Part Two: Early Moderns: Nicholas Copernicus (1473-1543), Johannes Kepler (1571-1630), and Sir Isaac Newton (1642-1727)

          Part Two:

    

Early Moderns: Nicholas Copernicus (1473-1543),  

                   Johannes Kepler (1571-1630), and Sir Isaac Newton (1642-1727)

Professor Alexander Jones’ lectures (University of Toronto, Winter 2002) on ancient Babylonian and Greco-Roman astronomy, for me, highlighted by the Greeks’ conception of the Great Celestial Wheel of the sun, moon, planets and stars, all revolving round the arth at the centre. He concluded those lectures with a brief account of what happened fourteen hundred years after Claudius Ptolemy completed his masterful exposition, Almagest, the accomplishments of Greco-Roman astronomers up to his time in the 2nd century CE..

In the early modern period, Copernicus advanced the idea that the sun lies at the centre is but one of the planets going around the sun (an unorthodox idea first proposed by the ancient Greek astronomer, Aristarchus of Samos, 310-230 BCE). In 1510, Copernicus circulated a small paper he called Little Commentary (not published until the 19th century) “All the orbs encompass the sun which is, so to speak, in the middle of them all, for the centre of the world is the Sun” Our “terrestrial orb,” Earth, revolves round the sun like any planet. He went on to say that the arth accomplishes a rotation around its fixed poles, while the heavens remain motionless (not quite true).

Copernicus spent the rest of his life labouring at six books entitled Revolutions of the Heavenly Spheres, only published at his death. Evans that Copernicus thought he had discovered “the true system of the world,” a system that unified all the parts in that the six known planets: Mercury, Venus, Earth, Mars, Jupiter and Saturn encircle the sun in this orderly concentric pattern (not unlike Eudoxus in Plato’s time who conceived of the “nested spheres” of sun and planets). According to Evans, because Copernicus assumed that Earth moves around the Sun at uniform speed on a circle eccentric to the Sun, was essentially Ptolemy’s modelcircular motion around an off-centre point in the circle.

Kepler began his university studies in Italy in philosophy and theology, but on being introduced to Copernicus’ theory, he moved to astronomy. Evans illustrates a diagram that inspired Kepler Mysterium cosmographicum ( in Latin, ‘The Mystery of the Universe’998:428) show(like the ancient Greek mathematician, Archimedes) that angles could be inscribed within a circle. He used each angle as the point of an equilateral triangle to represent the successive conjunctions of Jupiter and Saturn as they rotate on their respective orbits inside this larger circle. Much later, Kepler would determine Earth’s own orbit by triangulations, adapting this similar geometric device from Ptolemy, but by this time, Kepler was inscribing unequally-shaped triangles that  elliptically-shaped pattern.

Kepler’s major work was published in 1609 entitled Astronomia nova (New Astronomy). His life-time achievements were monumentally important thereafter. Evans notes that part of the significance of work was that he moved astronomy away from mathematics into the realm of physics (likely an inspiration to Newton), by relying on observational data for his breakthrough interpretations of planetary orbits like Mars’.

As found in “New Astronomy,” Kepler speculated regarding a physical solution for understanding planetary behaviours – the answer might lie in “Magnetic motive forces” (Evans 1998:440), an idea which Newton was to develop much further.

                         Newton explaining Solar System by Physics

      The genius of Newton is recognized for his explanation as to why the planetary bodies continually rotate around the sun. His theory rested upon the insight that the more powerful gravitational force of the sun (today set at 27 times the gravity of Earth at 1) keeps pulling the planets around itself. The planets are satellites of the sun, just as moons notably Jupitertwelve(Jupiter’s gravity field is twice that of Earth’s). Newton saw that there are inter-planetary gravitational influences, most significantly Jupiter, of course, along with its large planetary companion, Saturn. When these two are in conjunction, closer together, their combined force-field impacts to some degree on the force-field of the sun itself, provoking solar eruptions and flares of such exceedingly great physical energy that these solar particles of energy stream down into our atmosphere in greater abundance.

Kepler’s discovery of the elliptical shape of planets led to Newton’s gravitational theory, explaining why Mars’ orbit is rather elongated; it is affected by proximity to Jupiter, as is Mercury’s orbit more elongated because it  the sun. Earth’s orbit is only slightly elliptical; at times, it tends towards near ut its gravitational  smaller-sized Venus deforms that planet’s orbit to some degree.

           In order to appreciate Newton’s Laws of Universal Gravitation, e.g. F= G and M divided by R, which took some twenty years for him to develop, we shall select some important considerations that occurred to NewtonBernard Cohen discusses ‘Newton on the Laws of Motion’; William Harper examines ‘Newton’s argument for universal gravitation;’ and Curtis Wilson  discusses the definitions offered by Newton in his Principia, including what Newton meant by “gravity”

Cohen says that Newton’s understanding of terrestrial gravity is that it is the force that causes bodies to descend downward “… toward the centre of the Earth.” This became part of hislaws of universal gravitation. Then, he said of gravity, there is “… the force by which the planets are continually drawn back from rectilinear motions and compelled to revolve in curved lines.” Cohen quotes Newton from the Principia, that, starting from the law of inertia, a body moves uniformly straight forward unless compelled to change its state by forces impressed.

Wikipedia explains the above idea more simplistically. If the sun with its powerful force-field, 27 times the gravity of Earth, were not holding Earth in a quasi-circular orbit, Earth might just keep heading off into space in a straight line. In Newton’s time, his contemporary Halley calculated the orbital path of the comet named after him. The elongated orbit of Halley’s comet, originating like other comets and asteroids from the area in space between Jupiter and Mars, while en route to the sun, must deviate in this path whenever it by-passes an intervening planet like Earth.                 

