in the ground or a few stones.

      But many prehistoric peoples and early historic peoples built very elaborate artificial horizons or other structures embodying their astronomical lore.

      These structures can be justly called astronomical monuments.

      By definition, prehistoric people were illiterate, and so they didn't write anything down.

      The astronomical monuments are their records of their astronomical knowledge.

      The study of such astronomical monuments is a main part of archaeoastronomy and archaeology too.

      The most famous astronomical monument is Stonehenge.

      But there are many other astronomical monuments or possible ones from prehistoric cultures and early historic societies all over the world.

      We consider some famous astronomical monuments (including possible ones) in the subsections below.

    4. Stonehenge: The Prime Astronomical Monument:

      Where is Stonehenge? See the physical map of the Hiberno-British Isles in the figure below (local link / general link: map_british_isles_physical.html).

      What is

      It's a circular structure of megaliths which are large stones used in structures. See the figures below (local link / general link: sullivan_stonehenge_001_far_off.html; local link / general link: sullivan_stonehenge_002_whole.html; local link / general link: sullivan_stonehenge_003_remains.html).

      A particular
      Stonehenge megalith of interest is the Heelstone: see the figure below (local link / general link: sullivan_stonehenge_004_heelstone.html).

      Some of the
      geology and history of Stonehenge is given in the figure below (local link / general link: stonehenge_map_modern.html).

      For the
      alignment astronomy, (probable and unlikely both), embodied in Stonehenge, see the Stonehenge map in the figure below (local link / general link: stonehenge_map_refined.html).

      The most certain intentional alignment is set by the Heelstone.

      Below are two figures illustrating the
      Heelstone and the Sun rising over Stonehenge on the morning of the summer solstice.

      There are other possible astro alignments at Stonehenge that can be found when viewing the horizon from the Altar Stone (see Wikipedia: Archaeoastronomy and Stonehenge).

      But we won't go into them.

      More extravagant claims of astronomical functions for Stonehenge are certainly false: e.g., that Stonehenge was an analog computer used to calculate eclipses (see Wikipedia: Archaeoastronomy and Stonehenge: Gerald Hawkins's work).

      They demonstrate the ingenuity of posterity.

      For more thrills, see Stonehenge videos below (local link / general link: stonehenge_videos.html).


    5. The Great Serpent Mound:

      The Great Serpent Mound is a Native American structure in Adams County, Ohio. See the figure below (local link / general link: great_serpent_mound.html).

    6. The Giza Pyramids:

      The Giza Pyramids are the tombs of the pharaohs of the 4th Dynasty of the Old Kingdom of ancient Egypt. See the figure below (local link / general link: giza_pyramids.html).

    7. Newgrange in Ireland:

      Newgrange is a Neolithic structure in County Meath, Ireland. See the figure below (local link / general link: newgrange_1905.html).

    8. El Caracol, Chichen Itza in Yucatan:

      El Caracol, Chichen Itza is a likely astronomical monument of ancient Mayan astronomy: see the figure below. (local link: File:Chichen Itza 4.jpg)

      Note Chichen Itza is an ancient Mayan city in the Yucatan state of Mexico.

    9. The Functions of the Astronomical Monuments:

      It must be absolutely emphasized that Stonehenge and ALMOST ALL the other prehistoric and early astronomical monuments embodying astronomical lore were almost certainly NOT observatories: i.e., buildings for gathering new astronomical data.

      They probably embodied astronomical lore discovered by simpler artificial horizons---stakes and stones.

      They were monuments recording the astronomical lore---for illiterate peoples, there was no other way of recording it.

      And it also must be absolutely emphasized that the monuments were probably in most cases NOT primarily for recording astronomical lore.

      The monuments embodying alignment astronomy probably in most cases (including Stonehenge) had multiple uses and significances. Their astronomical use/significance was probably only one among many uses/significances.

      Stonehenge, for example, was obviously a cult center with religious and cultural meanings that only included astronomical ones among others (see Wikipedia: Stonehenge: Function and construction). In fact, people attended religious and cultural ceremonies at Stonehenge and may have gone there for trade and holidays too. For Stonehenge in use in modern times, see the figure below (local link / general link: stonehenge_neo_druids.html).

    10. Later Monuments:

      In later ages, when astronomy become much more developed, incorporating astronomy lore into buildings for recording or symbolic reasons declined it seems, except for some simple cases: e.g., cathedrals are often aligned approximately west-to-east so that worshippers face approximately the rising Sun (see Wikipedia: Cathedral: Symbolic functions of the building).

      In the modern age, incorporating astronomy lore into buildings is rare, but it is occasionally done for ornamentation such as for the UNLV's Bigelow Physics Building (see Physics Building Dedication, 1994) and, more prominently, Grand Central Station: see the figure below.

      Astronomy lore is also sometimes incorporated into buildings for historical/cultural/educational/fun reasons such as for Stonehenge replicas: see the figure below (local link / general link: stonehenge_carhenge.html).

      Of course, buildings ancient and modern often embody solar astronomical science for the practical reasons of lighting and/or heating (see
      Wikipedia: Passive solar building design).

    11. Why Did Early Peoples Do Astronomy?

      As mentioned in the Introduction, there may well have been a few individuals with some purely astronomical interest, but probably that was NOT the main interest of early peoples.

      There were calendrical reasons as we also mentioned in the Introduction, but these need only very modest input from astronomy:

      But more elaborated societies have terms of office, contracts with termination dates, and religious observances/events all of which are thought to require exact times.

      Such societies needed elaborate calendars depending on the natural astronomical clocks provided by the astronomical cycles of the Sun, Moon, planets, and fixed stars (e.g., via their heliacal risings).

      Those natural astronomical clocks were considered to measure true time---which they do to high, but NOT perfect, accuracy in our modern physics view.

      However, in traditional societies, the rather obscure natural astronomical clocks of highly detailed astronomy were well beyond calendrical needs for civil purposes and were probably mainly for cultural and astrological purposes, and eventually horoscopic astrology.

      We know this was true for the ancient Babylonians and can assume it confidently for other early societies including that of the Stonehengers (AKA Neolithic Britons).

  7. Babylonian Astronomy: Reading Only

  8. The ancient Mesopotamians developed one of the world's first two literate civilizations in what is now Iraq and what historians call Mesopotamia.

    In the early literate phase circa 3000---2000 BCE, the region was called Sumer and we call the people Sumerians.

    To later
    Mesopotamians, the time of Sumerians was a classical age---as Classical Antiquity was to later times.

    1. Babylonia:

      After circa 1800 BCE, Babylon became the principle city of Mesopotamia.

      Because of this fact, we moderns tend to call the southern part of Mesopotamia Babylonia after circa 1800 BCE until its culture and political nature gradually got rather thoroughly transformed in the 1st millennium CE (see Wikipedia: Babylonia: Persian_Babylonia). See the map of Babylonia in the figure below.

      Below are two figures of Babylon the great.

      The science and astronomy of Babylonia written in cuneiform script (see below) tends to be called Babylonian too after 1800 BCE until cuneiform faded from history in the course of the 2nd century CE (see Wikipedia: Cuneiform).

      Mathematical Astronomy:

      The Sumerians and Babylonians developed novel mathematical and astronomical techniques.

      The Babylonian astronomers, in fact, developed a sophisticated predictive mathematical astronomy far in advance of the simple alignment astronomy of earlier civilizations.

      What is mathematical astronomy and why does anyone do it?

      Mathematical astronomy predicts where astro-bodies will be on the celestial sphere on given dates and related phenomena such as conjunctions, oppositions, and eclipses.

      The predictions are written up in tables called ephemerides (singular ephemeris).

      See an example ephemeris from Medieval Islamic astronomy in the figure below (local link / general link: al_khwarizmi.html).

      mathematical astronomy was probably mainly for calendar making, religious purposes, and divination.

      Later horoscopic astrology required mathematical astronomy. The astrologer NOT only has to know that Heavens said yesterday, but what they will say tomorrow.

        To repeat myself, yours truly thinks there must have been some interest in astronomy for its own sake from the earliest times, but this was almost certainly a minority interest until perhaps the 17th century. It is human nature for activities to become an end in themselves.

      The Babylonian astronomers circa 1600 BCE were probably the first to develop mathematical astronomy beyond the level of simple alignment astronomy.

      Modern astronomy largely descended from this beginning.

      Independent traditions of mathematical astronomy were developed by, e.g., Chinese astronomers and Mayan astronomers. Although these traditions contributed relatively little to modern astronomy in a direct sense, they are significant demonstrations of intellectual prowess.

    2. How Do We Know about Babylonian Astronomy?

      They Wrote on Clay (1938, Edward Chiera, 1885--1933).

      The cuneiform script used by the ancient Mesopotamians was written on clay tablets.

      Fired clay tablets stored in dry conditions are highly non-volatile memory---they last millennia---our disk storage won't last as long---when archaeologists excavate our lost civilization, our disks will NOT readable. See an example of a modern clay tablet made by ancient means in the figure below (local link / general link: cylinder_seal.html).

      From caches of
      cuneiform clay tablets excavated in the Mideast, we know a great deal about ancient Mesopotamia.

      Many of the clay tablets are inventories and tax records---they are still being audited.

      There is some Babylonian literature like Epic of Gilgamesh: see the figure below (local link / general link: gilgamesh.html).

      And there are astronomical texts.

      These are mostly calculations, observations, and ephemerides.

      There is virtually no records of astronomical theories.

      There is some Mesopotamian mythology which contains astronomy lore---but that's NOT science. See the figure below (local link / general link: sumerian_gods_tablet.html).

      From the
      cuneiform clay tablets, we actually know a great deal about how the ancient Mesopotamians did astronomy---just NOT what they thought about astronomy.

      For example, we know a fair amount about Babylonian mathematics and the Babylonian sexagesimal system.

    3. Babylonian Mathematics:

      The Babylonian mathematicians (and their predecessors in ancient Mesopotamia the Sumerian mathematician) used a sexagesimal system (i.e., base-60 system) for mathematics and astronomy.

      Babylonian mathematics is explicated a bit in the figure below (local link / general link: babylonian_cosmos.html).

      animation in the figure below gives a visual proof of the Pythagorean theorem.

      After that, we turn to Babylonian astronomy.

    4. Babylonian Astronomy:

      The predictive mathematical astronomy of the Babylonian astronomers had simple beginnings in using cycles of repeated astronomical motions.

      Early evidence of this is the Venus Tablet of Ammisaduqa: see the figure below (local link / general link: venus_tablet.html).

      Venus Tablet shows that the Babylonian astronomers as early as 1600 BCE could rely on cycles to make relatively accurate predictions.

      You can build up cycles for the other planets and for eclipses.

      For example, all eclipse phenomena repeat approximately about every 18 years: this is called the Saros cycle by moderns.

      We can see that a primitive mathematical astronomy can be built up from cycles. The Babylonian astronomers did this first.

      But they advanced.

      In the period 400 BCE--100 CE, Babylonian astronomers reached their highest level.

      Some of their most notable achievements:

      1. The Babylonian astronomers divided the circle into 360° as explicated in the figure below (local link / general link: babylonian_360_degrees.html).

      2. Certainly the idea of sexagesimal divisions for angular measurement goes back the sexagesimal system of the Babylonian astronomers, but yours truly can't find out if they introduced 60 arcminutes to a degree and 60 arcseconds to an arcminute.

        The ancient Greek astronomers Timocharis (c.320--c.260 BCE) and Aristillus (fl. 260 BCE) introduced the arcminute in Classical Antiquity (see Wikipedia: Hipparchus: Babylonian sources). The arcsecond may have been too small an angular unit for the Ancients to have bothered with. They could NOT measure to that accuracy to anything close to arcsecond accuracy Ptolemy (c.100--c.170 CE) via his treatise the Almagest passed the arcminute to posterity???.

          The 60 minutes in a hour and 60 seconds in a minute also traces back to their sexagesimal system.

      3. The Babylonian astronomers introduced the zodiac signs circa 500 BCE (see John North 1994, The Norton History of Astronomy and Cosmology, p. 66). The zodiac signs are NOT the zodiac constellations, but 30 degree regions of the ecliptic that the zodiac constellations occupied circa 500 BCE. Due to the axial precession of the Earth (AKA precession of the equinoxes), each sign is now about one zodiac constellation west of where it was then (see Wikipedia: Zodiac: Precession of the equinoxes).

      4. From the late 5th century BCE at least, the Babylonian astronomers were practicing horoscopic astrology (see John North 1994, The Norton History of Astronomy and Cosmology, p. 41). This astrology would be greatly elaborated in the world of Classical Antiquity and got passed on to us. You can check out your horoscope at your horoscope.

      5. The Babylonian astronomers developed elaborate algebraic techniques to create ephemerides. This is certainly their greatest achievement---but we won't go into it.

          Question: What is an ephemeris?

          1. A table of dates.
          2. A table of astronomical predictions for dates.
          3. None of the above.

          Answer 2 is right.

          Ephemeris is a singular which is hard to remember.

          Ephemerides is the plural ephemeris which is also hard to remember.

      In mathematical astronomy, we can certainly say that Babylonian astronomy was scientific.

      There clearly was a cycle of theory and observation leading to better and better predictive results and a deeper knowledge of mathematical technique---the scientific method was practiced.

    5. Babylonian Astrophysics and Babylonian Cosmology?

      In fact, we don't know that much about what the Babylonian astronomers thought about astronomy.

      Our understanding of their mathematical astronomy just comes from observational, calculational and ephemeris clay tablets.

      All we know is that the astronomy tablets were written in a clerical environment it seems

      We have no/little evidence that there was any Babylonian astrophysics: i.e., an attempt to understand the celestial motions in terms of some physical laws.

      Also there are only traces of any scientific Babylonian cosmology. Even the Wikipedia section on Babylonian cosmology fails to convey much of anything (see Wikipedia: Babylonian astronomy: Babylonian cosmology).

      There was a Babylonian mythological cosmology, but that is another subject.

      The Babylonian astronomers may well have been satisfied with a DOME MODEL of the cosmos in which the astronomical objects were manifestations of the gods.

      The figure below (local link / general link: babylonian_cosmos.html) illustrates a possible DOME MODEL.

    6. Dome of the Sky Cosmological Models:

      The category of DOME MODELS is a modern catchall category for some mythical cosmologies that could also be considered philosophical cosmologies.

      The category that can only be vaguely specified since various peoples at various times had various ideas that were probably often vague.

      But one can say that a DOME MODEL probably posits a flat Earth and posits that the astro-bodies travel over the sky dome-like surface and then under the Earth's surface from their setting to their rising positions.

      Under Earth's surface may in some cases have been regarded as the underworld or land of the dead.

      See the DOME MODEL of Norse mythology in the figure below (local link / general link: cosmos_norse_yggdrasil.html).

    7. Why Babylonian Astronomy?

      Why did the ancient Babylonians do astronomy?

      Almost certainly the main reasons were for religious and astrological purposes.

      The astronomical tablets were written in a clerical environment it seems.

      Purely calendrical reasons for astronomy also existed. But the astronomy needed for the calendar is far less than the elaborate astronomy developed by the Babylonian astronomers.

      A few people may have been interested in astronomy for its own sake---as we have mentioned before.

      But we know nothing about them.

    8. Golden Ages and the Scientific Revolution:

      Before going on we should mention that Babylonian exact sciences had only two golden ages: (1) circa 1800 -- circa 1600 BCE in pure math (Ne-30); (2) circa 400 BCE -- circa 100 CE in mathematical astronomy.

      There were long stretches of time in a literate culture that spanned from circa 3000 BCE to circa 200 CE in which NOT much development happened---periods of stagnation.

      The pattern of golden age and stagnation seems to be typical of science in traditional societies.