Harper  Newton’s consideration of the orbits of the four moons (then known) of Jupiter. From other’s observations, understood the orbits of those moons approximate uniform motion on concentric circles. Jupiter is the centre that directs their orbits. Harper says that Newton saw the sun as centre of planetary motions, and their departure from uniform “ a little more swiftly in their perihelia and more slowly in their aphelia” Regarding inter-planetary relationships, Newton said that:

“We have proved that all planets are heavy [or gravitate] toward one

another and also that the gravity toward any one planet, taken by

itself, is inversely as the square of the distance of places from the

centre of the planet (2002:190)

Wilson (2002:202) looks at some observations  Jupiter and Saturn. In the 1690’s, Newton was asked to help correct Kepler’s values; it seemed that Jupiter was moving faster Saturn. What Newton proposed was complex. From his acquaintance with Kepler’s elliptical model, he advised that he would take the focus of Saturn’s orbit by the centre of gravity in Jupiter and the Sun. Then, he would introduce oscillations into Saturn’s eccentricity of orbit.  Newtondid not offer the mathematical calculations for the preceding suggestions.

In 1787, Laplace dealt with such anomalies in eccentricity by giving an explanation for the acceleration in the motion of Earth’s moon. He said that, “if there was a decrease in Earth’s eccentricity, this would lead to a diminution of the Sun’s perturbing force – and thus, the moon’s motion would accelerate”2002:216).

Earth’s orbit is only slightly elliptical at present, at 0.015 degrees its closest approach to the sun in early January some five million kilometers

By our calendar, the effect of the above is that the  four seasons  not exactly equal. James Evans sets the dates as follows: the spring equinox is March 21; on June 22, it reaches its northerly limit at summer solstice Autumn equinox occurs on September 23; and the winter solstice on December 22 – explained according to Earth’s slightly elliptical orbit at present.

Today’s astronomers, A. Berger and M.F. Loutre, calculate that Earth’s orbitmoving towards near-circularity in 10,000 years’ timEarth’s orbit is due to become almost a perfect circle. Eccentricity will no longer be a major factor in altering Earth’s speed of motion at different times of the yearow will its uniform and constant motion affect the Moonrotational phases? Or, for that matter, how will it affect the specific dates in our calendar that currently separate the four seasons?

                   Accounting for the Great Ice Age: Earth’s Elliptical Orbit

        In 1837, the Swiss scientist, Louis Agassiz, an authority on fossil fish, made a presentation to the Swiss Society of Natural Sciences which soon to become known as his theory of the “Great Ice Age.” Agassiz had been struck by seeing boulders, later called “erratics” strewn about in the Swiss Alps which he proposed must have been deposited by glaciers as they retreated. With new eyes, he and his colleagues looked at layers of till composed of dirt and stones which must have lain at the edges of the vast ice fields that once covered most of Europe.

During the 1860’s, a Scottish scientist, James Croll, proposed a theory of glacial-interglacial phases which he linked directly to changes in Earth’s elliptical orbit. According to Croll, whenever Earth was farthest away from the sun, at aphelion in the season of winter, then there would be colder winters and glacial conditions. On the other hand, if Earth was passing  to the sun when perihelion was in the season of summer, this brought about interglacial conditions. Furthermore, he that slight changes in the tilt of the earth’s axis could influence the creation of an ice age. Whenever the tilt was closer to upright, this would reduce the amount of sunlight reaching high latitudes. , whenever the tilt was pointing downwards to a more pronounced degree, more ice would melt in the northern regions and an interglacial would be initiated.

Croll proposed that the last Ice Age began some 250,000 years ago and then ended 80,000 years ago, at which time he thought the present interglacial had its inception. This chronological aspect of Croll’s theory was discounted after scientists found that the present interglacial began some 15,000 years ago. , Croll’s idea of combining two astronomical factors, the eccentricity of Earth’s orbit and axial tilt, was the prelude to Milutin Milankovitch’s more ambitious attempt to track past climate epochs according to the interactions of the three different cycles: orbital eccentricity, the degree of obliquity of Earth’s axis, and the precession of the seasons of perihelion/aphelion.

                            Gribbin’s and Gribbin’s Ice Age, 2001

          John and Mary Gribbin’s treatment of past ice ages in Ice Age (2001) focuses on the importance of the astronomical cycles formulated by Milutin Milankovitch (dates 1879-1958). Early in the 20th century, Milankovitch, a Serbian mathematician and astronomer, undertook the mammoth task of computing, with pencil and paper, the “mean irradiance” of sunlight received in the higher latitudes, 55-60-65 degrees North over the past 650,000 years. According to the Gribbins (2001:45), drew from calculations made by a contemporary,  Ludwig Pilgrim (1904), who computed variations in orbital eccentricity, precession and tilt over the past million years

Milankovitch published papers in 1912, 1913 and 1914 in his own Serbian language without attracting any attention from astronomers or geologists. In 1924, the Russian-born Wladimir Koppen and the German geologist, Alfred Wegener (the latter became known for his theory of continental drift), collaborated on Climates of Geological Prehistory wherein they referred to Milankovitch’s theory of glacial-interglacial epochs.

In contrast to Croll’s theory, as above, Koppen, a climatologist, suggested that an interglacial takes place whenever snow from the preceding winter season melts away in the summertime precluding the build-up of ice sheets from year to year. The latter argument for the importance of ice accumulations surviving through summer seasons came to be accepted by Ice Age theorists.

                         Substantiating Milankovitch’s Climate Cycles

        The Gribbins the efforts by earth scientists during the mid-20th century who searched for the physical evidences of Milankovitch’s cycles, chronologies that could fit the astronomical indications of past glacial and interglacial epochs. In the chapter, ‘Deep Proof” (2001:62-90), the detail successive attempts to read a dating-framework sea-core material of ooze drilled up from ocean depths, paying close attention to the shells of little sea creatures called “forams.” Eventually, scientists realized that changes in global temperatures could be read according to two different kinds of oxygen isotopes. During the interglacials, oxygen 16 prevail in fresher waters in the oceans, and during a glaciated period, oxygen 18 show greater salinity in the colder ocean waters. During warmer periods, the lighter oxygen 16 evaporates from the surface waters, turning into the snowfall that steadily built up in northern regions, then stored in the ice as an ice age progresses. With oxygen 16 locked up in the ice and with global temperatures lower, the heavier element of oxygen 18 predominate in ocean waters to form the shell bodies of little sea creatures.

Beyond these ocean core studies, other earth scientists looked at raised beaches high above present-day beaches. These raised beaches existed when sea levels were much higher during interglacials. As well, in various landscapes, scientists found great layers of loose soils, loess, deposited during the preceding ice age when atmospheric conditions were very cold and dry, and the winds blew the dry soils across the barren landscapes.