        By traditional societies, we mean in this context those without modern science which is all societies before about 1600 and some societies to arguably the 20th century.

      The ancient Greeks had a golden age of science, and so did the Medieval Islamic society.

      Traditional Chinese and Indian societies probably a few golden ages---but yours truly is NOT so well informed on these societies.

      Part of the explanation for the pattern of golden ages and stagnations is that science is a marginal activity in traditional societies. Only a few individuals practice it and societal support, tangible and intangible, is chancy.

      A few atypical individuals---well let's call them geniuses---may feedback to each other over a few generations to create significant progress. But the chain is broken by chance and stagnation seems to result.

      Fortunately, the achievements are usually preserved in writings and can be built on later.

      Science in modern society since circa 1600 (i.e., modern science) is radically different. It is relentlessly progressive and strongly supported by society.

      The change in the nature of science is called in historical research the Scientific Revolution.

      The Scientific Revolution occurred in the 16th century and 17th century in Europe. See the figure below for an illustration of the Scientific Revolution in progress.

      The Scientific Revolution occurred in the 16th century and 17th century in Europe.

      Some historians of science consider the Scientific Revolution to be spread out over a longer time period, but even they probably concede that the inner core of it was in the 16th century and 17th century.

  9. Ancient Greek Astronomy to Aristotle: Reading Only

  10. Ancient Greece (or Ancient Hellas) was more extensive than modern Greece. It included the west coast of Turkey, the littoral of the Black Sea, and southern Italy including Sicily.

    As the map in the figure below (local link / general link: map_hellas_circa_550_BCE.html) illustrates, Ancient Greece was spread around much of the Mediterranean Basin.

    Ancient Greece is famous in many respects.

    It's well known Greek mythology as illustrated in the figure below (local link / general link: achilles_ajax.html).

    Among other things, it was arguably the greatest period of enlightenment in
    history before the Enlightenment.

    Ancient Greece saw the beginning of western philosophy and natural philosophy, and surpassed Babylonian astronomy with Greek astronomy---which began with natural philosophy.

    Ancient Greece and ancient Rome collectively constitute Classical Antiquity (AKA Greco-Roman Antiquity).

    A timeline of significant intellectuals of Classical Antiquity is shown in the figure below (local link / general link: intellectual.html)---created on day when yours truly had too much time on yours truly's hands.

    1. Greek Mythical Cosmology:

      The Greek mythical cosmology is NOT completely specified in any source.

      In fact, there were probably all kinds of variations and NO definite or original version probably ever existed.

      But the primary source is the poem Theogony by Hesiod (circa late 8th century BCE): see an imaginative portrait in the figure below (local link / general link: hesiod.html).

      To expand a bit on
      Hesiod's Theogony and mythical cosmology in general, see the figure below (local link / general link: leonardo_da_vinci_deluge_creation.html).

      geneology of the Greek gods---with a few nifty additons by yours truly is shown in the figure below (local link / general link: theogony.html).

      The overall structure of the universe in
      Theogony is NOT well specified, but it may be a lot like the Norse mythology universe: dome of the sky, underworld, and Midgard (flat Earth and ocean) sandwiched between. See figure below (local link / general link: cosmos_norse_yggdrasil.html) showing a 19th century reconstruction of the Norse mythology universe.

      Probably, many
      mythological cosmologies were similar to Greek mythical cosmology and the Norse mythology universe.

      For societies that are geographically very localized the dome of the sky, underworld, and flat Earth and ocean seem pretty natural.

      It is also natural to see the underworld as the land of the dead and where astronomical objects / sky gods were when they were below the horizon.

      What was beyond the boundaries of the world?

      One answer is: there is a special place in Tartarus for people who ask such questions.

      But the question can't be put off forever.

    2. Birth of Philosophy Circa 600 BCE:

      A short definition of philosophy is the study of the reality in terms of first principles which usually/always have to be discovered from their consequences.

      Two main components of philosophy have always been natural philosophy (philosophy applied to nature in the broadest sense including human aspects) and ethics (philosophy applied to behavior of humans or, more generally, any intelligent beings).

      The philosophy involves reason and observation/experiment.

      The ancient Greek philosophers were relatively strong on the former and pretty weak on the latter.

      For Ancient Hellas (AKA Ancient Greece) illustrated by the Acropolis of Athens, see the figure below (local link / general link: acropolis.html).

      Philosophy was born (by usual reckoning) in Ancient Greece circa the early 6th century BCE.

      Why then and there?

      There probably can be no indisputable answer, but one can try.

      Ancient Greece at that time (i.e., Archaic Greece (circa 8th century -- 480 BCE)) was a confident society.

      The confidence was probably in large measure to its success in expansion: settling colonies around much of the Mediterranean Basin.

        It's a glum fact that this colonization involved conquest and enslavement, but in ancient times this was generally regarded as OK if you did it to others, but NOT if it was done to you.

      However, confidence also came from self-aware progressive achievement in trade, crafts, art, literature (Homer (circa 700 BCE) Hesiod (circa late 8th century BCE), etc.) and sports (e.g., ancient Olympic Games)---the ancient Greeks generally thought well of themselves---but who doesn't? For Greek sculpture illustrated, see the figure below (local link / general link: charioteer_delphi.html).

      Societal confidence plus the fact that the
      Archaic Greeks were aware they had much to learn from older societies of the ancient Near East and ancient Egypt made them relatively open to new ideas and innovations. The Archaic Greeks were, in fact, emerging from the Greek Dark Ages (circa 1100--circa 800 BCE) when they were illiterate and rather out of touch with the world at large.

      For big example of an innovation, the Archaic Greeks accepted the alphabet from the Phoenicians---they modified for the ancient Greek language and added vowels (see Wikipedia: Alphabet: Ancient Northeast African and Middle Eastern scripts)---which meant they no longer had to say "grk".

      Contact with other societies also made the Archaic Greeks aware that their mythology was NOT universal---others had other mythologies. One can react in three ways to this information:

      1. Our mythology is right and theirs is wrong---or vice versa.
      2. All mythologies are about the same when you identify enough correspondances.
      3. Maybe all mythologies are just stories and you have to do philosophy.

      Probably, all reactions occurred to the Archaic Greeks. The case for philosophy is pretty certain since the Presocratic philosopher Xenophanes (c.570--c.475 BCE) tells us that was his reaction, more or less: his fragments:

      1. But mortals think that the gods are born
        and have the mortals' own clothes and voice and form.
      2. One god, greatest among gods and humans,
        like mortals neither in form nor in thought.
      3. The gods have NOT, of course, revealed all things to mortals from the beginning;
        but rather, seeking in the course of time, they discover what is better.

      For philosophy to flourish, free debate is probably essential.

      Free debate the Archaic Greeks had to some degree.

      Their society was politically pluralistic: it was divided into many independent city-states (poleis: singular polis) with varying kinds of government.

      Very few city-states were ancient Greek democracies, but in most, sufficiently high-ranking men (but NOT women) debated political and legal issues.

      This means these high-ranking men (and probably others too) could easily slide over to debating other issues in art, literature, sport (inevitably), and, if they were so inclined, philosophy.

      It seems that given the right societal conditions some individuals will always be interested in philosophy and, in particular, in natural philosophy.

      In fact, in Classical Antiquity (AKA Greco-Roman Antiquity), the number of people interested in natural philosophy was always pretty small: just few recorded persons in any generation though probably a much larger number of unrecorded persons of generally lesser importance.

      ancient Greece (prior to Alexander the Great (356--323 BCE) and his father Philip II of Macedon (382--336 BCE)) had pluralism (multiple independent city-states) and at the same time unity (same language, culture, mythology) was probably of critical importance in the development of impressive natural philosophy. There could be many experiments in thought and at the same wide cultural communication.

      The period of continuous progress in ancient Greek science/nature-knowledge (i.e., natural philosophy and, speaking a bit more generally, nature-knowledge) is arguably from circa 600 BCE to circa 200 BCE---this was the golden age of ancient Greek science/nature-knowledge. After 200 BCE, ancient Greek science/nature-knowledge petered out with sporadic achievements until finally extinguished in the 6th century CE.

      Why the petering out is the story for another day. In fact, we've already covered part of it in the subsection Golden Ages and the Scientific Revolution.

      The societal situation that gave rise to the great achievements in ancient Greek science/nature-knowledge is similar to that of Western Europe in the Renaissance---a relatively confident, open society with pluralism and unity. So it is NOT surprising that the Renaissance was, among other things, the golden age of Renaissance science. The Renaissance, however, was at a much higher scientific and technological level actually than Classical Antiquity.

      Renaissance science did NOT, however, peter out, but accelerated into the Scientific Revolution.

      But that is also a story for another day. For a large part of the story, see H. Floris Cohen (1946--), How Modern Science Came into the World: Four Civilizations, One 17th-Century Breakthrough, 2011.

    3. More on Natural Philosophy:

      Natural philosophy is the study of nature.

      Modern science developed from natural philosophy and can still be considered a part of it.

      However, a large part of natural philosophy---which yours truly will call a priori natural philosophy---is NOT modern science in that it does NOT do experiments or detailed observations.

      A priori natural philosophy is largely a priori reasoning: first principles are assumed and the world behavior is derived from those first principles in a vague manner with only casual observations providing plausible and often specious validation.

      To us moderns, a priori natural philosophy seems naive and a very weak way of studying nature---but this is presentism.

      Before the Scientific Revolution (of the 16th century and 17th century), a priori natural philosophy seemed reasonable to people and the only path to more than superficial knowledge of nature.

      However, the a priori natural philosophy could only give speculative knowledge as proven by the fact were competing a priori natural philosophies that were inconsistent and that a priori natural philosophies are often NOT subject to falsification.

      Now there was some experimentation and---especially in astronomy---detailed observation before the Scientific Revolution, but the dogmatic insistence on those procedures did NOT exist then and practitioners of a priori natural philosophy often regarded those procedures as just ways to superficial nature knowledge.

      See angel of melancholia reflecting on superficial nature knowledge in the figure below (local link / general link: melancholia.html).

      Of course, some
      natural philosophers did do experimentation and/or detailed observations. But the scientific method was NOT explicit in reports of their work.

      For example, natural philosophers of ancient Greek science/nature-knowledge Aristotle (384--322 BCE), Archimedes (c.287?--c.212 BCE), Ktesibios (c.285--c222 BCE), and Hero of Alexandria (c.10--c.70 CE) must have done some experimentation. But that aspect of their work was NOT picked up by posterity.

      Aristotle (384--322 BCE) (who we discuss below in the section Aristotle) is an especially noteworthy case. His followers, the Aristotelians, largely followed Aristotle the a priori natural philosopher, NOT Aristotle the experimenter in biology, his favorite science,

      Ancient astronomy is somewhat different than other ancient natural philosophy since detailed accurate observations were always seen as necessary. But in practice, the ancient astronomers were often sloppy with new observations being no better than the old ones.

      Now a priori natural philosophy is NOT worthless.

      It is where the study of nature as a science began in Ancient Greece.

      More importantly, the speculations of a priori natural philosophy treated, NOT as dogma, but has hypotheses that lead to further investigations are important to science.

      One may say poetically that all scientists have an inner a priori natural philosopher who they consult for wild and crazy ideas.

      Let's now start our march through the glory that was Greek astronomy.

    4. The Presocratic Philosophers:

      The first natural philosophers were the Presocratic philosophers of ancient Greece.

      They were definitely a priori natural philosophers in the terminology of the last subsection.

      The Presocratic philosophers were NOT aware that they were Presocratic since they were NOT aware that Socrates (c.469--399 BCE) was coming along.

      In fact, some of the Presocratics were contemporaries of Socrates and even lived until after his death: e.g., Democritus (c.460--c.370 BCE). See the two figures below (local link / general link: presocratic_timeline.html; local link / general link: socrates_death.html).

    5. The Earliest Presocratic Philosophers:

      The earliest Presocratic philosophers---were from Ionia (now western Turkey). See the map and image of Ionia in the two figures below (local link / general link: ionia.html; local link / general link: ionia_samos.html).

      The most prominent
      Presocratics are Thales (c.624--c.546 BCE), Anaximander (c.610--c.546 BCE), Anaximenes (c.585--c.528 BCE), and Pythagoras (c.570--c.495 BCE) all in the 6th century BCE.

      Thales, Anaximander, and Anaximenes, all tried to create theories of the cosmos that were based on ELEMENTARY PRINCIPLES without invoking anthropomorphic gods---no Zeus, no Hecate. See the image of Hecate in the figure below (local link / general link: hecate.html).

      Thales---the first philosopher by everyone's reckoning---thought the basic substance was water, Anaximander thought it was the apeiron (i.e., the Boundless), and Anaximenes thought it was air.

      They were trying to understand how the world could arise out of some basic "element". In modern times, we know the elements and lots of sub-atomic particles too.

      Pythagoras was different kind of cat. He founded a sect, the Pythagoreans, that believed that the world is based on mathematics. This belief could have led to mathematical physics, but in fact led to mathematical mysticism (see Wikipedia: Pythagoreanism: Natural philosophy) and a sort of religion (see Wikipedia: Pythagoreanism: The akousmatikoi). See imaginative Pythagoreans in the figure below (local link / general link: pythagorean_sunrise.html)

      Another core belief of
      Pythagoreans was in metempsychosis (their version of reincarnation).

      The scientific ideas of the earliest Presocratics seem naive at first glance.

      This is partially because they were naive---the earliest Presocratics were just starting out in philosophy after all.

      But it is also because that only fragments of their writings/arguments have been passed down to us from Classical Antiquity. If we had more of their writings/arguments, their ideas might seem more cogent.

      Some reconstruction of their thinking is possible (see, e.g., David Furley (1922--2010), The Greek Cosmologists, 1987).

    6. The Cosmologies of the Presocratics:

      The cosmological models of the Presocratic philosophers were largely based on reasoning from simple, crude observations, with almost NOTHING that can be called detailed observation or experiment. The models can be described as rational myths.

      But the were very interesting in themselves and in being the origin of physical cosmology.

      We can't discuss all the cosmologies.

      But we will discuss below aspects of those of greatest interest for the development of astronomy: the cosmologies of the Atomists, Parmenides (early 5th century BCE) (the spherical Earth theory), and the Pythagoreans (the Philolaic system).

      After that a few more pertinent topics before moving on to Aristotle (384--322 BCE) and Aristotelian cosmology.

    7. The Atomists and the Cosmology of the Atomists:

      The atomists Leucippus (first half of 5th century BCE) and Democritus (c.460--c.370 BCE) invented the original concept of atoms: atomist atoms to coin an expression.

      See the imaginative portrait of Democritus (c.460--c.370 BCE) in the figure below (local link / general link: democritus.html).

      1. Atomist Atoms:

        The reasoning of the atomists (as reconstructed by David Furley (1922--2010), The Greek Cosmologists, 1987, p. 124) was there had to be something to give stable structures. But all macroscopic structures are subject to change (are divisible). So what is unchangeable (indivisible) must be below perception: i.e., microscopic.

        And there is some truth as we now know to the reasoning of the atomists. The microscopic stability of the world is supplied by the quantization of quantum mechanics---every kind of fundamental particle is an identical particle, every kind of composite particle in the limit of being unperturbed is an identical particle, etc.

        The atomist atoms were absolutely indivisible (i.e., unbreakable) and were eternal. They had shapes that gave them their particular properties and they moved in the atomist void which was absolutely empty space.

        In fact, the atomists made very little real progress in making atomist atoms a useful scientific theory. To do that you have to use atoms in chemistry and that did NOT happen until John Dalton (1766--1844).