According to the Gribbins (2001:75), raised beaches have been found in Atlantic and Pacific regions indicating that during the last interglacial termed the “Eemian,” c 120,000 years ago, the sea level was six meters higher than today. Various methods of dating show that sea levels were highest at 125,000 years ago, 105,000 years ago, and 82,000 years agoperiods roughly correspond to Milankovitch’s warming epochs.

                     Updating Astronomical Imprints on the Past Ice Age

                                       and the Last Interglacial

           Belgian astronomer and paleo-climatologist M.F. Loutre (2003), looks back at previous astronomical calculations of climate changes by orbital factors, still of historical interest in having influenced, for instance, Croll’s chronologies as above. More importantly, he presents his colleague, Berger’s more accurate refinement of these astronomical factors in keeping with the basic Milankovitch model.

First, let us briefly look at Loutre’s examples of past efforts in this regard – Figures 2 and 4 present two graphs outlining astronomical calculations of major changes over the past 600,000 years for high latitudes 60-75 degrees N (the main focus of Milankovitch’s calculations)the first graph, ‘A,’ represents Stockwell and Pelgrem (the latter, presumably Pelgrem’s calculations from 1904 which Milankovitch utilized)second graph, ‘B,’ replicates Leverrier (19th century) and Miskovitch’s  “astronomical solution.”  graphs correspond to each other in indicating similar timing of peaks and troughs; the latter indicating cooler epochs are shown as shaded notches pointing downwards – most marked at 230,000 and 200,000 BP. A smaller depth of trough is shown at 115,000 and at 75,000 BP. At 25,000 BP, there is a very little notch (though it is now known that the climate was moving towards the Last Glacial Maximum which ended c 18,000 BP). Likely Croll’s mistaken supposition that the last Ice Age began some 250,000 years ago and ended at 80,000 BP was based upon the comparative depths of notches for cooler conditions at 250,000 and 200,000 BP.

Looking at Part C, Berger’s calculations for mean irradiance the past 600,000 years, I select the time frame from 130,000 BP to the present. extremely high amounts of sunlight/heat at 130,000 BP during the last interglacial epoch known as “the Eemian.” Then he line descends sharply to lows at 115,000 BP Loutre  higher vegetation levels (which presumably were associated with the luxuriant growth of the Eemian) could have prevented the inception of another ice age at 115,000 BP. his is an important consideration for today’s concern regarding  CO 2 concentrations. During present interglacial, carbon concentrations have now reached 390 ppmv, versus the levels of 270 ppmv during the Eemian.

Berger’s graph line rises again at 100,000 BP, after which up and down lines show that at 80.000 BP there was still ample sunlight at higher latitudesAt 70.000 BP, the Last Ice Age must have gotten underway. The obliquity of the axis was closer to upright at 22.5 degrees off vertical, reducing amount of sunlight reaching polar regions. Although eccentricity remained fairly high at 0.0degrees, perihelion was in winter and aphelion in summer, the latter effect tending to  new ice levels from completely melting away during summer months.

a global crisis. Sometime around 75,000-70,000 BP, a super-volcano explosion took place in the Far East, on Toba, causing a world-wide winter. As vegetation died, there was famine, and many early human groups died out. Likely that volcanic event was a primary factor in triggering the onset of the Great Ice Age which, for the most part, endured until the very deep freeze of the Last Glacial Maximum, c 20,000 BP. We may also note that, at 50,000 BP, the obliquity of earth’s tilted axis was at its smallest angle from the vertical, at 22.1 degrees, further reducing the receipt of sunlight at the high latitudes

Some 40,000 years ago, paleo-climatologists speak of a period of fluctuating temperatures, the saw-toothed episodes of weather changes. Environmental Change: The Evolving Ecosphere, speaks of  “stadial-interstadial climatic shifts known as Dansgaard-Oeschger cycles of short-lived climatic deteriorations” throughout the last glacial epochthat, “rbital forcing is unlikely to drive these swift climatic changes”We can suppose, however, that the short-lived weather fluctuations often generated wetter and more moisturous conditions producing abundant snowfalls, converted over time into ice fields.

Returning to Loutre’s article, Figure 4 (2003:999), taken from Berger, separates out the orbital features of eccentricity, climatic precession (opposite seasons of perihelion and aphelion), and obliquity of Earth’s axial tilt. What can we read here of the highlights of the Last Interglacial, the Eemian, at 125,000 BP? At 130,000 -125,000 BP, eccentricity was high at 0.04 degrees (compared to present eccentricity at 0.015 degrees). Warmer summers would have been the case with perihelion in summer, and aphelion in winter. The obliquity of earth’s axial was pronounced c 24.5 degrees, exposing higher latitudes to maximum amounts of sunlight (compare to today’s obliquity at medium range of tilt, 23.5 degrees).  Even though at 115,000 BP, obliquity reached an extremely reduced tilt at c 22 degrees, eccentricity of orbit remained high which would have helped to sustain higher temperatures.

Loutre’s Figure 7 (2003: 1003) shows estimated ice volumes connected to ocean core data regarding the oxygen isotope records. It shows the most increase in ice volumes at 140,000 BP (prior to onset of the Eemian) and then at 20,000 BP – the Last Glacial Maximum. Loutre concludes: “This model confirms that the orbital forcing acts as a pacemaker for theglacial-interglacial cycles and that climate response to orbital forcing isamplified by CO 2.” Elsewhere, Loutre comments upon the extended epoch of warmth during the Eemian epoch

” At the last interglacial, some 125 ky BP, modeling experiments led to

warmer conditions, especially in the high latitudes, reduced sea-ice,

enhanced northern tropical monsoon, and northward displacement of

the tundra and taiga…However, the strong cooling induced by changes

in the orbital parameters at 115 ky BP are not sufficient to initiate

glaciation, at least if vegetation changes are not taken into account.”

Anatomically Modern Humans South Africa during                                              

            Several years ago, during classes at the University of Toronto on

paleo-anthropology, we students learned of the exciting new reports from archaeological sites in South Africa. The findings at Blombos Cave and Klasies River point to the last interglacial, the Eemian, as a period that favoured exceptional advances for anatomically modern human beings, our inventively-minded, Homo Sapiens ancestors. Towards the end of the last Interglacial, c 110,000 BP, in cave sites at Klasies River, Eastern Cape, South Africa, archaeologists found specimens of teeth and jawbone fragments belonging to a modern human. They carefully measured the dimensions and wear on different molars and one incisor, finding that some appear smaller, more “gracile” or delicate-looking as the term implies. Other specimens are larger and more “rugged,” but still within modern ranges for size. Rightmire and Deacon ‘New human teeth from Middle Stone Age deposits at Klasies River, South Africa,’ deduce that this population exhibits what they call “sex dimorphism The size difference are between male and female remains of people who towards end of Last Interglacial.

Blombos Cave situated along the southern coastline of South Africa, dated 100,000 to 70,000 years ago, (lowest date-levelso far at 130,000 BP) found only seven human teeth (not described). But, here, the cultural remains tell the story of those early modern humans making new adaptations in this ideal beach-setting next to the Indian Ocean. At that time, the sea level was much higher and the cave opened onto the shores of the ocean where they foraged for marine foods like mussels and turtles, and adapted shells for vessels.

Since 1991, Blombos Cave archaeologists, led Christopher Henshilwood, have undertaken careful excavations, finding much use of coloured ochre for decorating stone and bone tools, perhaps body paint, as well perforated sea shells for ornamentation – altogether considered cognitive advances. Their diet was diversesea creatures like turtles, land mammals of different kinds, ostrich eggs and fish bones. They had begun to fashion nicely cut bifacial blades as spear points, leaf-shaped.

That interglacial epoch saw the beginning of the climate changed and deteriorated, they explored farther afield following continental coastlines. Some reached as far as the Middle East and south eastern Asia, ultimately reaching Australia some 60,000 years ago (thus escaping increasingly severe glacial conditions further to the north).

                Future Long Term Climate Projections: Berger and Loutre

      The mentioned A. Berger and M.F. Loutre of the Belgian Institute of Astronomy and Geophysics published an article entitled ‘An Exceptionally Lengthy Interglacial Ahead?’ in Science’s Compass, June 2008 ().  the common assumption held thirty years ago that interglacial interludes last about 10,000 years assumption was based on the approximate duration of last two interglacials.  understanding of the interglacial phases of the past Quaternary is now called into question.

Some 400,000 years ago, at the inception of the full cycle of variations in Earth’s orbit, there was a lengthy interglacial known as “marine isotope 11” which produced warm temperatures due to the particular astronomical forcings of that era. Berger’s diagram, Figure 4, showed that over the next 100,000 years from the present arth’s eccentricity of orbit will hardly rise beyond today’s very slight eccentricity. astronomers assert that, over the next 25,000 years, arth’s orbit will be moving towards almost perfect circularity at 0.00. such low eccentricity perihelion and aphelion times of the year will not bring Earth as close to or as far from the sun as took place in the past. The impact of such minimized eccentricity of orbit on Earth’s seasons will produce less extremes of cold and heat.

Naturally, Berger and Loutre discuss the ongoing issue of CO 2 concentrations, of such concern today, noting, as mentioned, that the current CO2 at 370 ppmv is higher than the 290 ppmv during the Eemian. They suggest these global warming trends due to human causes will need to be factored into any projections for future global temperatures.

                       Short-Term Variability in Weather Conditions

          Unusually, March 17th, 2015 brought a dazzling display of Aurora Borealis (Northern Lights) to this Toronto region, mid-latitude 43 degrees, even as Aurora Australis lit up the night skies over Australia and New Zealand, 40th parallel. One would not expect to see in one’s lifetime such a spectacle of green, red, orange and blue dancing in wavy patterns over the northern part of the night sky.

These few years of unexpectedly glacial winter conditions, marked by the Aurora Borealis appearing in Toronto environs, cannot be easily explained by Milankovitch factors. Another explanation is needed for shorter term weather conditions.

        Journal of Atmospheric and Solar-Terrestrial Physics‘A shared frequency set between the historical mid-latitude aurora records and the global surface temperatures’critiques the current anthropogenic (i.e. human-caused) global warming theorinclined to dismiss astronomical forcings of the climate system, such as the Milankovitch model proposed. He comments upon uncertain theorizing regarding “the aerosol forcings and climate sensitivity to GHG changes,” as well as, “their inadequate modeling of the cloud system, ocean dynamics and the biosphere”

In this paper focusing on mid-latitude aurora events, Zafetta synthesizes aurora frequencies with periodicities of sun, moon and the major planets, Jupiter and Saturn. He proposes a series of shorter-term temperature conditions in Earth’s climate, which fluctuate between warmer and cooler phases, and which periodicities closely correspond to the other cycles within our solar system”

Zafetta mid-latitude aurora events (such as happened in Toronto at 43 degrees latitude on March 17th, 2015) records kept since the 1700’s. He explains these events the excessive electrification of Earth’s electro-magnetic field due to incoming cosmic radiations and charged particles in the solar wind whenever they enter Earth’s electro-magnetic field with greater than usual penetration.

This is not a completely novel theory. Roy Gallant (Earth’s Changing Climate, 1979:33-35) discusses flares emanating as storms on the sun, extending over enormous distances from the sun, which predominate over an elevenyear cycle – the Jupiter effect and gravitational fields. He refers to a Manhattan observatory  1946 that “magnetic storms” could interfere with radio communications.

Zafetta explains that if Earth’shappens to be weak,  bombardment by electrically charged particles reaching Earth from solar eruptions or the solar wind. Normally, aurora displays are a remarkable feature in high-latitude polar regions butfails to keep the cosmic radiations at bay, they stream down into the mid-latitudes

As mentioned, Zafetta finds that mid-latitude aurora events (he also takes into account high-latitude aurora patterns) have a periodicity that is similar to other cycles in the solar system, most importantly whenever the Sun is reacting to presence of Jupiter and Saturn. Thus he suggests “a possible planetary origin of the aurora, and temperature oscillations” in Earth’s climate system. He refers to others who have related the physics of such relationshito the effect that”…. solar variation can be partially driven by the planets throughgravitational spin-orbit coupling mechanisms and gravitational  tides”

Jupiter’s orbital cycleequates closely with the Sun’s sun-spot cycle, c 11years. Jupiter with a gravity of 2 compared to Earth’s1 (the Sun at 27 times Earth’s gravity) generates the strongest gravitational tides when its orbit takes it most closely to the sun, but especially when conjunct with Saturn on the same side of the sun.