        However, the modern concept of atoms did derive from the atomist atoms. The chain of atomic thinking is unbroken: omitting quite a few names: Leucippus (first half of 5th century BCE), Democritus (c.460--c.370 BCE), Epicurus (341--271 BCE), Lucretius (c.95--c.55 BCE), Pierre Gassendi (1592--1655), Walter Charleton (1619--1707), Robert Boyle (1627--1691), Isaac Newton (1643--1727), John Dalton (1766--1844), Ludwig Boltzmann (1844--1906), J. J. Thomson (1856--1940, Jean Baptiste Perrin (1870--1942), Ernest Rutherford (1871--1937), Albert Einstein (1879--1955), Niels Bohr (1885--1962), Erwin Schroedinger (1887--1961).

        See Isaac Newton's (1643--1727) thinking on atoms in the figure below (local link / general link: newton_atoms.html).

      2. The General Rejection of Atomist Atoms:

        Aristotle (384--322 BCE), by the by, rejected atoms: there is NO smallest, the void is a vacuous concept.

        In fact, most of natural philosophy rejected atoms until the 19th century: they were often thought to imply atheism---a position to be avoided at all costs. Actually, Democritus (c.460--c.370 BCE) and Epicurus (341--271 BCE) did believe in gods, but thought they didn't do anything, except maybe flit around like ghosts (see Fu-161).

      3. The Cosmology of the Atomists:

        The cosmology of the atomists cosmology of the atomists (mostly due to Democritus (c.460--c.370 BCE) it seems) is impressive---but still a rational myth with only casual observations to support it empirically.

        Atomist cosmology is explicated in the figure below (local link / general link: cosmology_atomist.html).

        The use of
        vortices in the atomist cosmology was a remarkable insight/lucky guess since vortices are important ingredients in star formation and galaxy formation.

        In fact, vortices are everywhere---see the figure below (local link / general link: leonardo_da_vinci_deluge_creation.html).

        The idea of the
        celestial sphere as the inner surface of membrane swirled by a vortex is easy to appreciate when you think about how the celestial sphere rotates around the Earth.

        The animation in the figure below (local link / general link: sky_swirl_polaris_animation.html) dynamically illustrates this rotation.

    8. The Spherical Earth Theory:

      We now move westward to southern Italy (which was part of Ancient Greece) to where lived Parmenides (early 5th century BCE).

      For an example of a tourist attraction of western Ancient Greece, see the figure (local link / general link: hellenic_theatre_segesta.html).

      Parmenides is probably the first person in recorded history to propose the spherical Earth theory (see, e.g., Fu-41,56). The figure below (local link / general link: parmenides_earth.html) discusses his proposal and his reasons for it.

      Besides philosophical reasons,
      Parmenides may have had 3 empirical reasons for proposing a spherical Earth that were known to later writers. These empirical reasons for the spherical Earth theory were:

      1. Astronomical phenomena shift as you move north and south consistently with the spherical Earth theory. This argument was presented by Aristotle (384--322 BCE) without claiming originality (see Wikipedia: Spherical Earth: Classical Greece).

        For example, as you go farther north in the Northern Hemisphere, there are more circumpolar stars.

      2. The shadow (umbra) of the Earth on the Moon is round.

        This is true whatever the orientation of the Sun and Moon are to the horizon and whatever path the Moon takes through the umbra. Unless the Earth were round, the roundness of its shadow would be hard to arrange. (By the way, you had to believe that lunar eclipses were caused by the Earth's shadow for this idea to be valid.)

        This argument was presented by Aristotle (384--322 BCE) without claiming originality (see Wikipedia: Spherical Earth: Classical Greece).

      3. Objects seen moving out to sea sink below the horizon. For example, seen at 10 km, the bottom 10 m of ship is below the horizon. I think you have to have pretty sharp eyes and excellent conditions to notice this effect. See the discussion of the distancce to the horizon, see the figure below (local link / general link: horizon_types_formula.html).

        The sinking-below-the-horizon argument was presented by Strabo (64/63 BCE--c.24 CE) without claiming originality (see Wikipedia: Spherical Earth: Roman Empire).

      Assuming the spherical Earth theory and that the Sun is very distant from the Earth, it is possible using measurements of shadow lengths at different latitutes and a bit of geometry to find the circumference and radius of the Earth. This was done by Eratosthenes (c.276--c.195 BCE). See the figure below (local link / general link: eratosthenes.html).

      spherical Earth theory was a tremendous advance in Greek astronomy and in human knowledge.

      With the spherical Earth theory progress was possible in cosmology.

      The nature of the Earth would NOT be considered part of modern cosmology.

      It's much too small.

      But historically, the Earth, Moon, Sun, and the planets of the Solar System were key elements of the cosmos as it was understood. The fixed stars was soon thought to be larger, but NOT much larger. Nothing was known galaxies at all---except that Milky Way was a dim white band on the night sky.

      It is also necessary to point out that modern cosmology would NOT have been possible without having solved the "Solar-System cosmology" (planet theory) of the Ancients---which they never did solve.

    9. The Distance Problem:

      The Ancients had a major problem in "Solar-System cosmology" (AKA planet theory) which had been around since forever and would only start to be solved in the 17th century.

      The distance problem. See the figure below (local link / general link: distance_problem.html).

      In the subsections below and the next two sections (i.e., sections Aristotle and Mathematical Ancient Greek Astronomy) we will see how far the ancient Greek astronomers got in "Solar-System cosmology" without a solution to the distance problem.

    10. The Philolaic System:

      In the 5th century BCE, the first planetary model of the Solar System that we know of appeared.

      This is the model of the Pythagorean Philolaus (c.470--c.385 BCE). See Philolaus (c.470--c.385 BCE) and Pythagoras (c.570--c.495 BCE) in the figure below (local link / general link: pythagoras.html).

      We call the model of
      Philolaus the Philolaic system.

      The Philolaic system is illustrated in the figure below (local link / general link: philolaus_cosmos.html).

      Philolaic system was remembered in later Classical Antiquity and later ages, but was NOT influential.

      After the Copernican heliocentric solar system was introduced in 1543, some people referred to it as the Pythagorean system (meaning the Philolaic system)??? because they vaguely thought of the Copernican system as revival of the Pythagorean Philolaic system---which was absolutely NOT the case.

    11. Eudoxon Models:

      From about 4th century BCE, most astronomers in Classical Antiquity, the Islamic Golden Age (c.9th--13th centuries), and Medieval Europe thought in terms of a finite universe enclosed by a celestial sphere of the stars thought of as a real surface with surrounding an unmoving spherical Earth at the center.

      They were thinking of a purely GEOCENTRIC, FINITE COSMOS (with the Earth at rest).

      They were following Aristotle (384--322 BCE) in this regard---we get to him in the section Aristotle.

      The ancient Greek astronomers did try to qualitatively and quantitatively understand the GEOCENTRIC, FINITE COSMOS.

      This work began with Eudoxus of Cnidus (410 or 408--355 or 347 BCE).

      The figure below shows a simplified version of the Eudoxon model for explaining the motion of the Sun around the Earth and expands on Eudoxon models in general.

  11. Aristotle: Reading Only

  12. Now we come to Aristotle (384--322 BCE)---who is illustrated in the figure below (local link / general link: aristotle.html).

    1. Aristotle: The Philosopher:

      Aristotle (384--322 BCE) is, of course, a famous Greek philosopher---in fact, the Greek philosopher par excellence to many---and for long ages, the Philosopher.


      Aristotelianism (i.e., Aristotelian philosophy) seemed for two millennia up to circa 1600 in western Eurasia to offer a complete system---to those who had ever heard of it---though of course, NOT all of these accepted everything or anything. It seemed to many to be all reason could tell you. It had a long vogue.

      In his actual lifetime among other things, Aristotle established a school, the Lyceum in Athens, in order propagate the liberal arts (as we would call them), natural philosophy, and philosophy in general.

      But NOT in the Parthenon on the Acropolis of Athens. See figure below (local link / general link: acropolis.html).

    2. Aristotelian Cosmology Summarized:

      Aristotle also contributed to Greek astronomy by theorizing Aristotelian cosmology which we summarize in the figure below (local link / general link: aristotle_cosmology_summarized.html).

      We expand on the summary in the subsections below.

    3. Why a Spherical Earth?

      As discussed in the above subsection The Spherical Earth Theory, the ancient Greeks had valid reasons for believing the spherical Earth theory by Aristotle's (384--322 BCE) time. Aristotle summarized most of the valid reasons for believing it as mentioned in the subsection The Spherical Earth Theory.

    4. Why Earth at the Center?

      It seemed obvious that the Earth was at rest and the Heavens revolved around it.

      Also things fell down to the Earth, whereas in the Heavens things moved in circles it seemed.

      Clearly the Earth was a special place and could reasonably identified as the center.

      Aristotelian cosmology like most ancient cosmologies is geocentric.

    5. Why Earth at Rest?

      In a sense, it would make the universe more rational if the Earth rotated daily on an Earth axis. Then the universe would NOT have to race around the Earth at colossal velocities.

      Aristotle's contemporaries Hicetas c.400--c.335 BCE and Heraclides Ponticus (c.390--c.310 BCE), in fact, suggested that the Earth rotated daily on its axis as an explanation of the diurnal rotation of the celestial sphere.

      This suggestion was NOT accepted by almost everyone.

      Aristotle (and other ancient Greeks) argued that the Earth had to be at rest since otherwise we would be spun off or blown off by terrific winds. In any case, we would feel the motion. See the figure below for feeling it.

      In modern physics, we understand why we do NOT notice the tremendous angular velocity of the Earth.

      The Earth's surface is APPROXIMATELY an inertial frame for most purposes.

      Recall that relative to inertial frames, Newton's laws of motion apply directly: e.g., in a smoothly moving unaccelerated train or plane.

      There are no inertial forces (AKA fictitious forces) unless you accelerate: speed up, slow down, or turn.

      Now the Earth's surface is slightly accelerating since the Earth rotates on its axis and has other smaller accelerations in space too, but these accelerations are below human perception, and thus so are the accompanying inertial forces.

      Also the motion of the surface and everything on it is smooth. There are no jolts except for the occasional earthquake.

      So we on the surface of the Earth sense NO acceleration and almost everyone up to circa 1600 thought that that meant NO motion.

      In defense of a non-moving Earth, Aristotle did note that there was NO observable stellar parallax---see the figure below for an explication of Aristotle's argument and why it turned out to be wrong.

    6. The Eudoxon Planetary Models of Aristotle:

      Aristotle's main new development in cosmology was just to specify a complete set of Eudoxon models for all the known Solar System bodies.

      Aristotelian cosmology is explicated in the figure below (local link / general link: aristotle_cosmos.html).

      The whole
      Aristotelian cosmological system in simplified from with most of the celestial spheres omitted is shown below in a simplified Renaissance Europe figure.

    7. Uniform Circular Motion:

      Uniform circular motion in Aristotelian cosmology and in ancient Greek astronomy in general is explicated in the figure below (local link / general link: uniform_circular_motion_ancient.html).

    8. The Finite, Bounded Aristotelian Universe:

      According to Aristotle, beyond the celestial sphere of the stars was nothing---NOT even empty space---just nothing (e.g., Fu-137).

      The Aristotelian universe was a finite bounded sphere.

      But it was also eternal---unbounded in time.

      Aristotle had arguments for these conclusions---but we won't go into them---they were WRONG.

      The figure just below (local link / general link: aristotle_hoplite_spear.html) expands a bit on bounded the Aristotelian cosmos.

    9. Is Aristotelian Cosmology Any Good?

      Well the spherical Earth model is correct and Aristotelian cosmology does explain, incorrectly, but adequately relative to the Ancients why they did NOT observe stellar parallax.

      Otherwise, it is mostly wrong.

      But even as wrong, it could still give a correct description of the motions of the Solar System bodies. Qualitatively, it does although NOT very well I think???.

      Quantitatively, it is NOT a good description. You CANNOT produce accurate ephemerides from Aristotelian cosmology. I don't know that anyone ever tried to.

      Strict Aristotelians---those pesky varmits---rationalized that Aristotle had got it right as far as human understanding could reach.

      For Aristotle (384--322 BCE), the "supreme authority" see the figure below local link / general link: aristotle_supreme.html).

      On the other hand,
      Aristotelian cosmology provided a complete cosmology supported by some observations and some reasoning.

      Thus, in principle, Aristotelian cosmology is a useful hypothesis in that it provides the basis for refinement and counter-theories.

      It did, in fact, fulfill this role, but NOT very well.

      Nevertheless, for nearly 2000 years in western Eurasia, Aristotelian cosmology became a philosophical dogma to many intellectuals. For those people, it was just be accepted with only minor corrections.

      Why was this so?

      In later Classical Antiquity, Medieval Islamic society, Medieval Europe, and Renaissance Europe, Aristotle for many intellectuals---but NOT all---became the highest or even the SUPREME AUTHORITY in philosophy including natural philosophy.

      Aristotle seemed to offer to the intellectual or educated person a complete philosophy---except in the religious dimension. And, of course, there is a reason for this---he was a broad and deep thinker. And he did offer the aforementioned reasoning for Aristotelian cosmology. To us, NOT very compelling reasoning, but for nearly 2000 years in western Eurasia some people thought it was good enough.

      Also, it has to be said that the preeminence of Aristotle was partially just an accident of history. Once Aristotle was taken as the highest or even the SUPREME AUTHORITY, the conservativism of traditional societies tended to keep him being top dog.

        Traditional societies are often very conservative. Conventions, habits, beliefs, procedures just do NOT get questioned or changed very often.

      Particularly relevant to the history of astronomy is that Aristotelian physics and, as mentioned above, Aristotelian cosmology became philosophical dogmas.

      By being dogmas, they became impediments to advances in nature knowledge rather than theories that advance research.

  13. Mathematical Ancient Greek Astronomy

  14. Despite the emergence of Aristotelian cosmology as a philosophical dogma in the time after Aristotle (384--322 BCE), mathematical Greek astronomy did flourish that was only somewhat congruent with Aristotelian cosmology and other a priori natural philosophies.

    We will briefly discuss the most important ancient Greek mathematical astronomers in the subsections below and the most important one in section Ptolemy below.

    1. Eudoxus of Cnidus (410 or 408--355 or 347 BCE): We've already discussed him above in subsection Eudoxon Models.

      But to recapitulate, his Eudoxon models of compounded celestial spheres of the astronomical objects were the essence of Aristotelian cosmology and very qualitatively they could account for planetary motions including apparent retrograde motions.

    2. Aristarchos of Samos (c.310--c.230 BCE): He's a special case and we'll return to him in section Aristarchos.

    3. Apollonius of Perga (c.262--c.190 BCE) has a sort of ironic role in the history of science.

      As a mathematician, he was the greatest expert on ellipses until circa 1500 CE, but he did NOT use them for planetary orbits---if he did work planetary orbits which is NOT certain.

      We explicate in the figure below (local link / general link: ellipse_animation.html).

    4. Hipparchus (c.190--c.120 BCE) (see the figure below) is very important, but in many respects his work was incorporated into that of the next important mathematical Greek astronomer Ptolemy (c.100--c.170 CE), and so he doesn't need much individual discussion.

      Hipparchus' greatest discovery was the discovery of the axial precession (AKA precession of the equinoxes) (see Wikipedia: Hipparchus: Precession of the equinoxes).

    5. Ptolemy (c.100--c.170 CE) was the last of the great ancient Greek astronomers. He requires a fuller discussion which we give below in section Ptolemy.

  15. Ptolemy

  16. Ptolemy (c.100--c.170 CE), building on a long tradition of mathematical astronomy both in Babylonian astronomy and Greek astronomy, developed full epicycle models for the whole Solar System.