Zafetta (2011:151) combines Jupiter and Saturn as follows: Jupiter’s siderial period is 11.862 (similar to the sun), while Saturn’s is 29,457 periodicity; thus, their combined orbits when repeated or doubled approximates 59.6 to 61 years. There is the sunspot cycle, doubled, at c 22 years. he significant periods to bear in mind are: 10-11, 20-22, and 50-63 years. He relates certain solar-lunar cycles, e.g., the Saros lunar eclipse cycle of 18.03 years, to periodicities of mid-latitude aurora events.

Richard Huggett (1997: 40-43) covers these , beginning with the sunspot cycle, averaging 11.14 years; the whole “heliomagnetic cycle” is doubled at 22 years and involves the reversal of the sun’s magnetic field, which, he says, “influences cycles of terrestrial magnetic activity and the atmospheric production of isotopes.” In his section on planetary cycles, Huggett says: “… the jostling of the planets and the sun leads to variations in the Earth’s orbit.”

Zafetta suggestmid-latitude aurora eventcharacterized by frequencies a Soli/Lunar tidal cycle of 9.1 year period, the motion of the sun relative to the barycentre of the solar system, and overall periods of 10-10.5, 20-21, 30 and 60-62 ranges of years. proceeds to relate cloud system on earth to such astronomical cyclesassert “there exists anharmonic modulation of the electric properties of the earth’satmosphere that modulates the clouds and, therefore, theterrestrial albedo” He proposes that the level of atmospheric ionization and the global electric circuit must be involved somehow in regulating the cloud system. He further that cloud acts as an albedo mechanism in itself, helping to cool the Earth.

In keeping with the above 60 year full cosmic cycle, which Zafetta divides into 30 years of cooling and 30 years of warming,dentifies the following weather phases: a warming period from 1850-1880, a cooling from 1880-1910, a warming from 1910-1940, a cooling from 1940-1970, and a warming from 1970-2000. He speaks of a small cooling since 2000, which may last until 2030-2040.

                     Polar Vortex shifts impacting on mid-latitude weather

            Zafetta’ssuggestion of a cooling phase from 2000-2030-2040 would have seemed nonsensical during the last several years of record high average global temperature – until now. We have experienced unusually deep cold during the past two winters in northeastern mid-latitudes, North America.

so-called  “Cold-Snaps” of late have evoked discussions of the increased waviness of the northern Jet Stream, now dipping further to the south at times. Meteorologists regard this phenomenon as a response in some way to rapid Arctic warming. Jennifer Francis of Rutgers’ University observes that “very wavy jet stream patterns have been occurring since the 1990’s,” accounting for the recent weather extremes in North America.

More about “The Apocalypse” and Long Term Perspective on Earths Climate Changes

               More about “The Apocalypse” & Long Term Perspectives

                               on Earth’s Climate Changes

        Introduction to Part One: Cosmic Theories among the Ancients:

        The Darkness of Night, of the Cave, giving way to the Light of Day

        This chapter is inspired by a course I took with Professor Alexander Jones of the Classics Department at the University of Toronto. It was titled, ‘Ancient Naked-Eye Astronomy’  and addressed cosmological systems of ancient cultures. In the following pages, I would like to address the question: what religious constructs lay underneath those cosmological systems?

         What do we make of the ideas of the ancients about the heavenly luminaries that we can pick out in the sky by night and day, some apparently fixed and others pursuing changing paths like the sun, moon and planets? More especially, which emerging new ideas about these celestial patterns evoked the “apocalyptic-like concerns” of the ancients, or, actually lifted up their spirits?  What archetypal themes did the ancients inherit from their predecessors who had inhabited different epochs and different climate conditions?  What kinds of fears, concerns and preoccupations underlay their perspectives on the cosmos?

comparand contrast the thinking of the ancient Egyptianswhose cosmic ideas greatly influenced the later Greeksand earlier Paleolithic-cultured peoplee cannot fail to view the Great Pyramids at Giza as replicas of the mountain caves that had served  as homesteads, burial places and even art galleries.

Khufu’s Great Pyramid on the Giza Plateau at Cairo, dated mid-3rd millennium BCE, was constructed with a labyrinth of interior corridors that led towards the king’s burial chamber deep inside this man-made mountain. Other narrow openings angled upwards from the burial chamber towards exits in the walls. Undoubtedly, these openings were meant to encourage  the king’s spirit to focus upon certain fixed stars in the northern vault of the night sky. It was expected that, if the king’s spirit w successful in reaching those stars, he would reign there among the gods ever after.Professor Jones explaoriented by its foundation walls towards those little stars spinning about at the top of the night sky.

      Later New Kingdom pharaohs (late-2nd millennium BCE), such as Ramses IV, whose burial chamber I visited by descending a stairway from the upper paths of the Valley of the Kings near Luxor, were in rock-cut, underground tombshe ceiling overlying Ramses IV’s tomb chamber offers a splendid vision of the night-skypainted a dark colour interspersed with golden stars.

What I learned in Professor Jones’ lectures was that Khufu’s Pyramid is remarkable in that, in 2550 BCE, the builders were able to orient the foundation walls so precisely, especially towards True North. They might have used the sun-shadow-stick, the gnomon, set up at high noon to divide exactly east from west, thus north to south. Or, they might have used paired stars at night trying to determine the north celestial pole as the mid-point of the stars that spin in a little circle around the pole: Professor Jones said:”From cryptic remarks in funerary texts, it was intended that the spirit of the king was to project outwards, towards the north of the region of the sky where the stars never set.”