    1. Epicycle Models:

      With the epicycle models, Ptolemy could quantitatively predict the motions of the planets (including the Sun and Moon) and, in particular, explain their apparent retrograde motion which he, like all the almost all the Ancients, regarded as spatial retrograde motions.

      Although NOT a strict Aristotelian, Ptolemy basically followed Aristotelian physics and, in some respects, Aristotelian cosmology.

      Ptolemy did admit non-geocentric models were geometrically possible, but he thought that they were physically absurd:

      A simple epicycle model is shown and explicated in the figure below (local link / general link: epicycle.html).

      A model like this could be constructed for all the planets (including the Sun and Moon). Some extra complicating features were needed by Ptolemy to get good fits to the observations.

      animation in the figure below (local link / general link: helio_geo_epicycle_animation.html illustrates how apparent retrograde motion (i.e., westward motion of the planet on the sky) can be reproduced by an epicycle model.

    2. The Ptolemaic System:

      Ptolemy presented his complete epicycle model for the geocentric solar system model in his book the Almagest as we call it. The Almagest is a triumph of ancient mathematical astronomy and the greatest and last monument of ancient Greek astronomy.

      We call this complete epicycle model the Ptolemaic system.

      The full Ptolemaic system is illustrated in a cartoon in the figure below (local link / general link: ptolemy_system.html).

    3. The Deficiencies of the Ptolemaic System:

      The Ptolemaic system has deficiencies:

      1. The Ptolemaic System Is Wrong:

        Obviously, the Ptolemaic system it is wrong as we know today. So it could only be a step in the cycle of the scientific method. This deficiency is one that can only be recognized as a fact after more cycling through the scientific method. However, the fact, that predictions of Ptolemaic system were NOT perfect suggested in times after Ptolemy that the Ptolemaic system was NOT perfect.

        Although until Nicolaus Copernicus (1473--1543), a radical change away from the Ptolemaic system as a calculating tool was NOT suggested.

      2. The Ptolemaic System Is Not Consistent with Aristotelian Cosmology:

        The Ptolemaic system is NOT consistent with Aristotelian cosmology---which has NO epicycles.

        In fact, the epicycle motions CANNOT be reproduced by compounded celestial spheres of Aristotelian cosmology. A key point is that epicycles require Earth-planet distances to vary and this is NOT allowed by compounded celestial spheres.

        Ptolemy in another book, Planetary Hypotheses (see the figure below (local link / general link: ptolemaic_physical_model.html) attempted a compromise with Aristotelian cosmology.

        But this compromise was NEVER accepted by strict Aristotelians. In their view, the Ptolemaic system was just a calculating device that saved the phenomena (and they were right) and Aristotelian cosmology was right insofar as human reason could go (and they were wrong).

        The lack of consistency between the Ptolemaic system and Aristotelian cosmology seems unimportant to us since both theories are wrong.

        But this presentism. To the proponents of the two theories, it was a vital issue.

        It is possible that many astronomers and philosophers through later Classical Antiquity and the Middle Ages in the Mideast and Europe had no definite opinion on the respective validity of the Ptolemaic system and Aristotelian cosmology.

        They may have sat on the fence.

        Strict Aristotelians didn't sit on the fence.

        See the figure below (local link / general link: avicenna.html) of a Medieval Aristotelian.

      3. The Structure of the Solar System is Not Determined:

        The structure of the Solar System is NOT determined: i.e., the order and relative distances to the Solar System are NOT integral parts of the Ptolemaic system. It is NOT a coherent model of the Solar System.

        You could use the Ptolemaic system for astronomical predictions and calculating ephemerides without specifying order and relative distances.

        This is true for any geocentric epicycle model unless one makes extra hypotheses.

        In the Almagest, Ptolemy adopted standard ancient Greek astronomy ordering (going outward Moon, Mercury, Venus, Sun, Mars, Jupiter, Saturn, celestial sphere of the stars) based probably on the argument we gave in the figure above (local link / general link: ptolemy_system.html).

        Ptolemy did, in fact, make extra hypotheses in order to determine the distances to the astro-bodies in his book Planetary Hypotheses: see the explication in the figure below (local link / general link: ptolemaic_physical_model.html).

        It is a credit to Ptolemy's scientific ambition that he did write Planetary Hypotheses, but it does NOT seem to have led to any further research in and of itself in later astronomy history and, of course, the hypotheses in it are WRONG.

      4. Ptolemy's Extra Tricks:

        Ptolemy actually needed more tricks than in the ideal epicycle model in order to fit the observations well: i.e., to save the phenomena.

        One of these tricks was that he made Earth off-center making the circular orbits eccentric.

        So his models weren't exactly geocentric. This was a violation of a key axiom of Aristotelian physics and Aristotelian cosmology

        Strict Aristotelians objected to this.

        And Ptolemy would have to admit an inconsistency in his own thinking since he was fairly Aristotelian himself---NOT that he ever did admit it in the historical record.

        Another trick was the equant.

      5. The Equant:

        Ptolemy most scandalous trick was the equant---it was the crime of Ptolemy. For equant and the crime, see the figure below (local link / general link: ptolemy_epicycle_equant.html).

        Plato (428/427--348/347 BCE) and Aristotle had proclaimed that uniform circular motions were all that could be allowed for elementary astronomical motions.

        This was philosophical/physical dogma that conformed to the supposed perfection of circles and allowed one to avoid head-on confrontations with non-constant speeds.

        Complicated motions were constructed by compounding uniform circular motions with Aristotle's celestial spheres or by epicycle models.

        Ptolemy agreed in principle, with the dogma of uniform circular motion, but violated the dogma by making deferent angular velocities constant around an equant which was displaced from the center of the deferent on the opposite side from the Earth's displaced-from-the-center position.

        To modern science, the introduction of the equant is an unimportant issue, but to later astronomers working with the Ptolemaic system, it was a serious defect that implied that the Ptolemaic system was NOT completely realistic since it violated a philosophical/physical dogma that was assumed to be Plato-given truth.

      6. The Necessity of Updating the Parameters:

        Since Ptolemy's models are imperfect and the observations setting their parameters (i.e., controlling variables) are imperfect, the predictions of the models will deviate from observations and those deviations will increase with time.

        As the centuries rolled by after Ptolemy, the parameters had to be updated, but the updates were often pretty imperfect too.

        Of course, modern models of Solar System motions suffer the same problem. However, the size of the deviations for modern models is much, much smaller.

      7. The Uniquenss Problem:

        Finally and most importantly, the Ptolemaic system was NOT a unique fit to the observations with epicycle models.

        By varying the size of the deferent and epicycles and adding epicycles on epicycles, varying the orbital speeds, and fooling around with the equant, you can create endless models that give the same predictions to within about the same accuracy as those of the Ptolemaic system.

        There was no way to tell which epicycle model was right.

        In fact, none of them are as we know now.

        If the Ancients had been able to measure Solar System distances beyond the Moon, they would have known this.

        But they couldn't have measured such distances.

        Ptolemy was such a clever model builder that he must have at least suspected the non-uniqueness problem, but he doesn't discuss it.

        He probably hoped that a sufficiently accurate epicycle model would approach the unique true cosmological model and that his Ptolemaic system did approach the unique true cosmological model.

        Or perhaps, he indulged in wishful thinking about how good the Ptolemaic system was.

        For 13 centuries after Ptolemy, astronomers working in the traditions of Indian astronomy, Medieval Islamic astronomy, Medieval European astronomy, and Renaissance astronomy would try to develop epicycle models that improved on the Ptolemaic system.

        They found epicycle models that were as accurate, but NOT really more accurate and they couldn't tell which was right.

        Epicycle models are, in fact, mathematical decompositions of the Solar System motions---non-unique ones.

          Question: What is 7 really?

          1. 2 + 5.
          2. 3 + 4.
          3. 7 doesn't have a unique sum structure.

          Answer 3 is right.

          Of course, unlike 7, the Solar System really does have unique structure.

          Question: In order to break the deadlock of epicycle models and discover the true structure of the Solar System, you had to have:

          1. knowledge of astronomical distances, at least relative to the astronomical unit.
          2. the heliocentric idea of the Solar System.
          3. both of the above.
          4. either of the above.

          The rightest answer is 4. The first answer leads immediately to the second and, in fact as we will show below in subsection Heliocentrism, having the second answer leads immediately to the first.

    4. After Ptolemy:

      After Ptolemy (c.100--c.170 CE) in the 2nd century CE, the great age of Greek astronomy was over.

      There were NO more great advances.

      But there were a few Keepers of the Flame---i.e., the tradition/techniques of Greek astronomy.

      Theon of Alexandria (c.335--c.405 CE), possibly in collaboration with his daughter Hypatia (c.360--415 CE) (see the imaginative portrait in the figure below: local link / general link: hypatia.html), wrote commentaries and/or edited the works of Ptolemy.

      But after that there is NOT much more to say.

      But we can go backward a bit to discuss Aristarchos of Samos (c.310--c.230 BCE) in section Aristarchos.

  17. Aristarchos

  18. Did anyone think of heliocentrism before Copernicus?

    Yes. Aristarchos of Samos (c.310--c.230 BCE) about 4 centuries before Ptolemy (c.100--c.170 CE). See the figure below (local link / general link: aristarchos.html).

    It's reasonable to guess, that Aristarchos was led to heliocentrism by the same reasons that led Copernicus.

    We'll discuss those reasons below in the section Nicolaus Copernicus (1473--1543) and Heliocentrism.

  19. The Middle Ages: Ptolemy to Copernicus: 13 Centuries of Wheel Spinning: Reading Only

  20. My title is facetious, but it is still a half-truth.

    mathematical astronomers of the Middle Ages in the traditions of Indian astronomy, Medieval Islamic astronomy, Medieval European astronomy, Renaissance astronomy continued to fiddle around with geocentric epicycle models.

    They didn't really improve them.

    To see where the Medieval mathematical astronomers were, see the map of western Eurasia circa 1190 in the figure below (local link / general link: map_western_eurasia_1190.html).

    Medieval mathematical astronomers couldn't improve epicycle models since as discussed above in subsection The Deficiencies of the Ptolemaic System, the epicycle models were wrong and just mathematical decompositions of the celestial motions.

    But because epicycle models did work as calculating devices, the Medieval astronomers working with them were endlessly tantalized by them and the hope of improving them. A hopeless hope.

    There was a stall in the cycle of the scientific method in cosmological theory (i.e., Solar System models).

    But if the Medieval astronomers were stuck in a theoretical dead end in Solar System models, they made progress in other areas as we discuss below in subsection Medieval Progress in Astronomy.

    1. Medieval Progress in Astronomy:

      The Medieval astronomers did make some new observations---some of which were modest lasting contributions to astronomy.

      In Medieval Islamic society, a tradition of building great observatories was started that alas died away. Just the way things worked out, not the way they had to work out.

      The observations from those observatories seem to have little lasting impact. However, probably the progress in astronomical instrumentation made in the observatories did having a lasting impact when communicated in some way to Medieval astronomers in Europe. For an example of astronomical instrumentation, see the Fakhri mural sextant at the Samarkand Observatory in the figure below (local link / general link: samarkand_observatory.html).

      The mathematical astronomers did, however, improve MATHEMATICAL TECHNIQUES---a lasting contribution.

      The trigonometric functions were developed in the Medieval Indian society and the Medieval Islamic society (see Wikipedia: Trigonometry: History). Of course, the ancient Greek astronomers could do trigonometry, but their methods were klutzy.

      Also Arabic numerals were introduced (see Wikipedia: History of the Hindu-Arabic numeral system) and these eventually replaced the clumsy numeral systems of the past: e.g., cuneiform numerals, Greek numerals, and Roman numerals.

      With Arabic numerals beginning to dominate in western Eurasia, the decimal system (i.e. base-10 system) also began to dominate there.

      A duodecimal system (i.e., base-12 system) might have been handier, but since our hands have 10 fingers . . .

      Decimal fractions also started to come into use. They seem to have been developed independently several times (see Wkipidia: Decimal system: History of decimal fractions). An important treatise on them was written by Jamshid Al-Kashi (c.1380--1429) who worked at Samarkand Observatory (see John North 1994, The Norton History of Astronomy and Cosmology, p. 1200). In Europe, just a bit later and probably independently Giovanni Bianchini (1410--c.1469) used decimal fractions and may have been the first to use the decimal point (see Wikipedia: Giovanni Bianchini (1410--c.1469)). However, his decimal point work was not well known though it seems to have been passed on to some later Renaissance astronomers and early modern astronomers. Simon Stevin (1548/9--1620) later greatly promoted the use of decimal fractions in the Europe (see Wikipedia: Simon Stevin: Decimal fractions). Nicolaus Copernicus (1473--1543) it seems he did NOT use decimal fractions (see De revolvtionibvs orbium coelestium (1543, p. 110 facsimile of On the Revolutions of the Heavenly Spheres (1543)).

    2. Medieval Astronomers:

      There are many Medieval astronomers, but except to very interested persons, their names are mostly unknown and their accomplishments tedious to tell of.

      But there are three who are moderately well known---for reasons other than astronomy---the Persian Al Khwarizmi (c.780--c.850), the also Persian Omar Khayyam (1048--1123), and the Englishperson Geoffrey Chaucer (c.1343--1400) (see also Writers: Geoffrey Chaucer (c.1343--1400)).

      1. Al Khwarizmi (c.780--c.850):

        The Medieval Islamic mathematician Al Khwarizmi (c.780--c.850) is explicated a bit in the figure below (local link / general link: al_khwarizmi.html).

      2. Omar Khayyam (1048--1123):

        For Omar Khayyam (1048--1123), see the two figures below (local link / general link: omar_awakening.html; local link / general link: omar_reading.html).

      3. Geoffrey Chaucer (c.1343--1400):

        Geoffrey Chaucer (c.1343--1400) can only be considered an amateur adept in astronomy, but he did write A Treatise on the Astrolabe (1391). For more on Chaucer, see the two figures below (local link / general link: chaucer_astrolabe.html; local link / general link: chaucer_astrolabe_like.html).

        Chaucer certainly was a poet. See the figure below (local link / general link: chaucer_17th_century.html).

        The figure above (
        local link / general link: chaucer_17th_century.html) alludes to the Chauntecleer story which is The Nun's Priest's Tale from The Canterbury Tales (1387--1400). For The Canterbury Tales, see the figure below (local link / general link: chaucer_canterbury_tales_mural.html).

        The company of
        pilgrims of The Canterbury Tales (1387--1400) assembles at The Tabard Inn. See the figure below (local link / general link: chaucer_tabard_inn.html).

        The arrival at
        Canterbury (see the figure below: local link / general link: canterbury.html) was the intended end of The Canterbury Tales---the end of pilgrimage.

  21. Nicolaus Copernicus (1473--1543) and Heliocentrism

  22. The situation in astronomy in circa year 1500 in Europe, 13 centuries after Ptolemy (c.100--c.170 CE) and 18 centuries after Aristotle (384--322 BCE) was this:

    1. On one hand, you had Aristotelian cosmology that was a philosophical dogma, but that didn't really account for the APPEARANCES or, in ancient philosophical jargon, did NOT save the phenomena. But Aristotle (384--322 BCE) did offer the reasons for Aristotelian cosmology. To us, NOT very compelling reasons, but for nearly 2000 years in western Eurasia many people interested in natural philosophy thought Aristotelian cosmology was good enough.

      Strict Aristotelians probably believed Aristotelian cosmology was the best human understanding could do.

    2. On the other hand, you had the mathematical Ptolemaic system that did save the phenomena (to the standards of ancient accuracy anyway), but was vastly non-unique, and so could hardly be accepted as real as Aristotelians were probably quick to point out when explaining why the "rational" Aristotelian cosmology was to be preferred.