Such skill in building, though later attributed to Pharaoh Khufu himself, was more likely the expertise of the priests of Amun-Ra, the ancient sungod, who were attached to the nearby solar temples. Later, the Greeks called this place to the north of Cairo “Heliopolis,” meaning “City of the Sun.” The architectural task of those priests was to build a tomb for the king, of such grandeur that his spirit would inevitably rise up into the stars and dwell there for eternity.  Such a theme, an immortal life awaiting the human spirit or soul up in the glorious stars, was taken up by the Greek philosophers later, like Socrates, who, before his death, spoke of the soul’s great desire to reach its original homeland up in the stars.

Without going into detail, I can refer to Erik Hornung’s The Ancient Egyptian Books of the Afterlife (1997), which literature reveals their grave concerns regarding the fate and destiny of the personhood in the realms of the next life, whether pharaoh or ordinary citizen. As if contrasting their religious focus on the after-life, the ancient Egyptians loved their home-lands along the Nile River which annually was flooded with waters from the southern mountains to irrigate the soils of the lands all along the Nile River.

       

The Aztecs of pre-columbian times imaginatively proclaimed the sun at the centre of their earthly existence and documented their vision in the Aztec Calendar-Stone. Aztec priests informed the European newcomers of a legend regarding “the Fifth Sun” in which they lived. One of the early Aztec rulers visited the great monumental pyramid complexes at Teotihuacan, meaning “City of the Gods” (dated 1-550 CE). The Aztecs excavated underneath these great monumental pyramids that supposedly honoured the Sun and the Moon, unearthing marvelous works of art and culture.

They told the Spanish priest, Sahagun, the story of how Teotihuacan had been the place where the “Fifth Sun” was created: this was the cosmic era in which the Aztecs believed they were still living. The Aztecs said: “… when all was in darkness, when yet no sun had shown and no dawn had broken … the gods gathered themselves there at Teotihuacan… ” A long tale ensued of how the gods sacrificed themselves in the fire and under the knife to give energy to the sun (Carrasco, The Aztecs 2012:25-27).

the sacred mounta(th Egyptians) PaleolithicI have imagined I am wandering inside a shadowy moutain, following the contours of its winding corridors – searching for what? Amazingly, suddenly I see up through narrow rocky walls a column of Light pouring down. If only my spirit could simply rise up into that exit out of this interior world of rock-hewn Darkness! This is what I imagine our Paleolithic ancestors, exploring the seemingly endless winding tunnels inside a mountain, with a little oil lamp or torch, came upon as a of light high up above them. Along the way, they painted with charcoal and natural pigments images of the world that lay outside of these mountain caves and tunnels, theanimal wonders of landscapes filled with living creatures moving about under the glorious light of the Sun – the dream-landscapes of Paleolithic hunters.

also

As we shall see, the key image that lay at the centre of Greco-Roman astronomical thought was the “wheel,” which they envisioned as the Great Celestial Wheel whirling around the earth’s horizon.

The Sun, the most powerful image in our heavenly sights, revolves throughout the solar year shifting from its most northerly station in summer to its southern limits in winter.

                       “Lands of the Midnight Sun” to the North

          Six thousand years ago, the global temperatures of this interglacial epoch opened up northerly latitudes to agriculture. A little later than 4000 BP, settlers from southern parts of the British Isles arrived in the Orkney Islands to the north of Scotland. Jutting out from the main island is an isthmus of grasslands lying between two bodies of water, Scottish lochs. Around 3500 BP these green pastures attracted some cattle-raising people call “Picts”. Indeed, cattle bones serve in part for the dating of World Heritage site on this isthmus, “he Ness of Brodgar” I take most of this information from a BBC television   TVO December 2014

The Ness of Brodgar is a collection of what remains of stone-wallstructures which archeologists suppose was sacred iconography.  which were not simply established as adjoining households, but as a kind of assemblage of little temples.

Near the Ness of Brodgar stands another construction known as  “the Ring of Brodgar”huge stones set upright in the soil to form a stone-circle, stones likeldeposit by glaciers during the Ice AgeArchaeologists and visitors marvel at the skill and energy that motivated the settlers in transporting such large stones which archaeologists suppose were used for marking out time.

Wikipedia informs us that the Ring of Brodgar served as a ceremonial centre from 2600-2000 BP of megalithic building in different parts of the world (see the date of the Great Pyramids at Giza, 2550 BCE). The of Brodgar on the Orkney eemingly the stone-processional way at Avebury in Wiltshire in southern England and the monumental Stonehenge.

2200 BCE, there was world-wide drought. Soon the megalithic builders forsook these heavy labours as agricultural failures set in, and they could no longer place confidence in the gods of the cosmos to whom these grand constructions had paid such grateful reverence.

An Orkney archaeologist on the fore-mentioned television program interprets the Ring of Brodgar as having  by the light of sunset between two particular stones.Similarly, today Stonehenge in Wiltshire is understood as constructed so as to the same date of .

Orkney archaeologists, perhaps thinking Egyptologists, suppose that the Orkney Island megalithic builders erected stone circles that looked up to the immensity of the skies. They had begun to think of the spirits of the departed rising up into those heavens illuminated by myriad points of star-light. Earlier in Age, they built barrow-tombs in which they would inter the bones of departed ancestors, the mounds serving as landmarks of prior settlemen

One thinks that the Picts who came north into the Orkneys were on the move. What impressed them with this new landscape was that during warmer months, then as now, this northerly region was veritably a “Land of the Midnight Sun.” They had discovered a land blessed with lengthy days of sunlight. On Orkney today, located at 59 degrees north latitude, during summer months they are blessed with as much as eighteen hours of sunlight a day, only four hours of near-darkness at night.

he visitor to the Ring of Brodgar might wonder at skill in determining the time of winter solstice , one wonders why  Did th reveal something of their fears, or hopes and dreams? Were they petitioning the gods to nsure that the hours of daylight would progress towards the summer’s abundance of daylight?

As we shall see later, part of the mystery of the eighteen hours of sunlight in the Orkneys lies in the modern discovery that the earth’s axis is slightly tilted away from upright (its present angle at 23.5 degrees is mid-way between limits of 22-25 degrees). Whenever the axis is more vertical, the northern hemisphere are encased in ice, which was the case during the past lengthy Ice Age. The Orkneys at 59 degrees north lie almost parallel with the southern limit of Greenland, ranging from 60 degrees north, still heavily glaciated today.