      Ptolemy, himself, certainly must have hoped that his extension of Ptolemaic system in the semi-Aristotelian Ptolemaic physical model was physically realistic.

      But Ptolemy was such a clever builder of epicycle models that he should have known that neither the Ptolemaic system nor the Ptolemaic physical model was a uniquely good fit to the observations even if their basic assumptions were correct in his view.

    The general opinion among the natural philosophers of the 15th and 16th centuries in European context may have been Aristotelian cosmology was essentially right, but that reality was too complex to make it mathematically predictive.

    And the Ptolemaic system was just a calculating tool.

    So the natural philosophers had a compromise between Aristotelian cosmology and the Ptolemaic system.

    Of course, there are no opinion polls from the past, and so we must glean our knowledge of what the natural philosophers were thinking largely from what typical ones said.

    But at least one person did NOT accept the compromise between
    Aristotelian cosmology (philosophical dogma) and the Ptolemaic system (calculational tool).

    "What is truth?" as Copernicus may have asked.

    1. Nicolaus Copernicus (1473--1543):

      Nicolaus Copernicus (1473--1543) was German-Polish, physician, economist, and Church official and lawyer (of the Catholic Church). For more on Copernicus, see the figure below (local link / general link: copernicus/copernicus_portrait.html).

      There has always been some question as to whether
      Copernicus considered himself German or Polish.

      Probably both (see Wikipedia: Nicolaus Copernicus: Nationality).

      He certainly spoke German and had a German cultural upbringing, but he probably spoke Polish too, and he was born in the Kingdom of Poland. Of course, he also knew and wrote in Latin as most scholars of his time did.

      As a student in Italy, he enrolled as a German, but that may have just been to obtain certain privileges or conveniences open to being a German student (see Wikipedia: Nicolaus Copernicus: Languages).

      Copernicus studied in Italy for most of the decade 1496--1506.

      He was part of the time in Padua where he was at the University of Padua. Copernicus would have known---one assumes---the church of Sant'Antonio shown in the figure below.

        Question: Why did the building in the above figure use arches instead of lintels (those things on the tops of doors and windows and trilithons)?

        1. Arches were decorative.
        2. Arches can be made stronger since there is more use of the pressure resistance of building material.

        Maybe both. The small arches look decorative, but the big ones in the false doors look structurally necessary.

        Using arches both for structural support and decoration was one of the best ideas of the Romans.

        In the modern times, we often do NOT use arches in common buildings for structural support.

        It's usually cheaper just to build a stronger lintel. We just stick in another steel I-beam girder. But when we really need maximum strength, we use arches too: often for, e.g., bridges and trestles.

        Note our answer, mutatis mutandis, is also why planets and stars are ROUND. Their self-gravity overcomes pulls them into a round shape. Only compression resistance of their materials sustains them against collapse.

    2. Heliocentrism:

      From the early years of the 16th century or maybe even earlier, Copernicus had become convinced that heliocentrism would solve the chief problem of astronomy: i.e., the fact that the structure of the cosmos was NOT really known.

      Heliocentrism is the theory that the Sun at the center of the Solar System or, for Copernicus and some of his early followers, the center of the cosmos.

      Copernicus published his detailed theory in his book On the Revolutions of the Heavenly Spheres in 1543: the actual Latin title is De Revolutionibus Orbium Coelestium.

      ONE DIAGRAM shown in the figure below (local link / general link: venus_elongation.html) shows you why Copernicus turned to heliocentrism---or at least why he should have.

      The procedure shown in the figure above (
      local link / general link: venus_elongation.html) works just for inferior planets. The orbital radii of the superior planets can be found using a general procedure assuming the heliocentric solar system model.

      The general procedure is actually pretty easy, but it is a bit more than we want do here. See the General Procedure for Orbital Radius Determination for the general procedure and its derivation.

      The general procedure was used by Copernicus (probably with a much klutzier formulation) to deduce all the planet orbital radii in the heliocentric solar system model.

      Since heliocentrism gave the relative distances, the structure of the Solar System was revealed to Copernicus:

      Copernicus' own not-to-scale diagram of the Copernican system (i.e., Copernicus' full model for the Solar System) is shown in the figure below (local link / general link: copernican_system.html).

      Now the absolute distances were NOT known at all accurately since the
      astronomical unit was NOT known accurately in terms of the Earth's size.

      Only in the 17th century would the astronomical unit begin to be measured accurately (Wikipedia: Astronomical unit: History). Copernicus used the ancient Greek value for the astronomical unit which was about 23 times too small (see John North 1994, The Norton History of Astronomy and Cosmology, p. 294).

      But Copernicus had found the "chief thing", NOT by new observations, but just by having the right theory.

      Of course, heliocentrism could have turned out to be wrong.

      But the modern way of judging theories which CANNOT be tested yet by observation is by how many important results can be deduced from them and how fruitful they are in leading to new developments.

      In fact, even if a theory turns out to be wrong, it is still a GREAT THEORY if it is fruitful in furthering development---stimulating more research, suggesting better theories, be useful in teaching, just a darn brilliant idea, etc.

      So even it had been wrong, heliocentrism was great theory because one can deduce from it important results that can be tested by observations that were in principle possible if NOT practicable yet in Copernicus' time.

      Based on the deduced structure of the Solar System and other information and arguments, Copernicus became convinced that heliocentrism-predicted structure was right.

      And we can agree---without going into all the details---that he was right to think it at least very probably right.

      Copernicus' heliocentrism---or as one can call it in the century or so after Copernicus, Copernicanism---was recognized by as a great theory by those astronomers who we see retrospectively as most modern and progressive: the most important of these being Galileo Galilei (1564--1642) and Johannes Kepler (1571--1630) whom we cover below in, respectively, sections Johannes Kepler (1571--1630) and Galileo Galilei (1564--1642).

    3. The Copernican System:

      The Copernican system (i.e., Copernicus' full model for the Solar System) in its details was in many ways entirely conventional for Copernicus' time.

      In order to make a predictive model for the construction of ephemerides, etc., Copernicus had to use epicycles, uniform circular motion, and other ancient devices. He may believed that epicycles and uniform circular motion, had some sort of reality as fundamental elements of motion just like the ancient Greek astronomers, but it's hard to know.

      He also still used the celestial spheres of Aristotelian cosmology in some way.????

      Why did Copernicus want a predictive model anyway?

      Among other things, he had to make the Copernican system a predictive model or his contemporaries would NOT necessarily have considered it seriously. Probably, he himself believed it had to be predictive to have any chance of being real.

      In fact, except for the transposition of the Earth and Sun, Copernicus' epicycle models are much like Ptolemy's in mathematical construction. He was NOT an important innovator in the techniques of mathematical astronomy.

      Copernicus did used relatively modern mathematical innovations such as Arabic numerals which made calculations a lot easier than using Roman numerals. However, it seems he did NOT use decimal fractions (see De revolvtionibvs orbium coelestium (1543, p. 110 facsimile of On the Revolutions of the Heavenly Spheres (1543)). However, te does NOT seem to have made any purely mathematical innovations himself.

      In mathematical astronomy per se, a couple of noteworthy innovations used by Copernicus are given below:

      1. Copernicus did NOT use Ptolemy's equant which Copernicus thought was a great improvement. The principle of uniform circular motion was NOT violated in the Copernican system.

        Modern scientists tend to see the equant and the principle of uniform circular motion as dead isssues. But this is presentism. They were important issues to astronomers from Ptolemy (c.100--c.170 CE) to Johannes Kepler (1571--1630).

        Also it is still a living issue that scientific theories be self-consistent. The equant and the principle of uniform circular motion were NOT consistent with each other.

        So concern with their inconsistency is a mark of true scientific thinking.

        See the animation Ptolemy's (c.100--c.170 CE) epicycle model (with equant) for Jupiter in the figure below (local link / general link: ptolemy_epicycle_equant_animation.html).

      2. Copernicus did make use of the Tusi couple which was an innovation of the 13th century. See figure below (local link / general link: tusi_couple.html).

    4. Apparent Retrograde Motion:

      One major improvement (by modern as well as ancient standards) of Copernicus over Ptolemy was a natural explanation of apparent retrograde motion.

      That explanation is given in the figure below (local link / general link: apparent_retrograde_motion.html).

      In the
      Ptolemaic system apparent retrograde motion is modeled using epicycles.

      But the epicycle motion of astro-bodies had always defied simple phyiscal explanation, except for it is just so.

      Of course, Copernican system uses epicycle models, but in a heliocentric solar system.

      So Copernicus still had the physical inexplicableness of epicycles, but at least he had gotten rid of one reason for needing them. Johannes Kepler (1571--1630) would get rid of all epicycles and all physical reasons for them.

      The animation in the figure below (local link / general link: helio_geo_epicycle_animation.html) compares apparent retrograde motion as explained in a heliocentric solar system model and in a geocentric epicycle model.

    5. The Implications of Heliocentrism:

      Although Copernicus' epicycle models and mathematical techniques were NOT radical, the implications for physics of heliocentrism were completely radical.

      Heliocentrism totally upset physics as it was then understood: i.e., Aristotelian physics which we won't bother to detail here---but a key point of Aristotelian physics is that the Earth had to be at rest or else we would feel its motion and everything would need obvious forces to keep moving with the Earth.

      But heliocentrism demanded that the Earth orbited the Sun every year AND rotated on its axis every day. Somehow every bit of the surface of the Earth had its own frame of rest.

      Our modern understanding of relative motion and inertial frames and non-inertial frames allows us to understand this---but that understanding was NOT possible in 16th century.

      Also heliocentrism made the Earth a planet.

      If the Earth was a planet, the other planets therefore could be like the Earth---and therefore NOT eternally unchanging as posited by Aristotelian cosmology.

      Also again since stellar parallax was NOT observed, the celestial sphere of the stars (which Copernicus did retain) had to be extremely remote. The universe had to be big by comparison to what people had thought when they thought in terms of Aristotelian cosmology. Note that in the Copernican system, the celestial sphere of the stars is at rest and does NOT rotate once per day on the celestial axis at a fantastic angular velocity.

      Aristotelian physics and Aristotelian cosmology (with its unchanging Heavens and resting Earth) was totally wrong if Copernicus was right.

    6. Early Reactions to Copernicanism:

      There were some early reactions to Copernicanism up to circa 1600.

      In Europe, of course. No else in the world would hear or think much of it for one or more centuries.

      1. Popular: There was NOT much popular reaction. Copernicus' book was a treatise in mathematical astronomy---it was NOT a bestseller---but, hey, there were at least 601 copies printed in the 16th century (see Wikipedia: De revolutionibus orbium coelestium Census of copies).

        Actually, the first 10 chapters of Book I of On the Revolutions of the Heavenly Spheres (1543) are qualitative and readable. See Online text in English translation: Revolutions of the Heavenly Spheres (1543).

        Since their "betters" (i.e., the formal intellectual classes and the aristocrats) didn't believe or think much of Copernicanism, the "people" (everyone else) didn't bother much with it. See the "people" in the figure below (local link / general link: vincent_van_gogh_potato_eaters.html).

      2. The Astronomers: Their reaction seems paradoxical to us. Almost all rejected heliocentrism as absurd as physics or natural philosophy.

        But on the other hand, they esteemed Copernicus' book as a tour de force of mathematical astronomy: a proof that a modern could equal Ptolemy (c.100--c.170 CE). They were the ones who bought the 601 plus copies printed in the 16th century (see Wikipedia: De revolutionibus orbium coelestium Census of copies).

        The post-Copernicus Renaissance astronomers also hoped that Copernican system would be more accurate than the Ptolemaic system as a calculational device. For example, the Prutenic Tables (1551) of ephemerides were based on the Copernican system by mathematical astronomer Erasmus Reinhold (1511--1553) who did NOT accept it as physical reality. I think the Prutenic Tables (1551) were actually a bit more accurate than those based on the Ptolemaic system, but only a modern computer study shows this???. However, any improvement in accuracy was really pretty much accidental???.

      3. The Churches: Catholic and Protestant: The Bible in a few passages suggests that the Sun moves and the Earth is at rest. All those passages can be read most naturally as figurative or about relative motion as they are today. But the traditional reading before circa 1600 was literal and regarded motion as an absolute thing---probably because most everyone believed in the motion of the Sun and motionlessness of the Earth because that seemed obviously true (it still does in a way if you think about it)---and anyway Aristotle concurred.

        Copernicanism was potentially a heresy on both sides of the religious divide. See the figure above (local link / general link: copernicus_heretic.html).

        It could only be a very minor heresy---it's only about astronomy.

        Note that Copernicus' life spanned the early phases of the Reformation (c.1517--c.1648) and Counter-Reformation (c.1517--c.1648) and the beginning of the wars of religion in Europe and his hometown Frombork (German Frauenberg) was on the frontier between Catholic and Protestant regions in Poland. See the map in the figure below (local link / general link: map_europe_1560.html).

        So Copernicus was quite aware of the potential heresy problem of Copernicanism---he was a Catholic Church lawyer after all.

        Copernicus tried to defend his orthodoxy of his theory by dedicating his book to Pope Paul III (1468--1549, pope 1534--1549) and addressing his book only to astronomers, NOT to theologians or the general public.

        In fact, one of the reasons for delaying publication of his theory until he was near end of his life may have been to ensure he wouldn't be around to face awkward questions. We do NOT know this, but it's a reasonable hypothesis.

        It sometimes said that the heresy problem was NOT a concern of Copernicus because he never says anything about it. But yours truly's opinion is that he did NOT mention it because he really, really did NOT want to call anyone's attention to it.

        As it turned out, the immediate religious reaction was muted.

        On both Catholic and Protestant sides, there was some negative feeling, but a heresy in which no one believes doesn't excite a lot of official notice.

      4. The Copernicans: A very few people did accept Copernicanism before circa 1600 (the early adopters) probably mainly based on heliocentrism's ability to give the structure of the Solar System---but definite statements of their primary reasons for believing in Copernicanism are hard to locate---they said a lot of things.

        For some early Copernicans, see the figure below (local link / general link: copernicans_early.html).

        To explicate the early

        1. Nicolaus Copernicus (1473--1543), ex officio.

        2. Rheticus (1514--1574) who was an eager follower in of Copernicus in heliocentrism and who prodded Copernicus to publish the Copernican theory in On the Revolutions of the Heavenly Spheres (1543).

        3. Thomas Digges (1546--1595) in England who suggested that space was also infinite and full of stars in 1576.

          See the figure below (local link / general link: copernican_cosmos_digges.html) of Digges' illustration of his suggestion for the universe.

        4. Giordano Bruno (1548--1600) who is discussed in the figure below (local link / general link: giordano_bruno.html).

        5. Galileo (1564--1642) who we'll discuss in detail below in section Galileo Galilei (1564--1642).

        6. Johannes Kepler (1571--1630) who we'll discuss in detail below in section Johannes Kepler (1571--1630).

        7. Some other less notable early Copernicans, of course.

  23. Tycho Brahe (1546--1601)

  24. One important Renaissance astronomer who rejected Copernicanism was the Danish nobleman Tycho Brahe (1546--1601). A purely imaginative portrait is in the figure below (local link / general link: tycho_thor.html).

    Tycho is one of those people who history has decided to call by their first names---like Galileo (1564--1642), Napoleon (1769--1821), and Ann-Margret (1941--).

    Although Tycho rejected Copernicanism, his achievements greatly aided its advance from wild and crazy idea to the new paradigm of astronomy.

    Tycho's rejection seems to have been strongly based on the idea that the Earth could NOT move. This giant massive body just could NOT rotate on its Earth's axis once per day NOR revolve around in Sun once per year at fantastic speeds. The celestial bodies were somehow ethereal and could move at fantastic speeds.

    Tycho's early education in astronomy convinced him that new, high quality observations were necessary to modernization of this ancient science or to translate his own words the renovation of astronomy (translated roughly from instaurata astonomia: see Wikipedia: Tycho Brahe: Publications, correspondence and scientific disputes: Astronomiae Instauratae Progymnasmata (1588), transl. Preliminaries for the Renovated Astronomy).

    Tycho's great achievements in his renovation of astronomy can be discussed under 3 headings: 1) the aforementioned new observations of outstanding quality and quantity, 2) observations disproving key parts of Aristotelian cosmology, 3) the introduction of the Tychonic system.

    We need to note that Tycho was the most famous astronomer of his day, and so his achievements were noted by other Renaissance astronomers and to some degree by the intellectuals in general and the general public.

    1. New Observations:

      Tycho carried out a 20-year program of observational astronomy that achieved an accuracy never obtained before particularly for the planetary motions.

      Tycho used various divided circle devices: quadrants and the like. But it was all naked-eye astronomy. Tycho came just before the invention of the telescopes (see Wikipedia: History of the Telescope: The first known telescopes).

      His equipment (see the figure below) was NOT at all novel---in essentials, it had all existed for millennia. What was novel was his commitment to reducing observational errors.

      Tycho perceived that one of the problems of astronomy as practiced up to his day was that new observations were often as poor as the old ones.

      To RENOVATE ASTRONOMY you needed better observations, NOT just new ones. For Tycho at work on getting new better observations, see the figure below (local link / general link: tycho_wall_quadrant.html).

      The importance of Tycho's data---particularly for planetary motions---comes with its use in the Solar System models of Kepler which we'll come to below in the section Johannes Kepler (1571--1630).

    2. Observations Against Aristotelian Cosmology:

      These were two:

      1. In 1572, he observed a new star or, in Latin, stella nova---a transient star-like object that appeared and then disappeared over the time of a few months. We now recognize this new star as a supernova: a giant explosion of an old star at the end of its lifetime---an example supernova is shown in the figure below (local link / general link: sn_1987a.html).

        Tycho did NOT know that the new star was a supernova.

        But Tycho did prove that the new star was beyond the Moon. Thus he proved there was change in the Heavens, and thus that Aristotle was wrong.

        We now call this supernova SN 1572 or Tycho's supernova or, for short, Tycho. See Tycho's sky map for SN 1572 in the figure below (local link / general link: sn_1572_tycho_sky_map.html).

        For an
        animation of SN 1572, see Birth of the Tycho Brahe's 1572 supernova remnant | 0:45 in Supernova videos below (local link / general link: supernova_videos.html).


      2. In 1577, Tycho proved that the Great Comet of 1577 was also beyond the Moon. Aristotle had argued that comets were sublunary, and so didn't violate the immutability of the Heavens. See the figure below (local link / general link: great_comet_1577.html).

        Tycho also showed that the comet's orbit took it through the celestial spheres---those celestial spheres that carry the planets. He concluded the celestial spheres did NOT exist.

      Tycho's disproofs of Aristotelian cosmology were only verifiable by a few other astronomers, and so most of the scholarly world could and did ignore them.

      They were published, however, in books that were known to European astronomers.

      That Tycho's disproofs were NOT widely accepted, except by astronomers, is reasonable. There are many claims in science and other fields that are made and never verified. Often you have to wait until the issue matures.

      Aristotelian cosmology, however, was beginning to shake on its foundations.

    3. The Tychonic System:

      The last great achievement of Tycho's to mention is the introduction of the Tychonic system.

      The Tychonic system is the Copernican system turned on its head.

      The figure below (local link / general link: tychonic_system.html) explicates the Tychonic system.

    4. Tycho in Conclusion:

      Although Tycho rejected Copernicanism, his work undermined Aristotelian cosmology and the Ptolemaic system.

      Thus, he effectively advanced Copernicanism.

      The Tychonic system provided a only temporary refuge for some against the onslaught of rampant heliocentrism.

      Tycho's own protege Kepler---though personally loyal to Tycho---never wavered from the path of Copernicanism.

  25. Johannes Kepler (1571--1630)

  26. Kepler was Tycho's assistant and succeeded him as Imperial Mathematician to the Holy Roman Emperor, Rudolf II (1552--1612; reigned 1576--1612), in Prague. See Tycho and Kepler together again in the figure below (local link / general link: tycho_kepler_statue.html).

    Kepler, unlike Tycho, was a convinced Copernican from his college days at Tuebingen, graduated 1591:

    Using the correct theory and the best data every available, Kepler was able to find the true motions of the planets. Remember Copernicus still used epicycles and uniform circular motion.

    Kepler did NOT have the right physics although he tried to find it. But he did have one correct guiding physical principle: the distance from a planet to the Sun is the key variable in determining the shape of the orbits and the motions.

    So it is NOT true to say that Kepler's discoveries were mere empirical fits to the data.

    Kepler's discoveries did take a lot of calculations. See the figure below (local link / general link: kepler_work.html).

    1. Kepler's 3 Laws of Planetary Motion:

      Kepler's most important discoveries are his 3 laws of planetary motion:

      Kepler derived these laws semi-imperically by fits to Tycho's data. But only semi-imperically. He was guided by his theoretical heliocentrism and his conviction that the Earth-Sun distance as it varied in time were key factors as indeed they are.

      Isaac Newton (1643--1727) was later able to purely theoretically derive Kepler's 3 laws of planetary motion from Newtonian physics.

      The Kepler's 3 laws of planetary motion are:

      1. Kepler's 1st law: The planets orbit the Sun in ellipses. This as we now know is a consequence of the inverse-square law nature of gravity which is part of Newtonian physics.

        Kepler's 1st law is illustrated in the figure below (local link / general link: sun_planet.html).

      2. Kepler's 2nd law: A Sun-planet line sweeps out equal areas in equal times. The planets thus move faster at perihelion and slower at aphelion. The law follows from Newtonian physics---to be specific it is a consequence of the conservation of angular momentum in a system with a central force.

        Kepler's 2nd law is illustrated by the animation in the figure below (local link / general link: kepler_2nd_law.html).

        Kepler's 2nd law permitted Kepler and his followers to accurately calculate the motions of the planets. The calculations were tedious.

      3. Kepler's 3rd law: This law is explicated in the figure below (local link / general link: kepler_third_law.html).

      4. Kepler's 3 laws of planetary motion are summarized in the figure below (local link / general link: kepler_all_3_laws.html).

      Note Kepler's 3 laws of planetary motion dispense with the ancient devices of epicycles and uniform circular motion. Those ghosts from the Greeks were at last exorcized.

      Also, the solid celestial spheres of Aristotelian cosmology are mostly gone---but NOT quite. Oddly enough, Kepler did NOT make the mental leap to a large or infinite universe with stars spread throughout space. He retained the Aristotelian celestial sphere of the stars (see Wikipedia: Celestial spheres: Renaissance)---perhaps like The Astronomer in the figure below (local link / general link: vermeer_astronomer.html).

      We all live a bit in the past and in the future, but it was poignant to notice this tendency strongly marked in the pioneers of the Scientific Revolution.

      But even when
      Kepler was a child in 1576, recall that Thomas Digges (c.1546--1595) had moved on to a large universe full of stars (see local link / general link: copernican_cosmos_digges.html).

    2. Kepler's Modernized Heliocentrism:

      Kepler used his 3 laws and Tycho's data to create his own full model of the Solar System. The planets have elliptical orbits with the Sun at one focus of the elliptical orbits. The Sun is at the physical center though NOT at the exact geometric center of the elliptical orbits.

      Kepler's model is is a modernized heliocentric solar system model.

    3. Publication and Early Reception of Kepler's Discoveries:

      Kepler summarized his discoveries in the Epitome of Copernican Astronomy (1615--1621) and his tables for astronomical calculation in the Rudolphine Tables (1627) (named for his patron the Holy Roman Emperor Rudolf II (1552--1612, reigned 1576--1612)) based on Kepler's 3 laws of planetary motion and Tycho's data. The Rudolphine Tables allowed the calculation of the most accurate ephemerides ever achieved up to that time.

      Now Kepler's discoveries did NOT prove heliocentrism.

      Geometrically, his models are consistent with both the geocentric Tychonic system (a modernized Keplerized Tychonic system) and heliocentrism. You just had to make decision which point to take as the origin: Earth or Sun.

      But the Earth obeys the 3 laws just like a planet if you take it to be a planet.

      If you take the Earth to be center of a Tychonic system, then you have a double system with the Sun as secondary center. The physical explanation of the latter arrangement would have to be more elaborate than of the former. Nowadays, we'd call the latter arrangement an implausible ad hoc hypothesis.

      Why should the huge Sun (which was known to be much bigger than the Earth as Jupiter is much bigger than the Galilean moons) dominate all the planet motions, but then in turn be dominated by the tiny Earth? It didn't seem physically reasonable to Kepler and eventually to NO ONE.

      Recall, the Galilean moons strongly suggested the smaller astronomical objects orbit the larger astronomical objects.

      Kepler's discoveries with their rational interpretation from the perspective of heliocentrism and the accuracy/precision of the Rudolphine Tables did EVENTUALLY help to convince many people that heliocentrism was probably the right physical system even though the right physics had NOT yet been discovered. See the adjacent figure.

      Note the word "EVENTUALLY". Kepler's work in mathematical astronomy was inaccessible to many---particularly those steeped in Aristotelianism. Thus, his impact on the Copernican revolution in his lifetime was limited.

      Galileo's telescopic discoveries would have a much more dramatic and immediate impact as we will see below in subsection Galileo and the Telescope.

      Another statue of Kepler is shown in the figure below (local link / general link: kepler_statue_prophet.html).

    4. Kepler and Galileo:

      How did Kepler (1571--1630) and Galileo (1564--1642) interact?

      They were nearly exact contemporaries after all and they are considered the two most representative scientists of the Scientific Revolution of the 16th and 17th centuries.

      But they never met: Kepler never got south of the Alps and Galileo never north of them.

      They corresponded on two occasions, but never had a complete meeting of minds. To explicate:

      1. Galileo's Mind:

        Galileo never absorbed Kepler's prime work (i.e., Kepler's 3 laws of planetary motion) and he may never have read any of Kepler's important books which were all published before 1627 and all openly advocated heliocentrism. Galileo may have understood Kepler's 3 laws of planetary motion and the other important results of Kepler, but he never used them.


        We can only speculate.

        After 1616, when Copernicanism was effectively condemned as a heresy by the Catholic Church, it would have been impolitic for Galileo to have openly cited Kepler, who was an open Copernican and a Protestant.

        But even before 1616 and in private, Galileo made no use of Kepler. It's possible he distrusted Kepler's approach to science. Galileo was utterly unmystical: a true heir of Aristotle, the experimentalist (but NOT of dogmatic Aristotelians) and Archimedes (c.287--c.212 BCE) (the greatest Greek physicist). For example, Galileo had NO belief in astrology though he was required to teach it since, then as now, medical students needed astrology in order to diagnose and prescribe.

        Kepler, on the other hand, was a sort of mathematician mystic: an heir of Pythagoras (c.570--c.495 BCE) and Plato (428/427--348/347 BCE). He started out with a deep faith in astrology though he understood that contemporary practice was utterly corrupt. In later life, after failing to make any progress in developing a scientific astrology, he seems to have become a bit cynical about it and perhaps regarded it primarily as a funding source.

        We, with the ingenuity of posterity, can see that Kepler and Galileo were both working toward modern science, but along somewhat different paths. But that may NOT have been apparent to Galileo who may have thought Kepler a fantasist.

        It also has to be said that as mathematician, Galileo was NO innovator unlike Kepler who was one of the great mathematicians of the Scientific Revolution. Galileo may simply NOT have had the patience to assimilate Kepler's discoveries in mathematical astronomy.

      2. Kepler's Mind:

        As for Kepler's regard for Galileo: he highly valued Galileo's astronomical discoveries, but never fully understood Galileo's achievements in physics probably mainly because Galileo didn't get around to publishing most of them until after Kepler's death.

      See Galileo and Kepler's contrasting heroes in the figure below (local link / general link: raphael_plato_aristotle.html).

    5. The End of Kepler:

      Kepler---who was a German---died of natural causes in 1630 in the midst of the Thirty Years' War. See the two illustrative figures below (local link / general link: gallowglass.html; local link / general link: kepler_portrait.html).

    6. An Interesting Historical Tidbit:

      One often wonders if great contemporaries were even aware of each other.

      Two who were certainly mutually cognizant were Charles Darwin (1809--1882) and Abraham Lincoln (1809--1865)---but they probably didn't know they were born on the same day 1809 Feb12.

      But what of Kepler and William Shakespeare (1564--1616)?

      It's just barely possible that Shakespeare may have heard of Kepler, the famous Imperial Mathematician (i.e., essentially court astrologer) to the Holy Roman Emperor Rudolf II (1552--1612, reigned 1576--1612). But Shakespeare exhibits only very superficial knowledge of astronomy/astrology unlike Geoffrey Chaucer (c.1343--1400).

      On the other hand, Shakespeare's fame in his time was almost totally local to England, and so almost certainly Kepler never heard of him.

      But there is a connection: see the figure below (local link / general link: kepler_shakespeare.html).

  27. Galileo Galilei (1564--1642)

  28. Galileo was born a citizen of Florence and the son of Vincenzo Galilei (c.1520--1591), a well known musican, music theorist, and experimentalist with musical instruments.

    In fact, Galileo learnt a lot about science from dear old Dad---who wanted Galileo to become a doctor and earn money---but that didn't work out.

    Galileo, illustrated in a pugnacious mood in the figure below (local link / general link: galileo_ottavio_leoni.html).

    He trained as a
    mathematician---recall his father wanted him to become a doctor---and served as a professor of mathematics at the University of Pisa (1589--1592) and University of Padua (1592--1610) and later as the court mathematician and philosopher to the Dukes of Tuscany (i.e., the Medici) from 1610 until his death (see Wikipedia: Galileo: Timeline).

    Galileo is often cited as the single most important and most representative scientist (beating out Johannes Kepler (1571--1630) for top place) in the transition from traditional science (AKA proto-science nature knowledge) to modern science---the transition we call the Scientific Revolution of the 16th and 17th centuries.

    Galileo is also known for a number of scientific quarrels. He won most of those---but in some cases only posthumously.

    As far as yours truly can figure out, Galileo was pretty much a homebody and never went out of the Pisa-Venice-Rome triangle. The map of Italy in the figure below (local link / general link: map_italy_1494.html) is from a slightly earlier epoch than that of Galileo, but the main boundaries had NOT changed by Galileo's time.

    Let us now go over the salient features of
    Galileo's career:

    1. Dropping the Balls:

      Galileo is famous, among other things, for his demonstration of dropping balls from the Leaning Tower of Pisa. See figure below.

        Question: Ideally, in the absence of air drag and variations in release times:

        1. the balls hit the ground at the same time.
        2. the heavier ball hits the ground first.
        3. the lighter ball hits the ground first.

        Answer 1 is right.

      Aristotle held that qualitatively, the heavier ball should reach the ground first. And in many actual trials that is exactly what happens: e.g., paper and pen dropped. The acceleration due to gravity is mass independent (as is discussed Physics, Gravity, Orbits, Thermodynamics, Tides), but the acceleration (always a deceleration) due to air drag does depend on density in a complex way.

      Galileo held---eventually if not quite at the time of the dropping balls---that they should reach the ground at the same time in the ABSENCE of air drag and other complications like not exactly equal release time. You may never be able to reach the actual ideal case of no air drag and other complications experimentally, but you can approach it, and so envision it.

      The process envisioning of IDEAL CASES---scientific idealization---was one of Galileo's scientific principles---one that has passed on into modern scientific work.