                        Late Bronze Age Scandinavians’ “Sun-Wheel” – Symbol of the

                                       Changing Seasons of the Solar Year

        In Rock Pictures of Europe (1967),  reproduces numerous examples of Scandinavian rock-engravings, mostly found in Norway and Sweden. On the flat surfaces of glacial-smoothed stones, the drew pictures of gods. their daily life such as the axe ships. The distinctive shapes of these ships enable dating to different Late Bronze Age periods first phase from 1600-1400 BCE and the second from 1400-1200 BCE.

In the second phase Kuhn illustrates pictures of men holding the “sun-wheel” in their hands  “The Wheel is one of the commonest of the signs on the Scandinavian Bronze Age rocks” There are examples of a solar disk depicted upon wheels or upon a pole; of human figures pulling or turning solar disks, and of wheels standing tall over their ships. One such picture shows a cross inside a circle (like the Orkneys); here, this universal symbol is raised up on a pole over a boat.

Kuhn relates the imagery of the sun-wheel enclosing a cross to ancient Mesopotamia. He refers to Sumerians in the 3rd millennium BCE, who, he says, used four known planets to serve as “the four-boundary marks of the cosmos, to divide the year into four seasons.”

For the ancient Scandinavians, the sun-wheel would have represented the warmer seasons of the year when they set sail on their Viking crafts to explore surrounding lands and seas. Did they navigate by the sun’s daily movement from east to west? suppose that around summer solstice, when the sun is more directly overhead and the hours of daylight at their maximum,  to explore more of these northern Lands of the Midnight Sun.

In the northern Scottish district of Aberdeen today, descendants of Vikings who arrived in Scotland during the 8th-9th centuries CE, celebrate “Hogmanay,” the Scots’ New Years’ festival. They employ the antique symbol of the Scandinavian sun-wheel. In Aberdeen, the men of the town, dressed in Viking garb, swing fire-balls around, as they parade towards the harbour where the fireballs are cast into the water – re-enacting the sun sinking below the horizon for most of the day. What of their concerns? Surely it was that thehoped to see when the sun had shifted to its most northerly point the benefits of exceptionally long, sunlit days.

                Gudea’s Dream of the Ancient Mesopotamian

                                       Flood-God, Ningirsu

        Whether Herbert Kuhnis correct or not in assigning the design of the cross within the circle, to the ancient Sumerians, 3rd Millennium BCE, as a symbol of the changing seasons, I do not know. But, I can surmise why Kuhn’s thoughts drifted towards that periodI prepared the dream-vision recorded by the neo-Sumerian king, Gudea of the city-state of Lagash in southern Mesopotamiais dream of the revival of the springtime flood the “Spring Equinox” as the astronomers call it.

hat the ancient Sumerians had a concept of the annual floods as an annual springtime occurrence when meltwaters from the northern mountains poured down through the Tigris and Euphrates rivers into the plains of southern Mesopotamia. For later Babylonians, springtime was the occasion for a great religious celebration– e.g. the Akitu New Year’s Festival. In a temple atop the leading ziggurat, a kind of iconographic mountain whence their spring floods arose in the northern mountains, the king would couple with a priestess for the sacred Hierosgamos – the union of male and female energies of new procreation in nature. To the Mesopotamians, the annual springtime flood was important their dependence on the rivers for , swelling and overflowing bankscanals  away surplus waters into fields.

Gudea21412122 BCE (Georges Roux, Ancient Iraq Penguin Books, 1993)of the Third Kingdom of Ur, King Ur-n-Nammu’s period of rule at Ur (2112-2095 BCE, Roux). During that late-Sumerian era, the huge Ziggurat of Ur, still standing but crumbling away, was a major site of religious observances revolving around the days of lunar phases. On certain days marked by lunar phases, they sacrificed animals at the ziggurat to the gods presiding over the prosperity of the land.

Gudea’s mysterious dream-vision suggested to the king himself that he Indeed, he  temples throughout his kingdom of Lagash. In the  of a leading temple built by Gudea, archaeologists found the magnificent ‘Hymn to Ningirsu.’ It is recorded on two clay cylinders, written in cuneiform by some temple poet. This artistic work reveals that the Sumerians, who originally invented writing to keep track of the increases in herds and harvest stores were now creating sacred literature. Gudea’s scribe gave poetic voice to the main divine figure in Gudea’s vision, the flood-god, Ningirsu.

In Thorkild Jacobsen’s words ( The Treasures of Darkness: A History of Mesopotamian Religion, 1976) Ningirsu was “the power in thunderstorms and the yearly flood when the Tigris was swelled by its rain-fed mountain tributaries.”    Gudea describes another cosmic figure in his dream: “… a warrior who bent his arm holding a lapis lazuli [blue like the night-sky]plate on which he was setting the ground plan of a house…Seeking clarification of what  elements in his dream meant, Gudea sailed along the Ninagen canal to the shrine of Nanshe for interpretation. He told Nanshe“There was someone in my dream, enormous as the skies, enormousas the earth was he. That one was a god as regards his head, he wasThunderbird regarding his wings, and a floodstorm as regards hislower body. There was a lion lying on both his left and his rightside. He told me that his house should be built [but] I did notunderstand what he intended.”

cholars speak of that era as undergoing environmental desicationhe Tigris was failing to rise at the annual spring inundation. According to Frankfort the god Ningirsu as reassuring Gudea:

“I will call up in heaven a humid wind

It shall bring thee abundance from on high.

And the country shall spread its hands upon riches in thy time.

Prosperity shall accompany the laying of the foundations of my house”

Gudeapersonal god  that: “… like the sun he rose for you out of the horizon” (Kramer 1969:5). Also in dream, saw a woman, who “held a tablet reed of shining silver in the hand, placed a star tablet on the knee, takes counsel with it” Nanshe describes the woman in his dream as her sister Nidaba, “… who has called him to build the house in accordance with the holy stars”

                                   Ancient Babylonian Astronomy

        In Professor Alexander Jones’ lectures on Neo-Assyrian-Babylonian astronomy he made it clear thathey used basic timing devices and calendar divisions to map the movements of celestial bodies,laid the foundations for later Greek astronomy.