      With scientific idealization at the beginning of analysis of a system, you do NOT worry about all the complicating secondary effects. You analyze the main effect in the ideal limit where there are NO secondary effects and then add the secondary effects as perturbations as needed to improve your understanding.

      For the history of the dropping balls, see Leaning Tower of Pisa in the figure below.

    2. Galileo and the Telescope:

      In pure astronomy, Galileo is most famous for his telescopic discoveries and his advocacy of Copernicanism.

      Galileo did NOT invent the telescope. It was invented in about 1608 in the Netherlands by eyeglass makers (see Wikipedia: Telescope Invention).

      Eyeglasses had been invented circa 1290 in Europe (see Wikipedia: Glasses: Invention) and eyeglass makers were common by the 17th century. See the figure below (local link / general link: eyeglasses_history.html).

      Given that crude
      telescopes can be made just by fooling around with a couple of lens or a lens and spherical mirror, it seems that the telescope was discovered rather late in the day.

      But once the idea of the telescope was known, you did NOT need to see an existing telescope to build one. All you had to do was go to your local eyeglass maker and ask them to build one for you or build one yourself with for the right kind of lenses.

      Now when he heard of the invention of the telescope, Galileo put his experimental skills to work and quickly made the best in the world then available.

      See Galileo and telescope in the figures below (unlinked figure; local link / general link: galileo_doge.html).

      Galileo telescopes were still very crude instruments with much poorer optical quality than even a cheap modern telescope. For example, they didn't focus all colors in the same place: this is called chromatic aberration.

      However, as anyone who works with equipment knows, you can do a lot with a crude instrument if you put your mind to it.

      Galileo put his mind to it and made all the great early astronomical telescopic discoveries first or nearly first.

      Certainly, he reported them first---remember it's publish or perish---most of them in his popular bestseller Sidereus Nuncius (1610, in English The Star Messenger) which overnight made Galileo the most famous natural philosopher in Europe. The Sidereus Nuncius was written in Latin so that everyone could read it.

      The main discoveries and their major implications are summarized below:

    3. Telescopic Discoveries:

      1. Vastly More Stars:

        There are vastly more stars than had ever been seen by the naked eye.

        The naked eye stars (of which there are only about 5600 for ordinary good observing conditions: see Wikipedia: Naked-eye astronomy) were only a small fraction of all the stars. The bigger the light-gathering power of the telescope the more stars you saw. In other words, there was no obvious limit to how many stars there were. See the figure below for no obvious limit.

        Also the Milky Way was at least partially resolvable into stars. Previously the Milky Way was seen just a band of milkiness on the sky as it's name suggests---the milky road.

        And also the stars were still unresolved. They were still point-like.

        Nothing had been proven, of course, but the idea that stars varied in distance and NOT just in brightness and that they were suns spread throughout a large or infinite space as Thomas Digges (1546--1595) and Giordano Bruno (1548--1600) had at least partially suggested began to seem plausible.

      2. The Planets Seen Disks:

        The planets were seen as disks when magnified rather than as twinkly points like stars. Planets were much different than stars, much closer than stars, or both.

      3. New Features on the Moon:

        There were newly discovered features of the Moon. See the figure below (local link / general link: galileo_moon_map.html).

        Galileo was beaten in drawing Moon maps. by Thomas Harriot (c.1560--1621) (see the figure below: local link / general link: thomas_harriot.html)---but no one knew this because Harriot never published his Moon maps.

      4. The Galilean Moons of Jupiter:

        The 4 largest moons (i.e., the 4 largest natural satellites) of Jupiter which we now call the Galilean moons of Jupiter See the figure below (local link / general link: jupiter_galilean_moons_collage_far.html).

        moons orbited Jupiter, NOT the Earth nor the Sun. The Earth was NOT the only body that could be a center of motion.

        Also the smaller bodies clearly orbited the larger body. The Sun was known to be vastly bigger than Earth. Could a bigger body orbit a smaller body? It began to seem as if it shouldn't. Kepler had thought it shouldn't all along.

        Also it was now possible for Earth to be a planet and still have a moons. It had been argued that the Earth couldn't be a planet since planets don't have moons.

        See Galileo's own drawing of the Galilean moons of Jupiter in the figure below (local link / general link: galilean_moons_galileo.html).

      5. The Phases of Venus:

        Galileo's discovery of the phases of Venus was strong evidence against the Ptolemaic system and Aristotelian cosmology too. See the figure below (local link / general link: venus_phases.html).

      6. Sunspots:

        The Sun had spots that varied in time and were carried and the Sun's face. The Sun was rotating. The sunspots proved that the Sun was NOT an unchanging perfect sphere. As with the Moon, Aristotelian cosmology was shown to be wrong.

      7. The Appendages of Saturn:

        Saturn had odd little appendages. Not until Christiaan Huygens (1629--1695) in the 1655 would the appendages be identified as a ring (see Wikipedia: Christiaan Huyghens: Saturn's rings and Titan) which we now know is divided into the multiple rings of Saturn.

      The conclusion of all the new telescopic discoveries was that Aristotle was wrong and Ptolemy was wrong.

      Not just wrong in details, but wrong in essence: wrong that the superlunary world was unchanging and perfect and orbited the Earth only.

      Aristotelian cosmology and the Ptolemaic system were demolished.

      Also, the idea that Earth was a planet as it is in the Copernican system was made a lot more plausible.

      But, of course, NOT everyone admitted these conclusions at once.

      The observations were tricky and NOT everyone had adequate telescopes.

      Even when they had seen the new discoveries with their own eyes, some dyed-in-the-wool Aristotelians could NOT accept them. It isn't very easy to accept that your whole cosmology is evaporated---especially if you are getting on in years.

      But the telescopic discoveries were NOT abstract mathematical discoveries like Kepler's (see the adjacent figure) or hard to duplicate like Tycho's new star and comet observations.

      They were accessible to many people high and low.

      But the telescopic discoveries did NOT prove heliocentrism.

    4. The Galileo Affair: The Sequence of Events Leading to Galileo's Trial and Condemnation by the Roman Inquisition:

      Actually, so much is known about the Galileo affair that we can only do a very short presentation with all kinds of interesting details omitted.

      To begin, the phyiscal intuition of Galileo and Kepler was that heliocentrism would prove correct was correct as we know now.

        Note phyiscal intuition is a vague entity. Yours truly would define it as a person's ability to estimate what must hold in physics that is poorly understood based on physics is well understood. Clearly, this ability is fallible, but it is a guide to what is the promising path to truth and is used in the simple problem solving and the scientific method a whole lot.

      Personally neither of Galileo or Kepler had any strong doubts about the truth of heliocentrism.

      Of course, the reasonable person of the time surveying the evidence circa 1610--1630 might have suspended judgment as no doubt many did.

      As is well known, the leadership of the Catholic Church at that time did NOT suspend judgment.

      In 1616, heliocentrism as physically real was condemned by a Catholic Church decree as a very close to being a heresy.

      Hypothetical discussion of heliocentrism was formally allowed though:
      1. This is because heliocentrism was NOT officially a heresy.
      2. However, hypothetical discussion was seen to be a suspect activity.
      3. So effectively heliocentrism was close to being forbidden without explicit permission.

      Galileo did, in fact, in 1624 (see The Galileo Project: Galileo Timeline: scroll down ∼ 70% to year 1624) obtain explicit personal permission from an old friend who happened to have become Pope Urban VIII (1568--1644, pope 1623--1644) (see the figure below: local link / general link: urban_viii.html) to write a book that would treat heliocentrism favorably, but HYPOTHETICALLY as something that could NOT be proven---this being Urban's own opinion.

      Galileo's book Dialogue Concerning the Two Chief World Systems was published in 1632 February. As its title suggests, it is in the form of dialogue. See the figure below (local link / general link: galileo_dialogue.html).

      Galileo's Dialogue, in fact, is a vigorous argument for heliocentrism.

      Only at the end does Galileo in deus-ex-machina fashion revert to the stance that heliocentrism could NOT be proven, was just hypothetical, and that God could have arranged the cosmos in a way that was profoundly different from what human reason and observation could discover.

      Urban when he had become fully informed about the book---already then passed by the censor (who knew nothing about astronomy) and published---he, Urban, took umbrage.

      He thought Galileo was taking him for a fool. That very probably was really that (Fantoli 2003). (Certainly, NOT my own conclusion by the way.)

      There was a trial before the Inquisition for heresy in Rome in 1633 with all kinds of events and details. In fact, we know so much about the events leading to the trial and afterward that one is danger of losing oneself in details.

      But really once Urban had decided to punish Galileo, the consequences were pretty much determined.

      The Inquisition doesn't acquit.

      The figures below are some establishing shots and an artist's conception of the trial of Galileo (unlinked; unlinked; local link / general link: galileo_inquisition.html).

      Galileo was found guilty of "suspicion of heresy" and he submitted to the decision.

      He really had no choice: he was a faithful Catholic and he had to think of his family, friends, and his patron the Ferdinando II de' Medici, Grand Duke of Tuscany (1610--1670, reigned 1621--1670). He could NOT embarrass and harm them by dying a condemned heretic---he didn't want to for himself either very probably.

      In modern terms, Galileo accepted a plea bargain to avoid a worse fate.

    5. The End of Galileo:

      For the end of Galileo (1564--1642), see the adjacent figure and the figure below (local link / general link: galileo_samson.html).

      After Galileo's death there were, of course, many continuing developments in astronomy.

      But the next big innovation in astronomy would come with Newton: see section Isaac Newton (1643--1727) below.

  29. Isaac Newton (1643--1727)

  30. Isaac Newton (1643--1727) (see the figure below: local link / general link: newton_kneller.html) was born within a year of Galileo's (1564--1642) death.

    But when
    Newton reached maturity in the 1660s, he was in an already greatly evolved intellectual environment from that of the old Galileo.

    1. Newton's Intellectual Environment:

      The first thing to say was that Newton lived in a Protestant environment.

      In the Roman Catholic environment, Copernicanism had become effectively a heresy in 1616 as mentioned above in the subsection The Galileo Affair---a position from which the Roman Catholic Church would gradually retreat over next two hundred years (see Wikipedia: Heliocentrism: Age of Reason).

      On Protestant side of the religious divide, Copernicanism somehow never developed into a religious issue.

      It seems that the work of Galileo and Kepler, the telescope, and other things had largely evaporated Aristotelianism from religion. And without that support, purely Biblical objections to Copernicanism seemed far-fetched.

      There was also the Copernicanism-based vortex theory of Rene Descartes (1596--1650) (see the figure below). This very bad, but alluring, theory had a profound attraction for some of the physics-minded people in that time (e.g., Christiaan Huygens (1629--1695) (see Wikipedia: Mechanical explanations of gravitation: Vortex). Some folks found Copernicanism acceptable based on this theory---it's always possible to believe a true result for a wrong reason.

      Thus, in the course of the 17th century, the overall intellectual world in Europe had changed.

      Copernicanism became more and more accepted as the plausible theory.

      This was true in Roman Catholic countries too, but the official position on Copernicanism made Copernicanism a tricky issue to discuss or write on.

      Newton and his contemporaries in England were still being taught Aristotelianism, but he and probably others were already aware it was outdated. In fact, they may have learnt Copernicanism as soon as or before any other view of the Solar System.

      Newton himself as an undergraduate at the University of Cambridge studied the new astronomy of Galileo, Kepler, and their followers.

      Initially at least, he did NOT read the original work of Galileo and Kepler at all---like any good undergraduate, he read textbooks that simplified the presentation and omitted the out-of-date arguments and issues.

    2. Newtonian Physics and Astronomy:

      We will NOT go into the history of Newton's work on motion and the Solar System which he first published in his Principia (1687)---see the figure below (local link / general link: newton_principia_page.html).

      We will just say that
      Newton's three laws of motion and his law of universal gravitation form the essence of very accurate, quantitative physics, Newtonian physics.

      Newtonian physics applies both to the terrestrial environment and to the Heavens, and thus united terrestrial and celestial physics which were profoundly distinct in Aristotelian physics.

      Newton using Newtonian physics was able to account to very high accuracy for the motions of Solar System and derive Kepler's 3 laws of planetary motion. See the Kepler's 2nd law of planetary motion illustrated in the animation in the figure below (local link / general link: kepler_2nd_law.html).

      Newtonian physics and the Solar System bodies, heliocentrism follows as a result, NOT an axiom. In the Newtonian system, the planets are in accelerated orbits about a relatively unaccelerated Sun.

      Newton extrapolated the Newtonian system to the universe as whole assuming that it was infinite or, at least, very large and that the stars are other suns.

      After Newton's work had been assimilated among the astronomically interested people (which only took a few years), there were no more doubts about heliocentrism.

      The Catholic Church accepted heliocentrism as an allowable view in the 18th century.

    3. The Unification of Terrestrial and Celestial Physics:

      An absolutely key point about Newtonian physics for the future development of astronomy is that it unified terrestrial and celestial physics.

      The unification finally made astronomy somewhat experimental. For experimentation as it was in the 17th century, see the figure below (local link / general link: guericke_pressure_horses.html).

      We can NOT do experiments on
      stars, galaxies, etc.

      But experiments on Earth do reveal aspects of the physics of outer space the unification of terrestrial and celestial physics.

      To illustrate the unification, Newton's cannonball illustrates how free fall is the same on Earth as in outer space. For Newton's cannonball, see the figure below (local link / general link: newton_cannonball.html).

  31. Epilogue

  32. It's certainly been a long story from counting lunar phases on bone tally sticks to the infinite or quasi-infinite universe of Newton. And a lot of work got done as illustrated by the scientist in the figure below (local link / general link: vermeer_geographer.html).

    The story shows, as advertized, the
    scientific method in action: the cycle of theory and observation/experiment that yields advance toward truer, more general theories. The cycle is an upward spiral in terms of content.

    Of course, as mentioned in section scientific method---it's much too extended in time to be typical and most of the participants were NOT aware they were practicing the scientific method at least as a paradigm for how science should be done.

    But at the end with Galileo, Kepler, Newton, and other lesser lights, one sees the modern scientific method developing in which physical theories are found adequate or inadequate by testing them against nature, NOT by seeing how they fit in an overall philosophy of the universe and/or metaphysics.

    The development of the modern scientific method is a main feature, but NOT the only one of the Scientific Revolution of the 16th and 17th centuries.

    Philosophy and metaphysics still play a role. But describing that role is a lecture in itself---and one without consensus conclusions.

    As for the history of cosmology, which we have been covering in this IAL, we pick that up again and carry it on to the present in:
    1. IAL 26: The Discovery of Galaxies.
    2. IAL 28: Galaxies.
    3. IAL 29: The Large-Scale Structure of the Universe.
    4. IAL 30: Cosmology.

  33. An Essay on the Three Epochs of the History of Astronomy: Not a Required Reading

  34. This essay is NOT part of the required reading for this lecture.

    The history of astronomy can be divided into many different periods in many different ways.

    But yours truly believes that Julius Caesar was right.

    The history of astronomy does divide into three main epochs both from science topic and human interest points of view.

    An immediate qualification is that I mean
    history of astronomy that tracks through prehistory (archaeoastronomy), ancient Mesopotamia (Babylonian astronomy and precursors), classial antiquity (Greek astronomy), Middle Ages (Medieval Islamic astronomy, and Medieval European astronomy), early modern Europe (early modern astronomy), and the modern world (modern astronomy).

    Essentially, this path through history is the path that tracks along the most advanced astronomy of its time (e.g., Tycho's) in the judgment of many.

    It leaves aside other historically interesting astronomies (e.g.,
    Chinese astronomy and Mayan astronomy), whose contributions to modern astronomy are limited.

    What are the three epochs as yours truly perceives them:

    1. From the remote and misty beginnings in prehistory to circa 1700.
    2. From circa 1700 to circa 1900.
    3. From 1900 to the present---which is a moment that keeps trying to get away from us.

    Below I'll make an argument for the three epochs and other related issues.

    But I would like to emphasize I'm making an idiosyncratic argument and that is why I call this section of this lecture an essay. I'd like to believe others would NOT disagree too much.

    In point-form, the argument is as follows:

    1. From the Remote and Misty Beginnings in Prehistory to Circa 1700:

      Why is the first epoch from the remote and misty beginnings in prehistory to circa 1700?

      This is the history of astronomy to Isaac Newton (1643--1727) that was the topic of this lecture.

      We can now see that it is essentially an astronomy of the Solar System for two reasons.

      First, actual Solar System astro-bodies (Sun, Moon, planets, and comets when they were thought of as being above the ordinary air which we call the Earth's atmosphere) had the most complicated motions and needed the most observation and theory to explain.

      The fixed stars (which is all the stars that anyone knew about) just sweep around once per day (from the Earth's perspective) on the celestial sphere and are otherwise unchanging.

      Second, for much of the time and many of the astronomers, the fixed stars were part of the Solar System. They were on the outermost of the celestial spheres of Aristotelian cosmology. The study of the Solar System was often conceived of as cosmology itself.

      So there is a grand thematic unity to the astronomy epoch prehistory to circa 1700---it was really cosmology, NOT just astronomy.

      But, of course, there was a huge host of changes from counting lunar phases on tally sticks (from maybe as long ago as 33,000 BCE or earlier (see John North 1994, The Norton History of Astronomy and Cosmology, p. xxiv; Wikipedia: Lebombo bone) to the Newtonian universe.

      To recapitulate the epoch from prehistory to circa 1700:

      1. In prehistory and early history, the theoretical understanding seems to have been mostly that anthropomorphic gods ordered the universe). On the observational side, one just had casual observations and simple countings of events.

      2. Alignment astronomy was developed in prehistory in many cultures and carried on into early history.

      3. Exact, systematic, written-record observations started most notably in Babylonian astronomy which flourished from early beginnings (circa 1800 BCE: see Wikipedia: Babylonian Astronomy: Old Babylonian astronomy) and petered out, at least as an independent tradition, with the extinction of cuneiform script in the 2nd century CE.

        The theoretical understanding of Babylonian astronomy, aside from mythological understanding, is unknown and perhaps was meager or non-existent.

      4. Greek astronomy in Classical Antiquity had its heyday in period from Thales (c.624--c.546 BCE) to Ptolemy (c.100--c.170 CE).

        In observational technique, it doesn't seem to have surpassed Babylonian astronomy.

        On the theoretical side, there were two interconnected traditions both of which tracked into a geocentric picture of the universe.

        One tradition was that of philosophical astronomy of which the dominant theory became Aristotelian cosmology.

        The other tradition was one of exact
        mathematical astronomy based on epicycle models which culminated in the work of Ptolemy.

        We can see that epicycle models were all mathematical decompositions of the planetary motions that had little physical content and that there could be no uniquely good epicycle model for the Solar System. Ptolemy must have grasped the lack of uniqueness to some degree, but hoped that his own epicycle model was the best, and therefore truest. We can see that this was a mistake. Other epicycle models as good as his could and were built over the next 1300 years.

        The two traditions were NOT completely separate.

        Philosophic astronomy did try to match observations qualitatively, but simply deferred to mathematical astronomy in matters of exact astronomical prediction.

        Mathematical astronomy (as embodied in Ptolemy most obviously) attempted to reconcile itself with Aristotelian cosmology, but NOT could derive epicycle models from it.

        But the two traditions were certainly NOT really consistent and that became a recognized deficiency as the centuries rolled on to Nicolaus Copernicus (1473--1543).

      5. Medieval Islamic astronomy and Medieval European astronomy largely carried on the two traditions of Greek astronomy.

        There was some improvements in observational and mathematical techniques.

        On the theoretical side, there was virtually no progress other than cumulative result that there was no uniquely good epicycle model.

      6. Early modern astronomy (which developed in the physical context of Europe) saw the development of heliocentrism (beginning with Copernicus, the telescopes, and the eventual triumph the Newtonian universe.

        Both Aristotelian cosmology and epicycle models were swept away---NOT without a bit of a fight.

        But at first without any adequate replacement.

        Then came with Newton who was able to explain the Solar System quantitatively by exact physical laws that were also the physical laws of the terrestrial environment. He took the initial conditions of the Solar System as givens.

      Newton's achievement did NOT, of course, end the story of astronomy.

      In the century or so leading up to Newton, it had become very obvious that the universe was probably vastly bigger than the Solar System and that the fixed stars were other suns and so could have their own planetary systems.

      So having climbed a mountain, humankind found another larger mountain beyond.

      And humankind (as embodied in astronomers) had to ask itself what determined the structure of the universe as a whole and did it evolve.

      It seemed obvious to try to extrapolate Newtonian physics to the universe.

      But this did NOT lead to instant success. In unpublished work, Newton tried to construct a physically consistent STATIC MODEL of the universe---using Newtonian physics, of course (see John North 1994, The Norton History of Astronomy and Cosmology, p. 376). He failed and rested.

      A lot more data and theory were needed.

      Historically, that data and theory took time to accumulate starting from the plateau of the Newtonian universe.

      So certainly it is fair to regard the establishment of Newtonian universe as the end of the first main epoch of astronomy.

    2. Why is Cosmology So Important?

      Having defined the first epoch of astronomy as a phase of cosmology, one now has to justify why cosmology is so important.

      Humankind is concerned with its own meaning and nature and with that of the universe that supports it. That seems to be intrinsic.

      The study of the universe on the grandest scale is cosmology.

      So cosmology is and has arguably always been an intrinsic vital concern of humankind.

      Modern astronomers usually---but NOT always---stay away from "meaning" and stick to "nature".

      It's just hard to draw anything but idiosyncratic ideas about the meaning of the universe from scientific cosmology.

      But it has to be admitted that "meaning" probably hovers somewhere in the unexpressed concerns of astronomers.

      I think astronomy---beyond purely practical applications in timekeeping, navigation, and historically astrology---is supported by humankind because of humankind's concern with cosmology and one other important topic, extraterrestrial life---which we'll get to below.

      Why are other non-practical fields of astronomy outside of cosmology and extraterrestrial life supported.

      Well those are fields all interlock with cosmology and extraterrestrial life, and that is generally understood.

    3. Extraterrestrial Life:

      Now what of extraterrestrial life?

      Why is that a vital concern of humankind?

      Yours truly thinks it comes back to meaning and nature again.

      To humankind, life is an intrinsic vital concern.

      The universe would definitely seem barren and meaningless without life.

      And there would be no one to have vital concerns without life.

      Since life in general is a vital concern, so is life beyond the Earth.

      As cosmology has enfolded over history, the realm beyond the Earth was found to be bigger and bigger reducing Earth to a pinprick.

      This makes the role of extraterrestrial life bigger and bigger.

      The concern with extraterrestrial life prompts three age-old questions:

      1. Is there extraterrestrial life?

      2. Or are we alone?

      3. And "Where are they!"---which is a probably emphatic version of what Enrico Fermi (1901--1954) once said.

      The vital concerns of
      cosmology and extraterrestrial life have, of course, NOT always been evident in individuals or in societies.

      But I think the potential for those concerns to arise has always been there.

      Intrinsic to our nature I'd say.

    4. The Extraterrestrial Life Concern in the First Epoch of Astronomy:

      How do the extraterrestrial life concern fit into the first epoch of astronomy?

      Well I think there is a unifying story here too.

      It seems generally the case that for most of history, life in the Heavens was mythological: anthropomorphic gods and some non-anthropomorphic gods too I suppose.

      Even in religions where the Heavens---that thing you see in the sky---were NOT essentially the theological Heaven, there was for a long time a tendency to view it that way as in Dante's Divine Comedy.

      However, as the Heavens or outer space began to seem more like a physical realm, NOT unlike Earth, the idea---nowadays called cosmic pluralism (according to our own supreme authority Wikipedia)---could develop that there might be physical beings there that were NOT of religious significance---that are NOT directly aware of us or our concerns---just as we are NOT directly aware of them.

      Cosmic pluralism could NOT easily develop in Aristotelian cosmology where from the Moon outward was the realm of gods or later angels.

      However, there may have been some cosmic pluralism since Thales (c.624--c.546 BCE) and certainly since the Greek atomists Leucippus (first half of 5th century BCE and Democritus (c.460--c.370 BCE) and their followers.

      And cosmic pluralism never entirely went away after that, but it probably seemed just a by-product of certain philosophical systems that were NOT widely accepted.

      However, when heliocentrism made Earth a planet and the stars became probably other suns with their own planetary systems, cosmic pluralism became an almost inescapable probability---unless ruled out on some philosophical basis.

      In the last phase of first epoch of astronomy, that was the position reached.

      Of course, there was no empirical evidence for extraterrestrial life: therefore was just the nearly inescapable hypothesis it must exist.

      It could only be investigated in science fiction which it was starting with Kepler's scifi novel Somnium (published posthumously in 1634) about a trip to the Moon and the Selenites (Moon beings).

      But science fiction was virtually all that could be done for a long time.

      The study of extraterrestrial life had reached a plateau just as cosmology had.

    5. The End of the First Main Epoch of Astronomy:

      Yours truly argues that the discovery of the Newtonian universe and the arrival at the nearly inescapable hypothesis of extraterrestrial life (or cosmic pluralism) marks a logical end for the first main epoch of astronomy.

      The story from misty beginnings to that point is a unity.

      From misty beginnings, humankind arrived NOT at final knowledge, but at new platform.

      There are two other unities of the first epoch that can be mentioned too:

      1. The second unity is that the period from prehistory to circa 1700 was also the period of the transformation of nature knowledge of various kinds into modern science.

        Circa 1700 can be considered the end of that transformation story too.

        And, of course, astronomy was always involved in that transformation with frequently a starring role.

        In particular, in the Scientific Revolution (roughly 1500--1700), it had a starring role from Nicolaus Copernicus (1473--1543) to Newton.

        Independent of astromony qua astronomy, this second unity is of compelling intellectual interest.

      2. The third unity is that of a thrilling story that passes through the some of the great ages of humankind and that involves great brains such as anonymous Stonehengers (AKA Neolithic Britons), Democritus (c.460--c.370 BCE), Omar Khayyam (1048--1123), Johannes Kepler (1571--1630), Galileo (1564--1642), and Newton (1643--1727).

        It just seems to us that those times and people have become legendary to us: part of the general modern cultural inheritance and paradigms of the human condition. For the human condition, see the figure below (local link / general link: rodin_burghers_calais.html)

      Yours truly believes that it is because the first epoch is deeply concerned with cosmology, a vital human concern and has the three unities cited above that it has often been considered a suitable topic for introductory astronomy courses.

      That is why it is included in Introductory Astronomy Lectures (IAL).

      The vital concern of extraterrestrial life is NOT a big theme of the first epoch, and so is NOT covered for the first epoch, except in the discussion given in this section of the lecture on history of astronomy to Newton.

      Yours truly made a big deal of it in this section because it became inescapable to discuss what the other vital human concern was.

    6. The Second Epoch from Circa 1700 to Circa 1900:

      Why is the second epoch from circa 1700 to circa 1900?

      As argued above, astronomy and humankind had arrived at a plateaus in the vital concerns of physical cosmology and extraterrestrial life.

      But the "plateau" metaphor has to be modified to slowly rising slope.

      At least, subjectively to yours truly, it seems slowly rising compared to the 1500 to circa 1700 and the period since circa 1900 compared in advancing the vital concerns of physical cosmology and extraterrestrial life.

      From a modern perspective, yours truly views this epoch of the history of astronomy as one of preparation for the third epoch where rapid progress in the vital concerns resumes.

      Many new astronomical discoveries were made: e.g., new planets (Uranus and Neptune), asteroids, and spiral nebulae (which in the 20th century were discovered to be spiral galaxies).

      Advances were made in the tools of discovery. To name only the most obvious, there were vastly improved telescopes, photography, and spectroscopy.

      But a physically-consistent theory of the universe was lacking and the existence of other galaxies outside of the Milky Way was NOT known though some people thought there were.

        So on the "mountain beyond the mountain", humankind had NOT climbed very far by 1900---but the real ascent was about to begin.

      And the subject of extraterrestrial life seemed stalled, except for a little science fiction (mostly toward the end of the epoch due to H. G. Wells (1866--1946)) and the fabulous wrong theory of intelligent life on Mars as evidenced by the Martian canals (which turned out to be non-existent).

      Now it is certainly presentism to regard the epoch 1700 to circa 1900 just as preparation.

      But to regard it as preparation from the point of view of progress on the two vital concerns seems OK.

      Because it was an epoch of preparation rather than advance on the vital concerns, the second epoch is just less interesting to people in general.

      This conclusion by yours truly seems to be pretty general.

      It applies to astronomers as much as anyone else.

      It is true to say that only those who are interested in the history of astronomy for its own sake apart from the two vital human concerns are deeply interested in the second epoch.

      Of course, astronomers do know a lot of bits and pieces of it of the history of astronomy in the second epoch.

      One way or another, one just picks up lots of those bits and pieces if one is immersed in astronomy.

      The Introductory Astronomy Lectures (IAL) only covers a few bits and pieces since yours truly can't imagine the ordinary intro astro student having much interest.

      There are specialized sources for those that do want to know the detailed history of astronomy in the second epoch (e.g., John North, 1994, The Norton History of Astronomy and Cosmology).

    7. The Third Epoch from Circa 1900 to the Present:

      Why is the third epoch from circa 1900 to the present?

      Starting circa 1900 and continuing to the present, tremendous progress has been made on the vital concern of cosmology.

      We discuss that progress in IAL 30: Cosmology which besides being an introduction to modern cosmology also covers its history.

      What of the other vital concern, extraterrestrial life.

      Well from circa 1900 to circa 1960 most of the progress was only in science fiction.

      But that's NOT negligible: it's been the inspiration of the huge research done on the subject since both for the general public and astronomers---many (most?) astronomers grew up reading tons of scifi and watching scifi films (2001: A Space Odyssey (1968), Aliens (1986))---yours truly reached saturation as a teenager and has hardly read it since.

      The history of the subject of extraterrestrial life is NOT much covered in Introductory Astronomy Lectures (IAL). We can't do everything and it may NOT be of general interest.

      We do cover the Martian canals story in IAL 14: Mars: The Red Planet---it just part of the lore of Mars---the Martian canals don't exist, but we are still wishing they did---and are hunting for every scrap of evidence for Water on Mars.

      We might cover some other bits and pieces.

      The present-day search for extraterrestrial life is covered in IAL 18: Exoplanets & General Planetary Systems---well whenever that part gets written.

      The search of extraterrestrial intelligence (SETI) is covered in IAL 31: Intelligent Life in the Universe. See just-for-fun figure below (local link / general link: ufo_new_jersey.html).

    8. The Future of Astronomy:

      So much for the past, what of the future of astronomy?

      This is an invitation for vague speculation.

      Three vague, non-exclusive, possibilities occur to yours truly---just following the whole herd of scifi---that apply to all science including astronomy:

      1. Science asymptotically reaches the limit of knowing all that we can know, but NOT all that is to be known.
      2. Somehow we lose knowledge through societal collapse or absentmindness.
      3. Humankind reaches a transcendent state in which we know everything.

      None of the above possibilities seem likely anytime soon.

      A present, there seems no plausible way to elucidate them---maybe in science fiction---or maybe NOT even there.