What stands out in the several centuries of neo-Assyrian into Babylonian observations of the celestial bodies is that they kept a careful watch for exceptional cosmic events, particularly full moon eclipses. Their astronomers, sky-watchers employed in observatories throughout the land, were expected to produce prognostications to the king regarding the fertility of agricultural crops and the economy in general. Since they regarded the sun, moon and visible planets as gods and goddesses, certain celestial events became for them the “signs” of the intentions of the divinities. Over the centuries they developed tables of omen interpretation which they would consult to describe the effects of specific astronomical patterns and relationships.

The Mesopotamian Astrologers’ Universe: Celestial and Terrestrial (Canadian Society for Mesopotamian Studies, 1992: 33-44) :

“To a Neo-Assyrian living in Nineveh around 700 BCE, the sun, moon and

planets were luminous entities whose motions indicated the state of mind of

the gods in heaven – gods whose will affected every event on earth. The

astrologer was the official state interpreter of the will of the gods made

manifest in the heavens above.”

The Babylonian luni-solar calendar was based upon the 29 and one-half day lunar month (not quite 30 days), which presented a problem in predictability for they could not always observe the new crescent moon in daylight. The first day of their month was taken to be when the new crescent moon was visible in the sky to the professional sky-watchers. Subsequently, on the 14th day of that month, and the days surrounding it, at sunset in the west, they would look to see the full moon rising above the horizon in the east. They would have kept an anxious watch in case it turned out to be a full moon eclipse – for it could bear some kind of ominous meaning.

Over the course of the centuries Babylonian astronomers finally discovered that full moon eclipse events would fall at certain patterned intervals (eg every six months but with gaps) during a cycle that amounted to 18-19 years – a great discovery! After this cycle was completed, they realized the very same pattern of full moon eclipses was repeated on certain dates. According to Professor Jones, the Egyptians and the Hittites borrowed this knowledge of the 18-19 year pattern of full-moon eclipses from the Babylonians.

The Babylonians saw that usually a year contained twelve lunar-months; but sometimes thirteen full moons would occur in a solar year. They constructed their solar year of twelve months, roughly 30 days each, amounting to 360 days for the year, to which they added extra days.  The 360 days of the yearly calendar formed the degrees of their zodiacal circle. Later the Greeks and borrowed stellar constellations known to the Babylonians: wheat sheaf, bull, twins, goat-fish etc, By dividing the zodiacal circle into twelve sections, each of 30 degrees, the Babylonians had a sky map for observing the movements of the sun, moon and planets against the star-filled constellations.

The Babylonians calculated celestial positions of the major bodiesby arithmetic, e.g. using fingers/cubits to measure distance from some bright star. They used water-clocks to measure the time in hours, minutes and seconds, as  the movement of the moon . Towards the end of Babylonian astronomical practice, 300 BCE, likely under the influence of the individualist philosophy of Hellenism, the Babylonians constructed birth horoscopes, which astrologers have done ever since. The positions of sun, moon and planets in various zodiacal signs gave some predictive meaning to the person’s destiny in life; they would note,  the position of Jupiter for riches.

Plato’s Cosmic Myth about the Afterlife, the Tale of Er

      Towards the end of The Republic (Book X, 1991, translated …),  recorded Socrates’ story of the soldier Er. The seemingly lifeless body of Er lay on the battlefield for several days. When they finally placed him on the funeral pyre, Er came back to life and told them of the journeying of souls in the afterlife – a story clearly resembling a Near-Death Experience! Most of Er’s initial account was of souls entering the afterlife to different kinds of judgment, doors opening to doom, to heaven, or to the necessity of rebirth into earthly life. Er described an intermediate place, a meadow where new souls engaged in festivities for a time, conversing with others in remembering their earthly lives. Among them were some heavenly souls, clean and bright, who had come down to share with them their experiences of “heavenly delights and inconceivable beauties.” Nevertheless, some of the newly arrived souls learned they were to prepare for their re-entry into earthly existence.

In a different place after journeying for several days (1991:391-392), the newly arriving souls saw a column of light extending all the way from the higher heaven down through to the earth. It resembled the colours of the rainbow. Some souls were immediately called up into the realm of that higher light, and others waited to see what else would happen. In the midst of the light, they saw the ends of the chains of heaven let down from above Socrates : “This is the belt of heaven which holds together the circle of the universe.”

Esaw that from the ends of the chains dangling from heaven, the “spindle of Necessity” extended, “Necessity” the name of a goddess. The spindle, or whorl, like the weaver’s tool, was hollow, and within it, several whorls fitted of diminishing sizes. The seventh, the sun, is the brightest; the eighth, the moon takes its light from the sun; the others are differently coloured as Saturn, Mercury, Venus (whitest), Mars (reddish), and Jupiter.  The whole spindle revolved in one direction, but the seven inner circles moved in the other direction. The spindle turned on the knees of Necessity, and upon each circle a siren hymned a singing tone – the harmony altogether of the planetary spheres.

Lengthy passages follow describing the souls’ choosing among different samples of life. Then the returning souls were passed into the guiding hands of the goddess-fates and passed beneath the throne of Necessity, before re-entering earth, having forgotten everything they had experienced and seen in the afterlife.

The History and Practice of Ancient Astronomy (1998:79-83), illustrates a Greek astronomical instrument called “an armillary sphere” t has a fixed outer wheel and inner rings that are moveable in the opposite directionThe armillary sphere reproduced by Evans was used by astronomers to determine latitudes and longitudes. There is the outer, fixed greater celestial circle, which has an “equator” divides the whole sphere in halves. The earthly sphere is at its centre and there are several rings up and down indicating latitudes. The longitudes are read on the outer circle, divided into 10-20 degrees the coordinates of the celestial positions.

      Evans  the “craftsman-god” created the universe in two large circleshe daily motion from east to west, which is shared by the heavenly bodies, is the ‘master revolution.’ A second circle, the ecliptic, moves in the contrary direction inside the larger circle. Evans : “There is no doubt, then, that Plato’s conception of the universe owed something to the concrete example of the armillary sphere”

The mathematician , associated with Plato, devised a complex visual diagram of “nested spheres,”Platospindle and interior whorls. Eudoxus used this model, according to Evans, to reproduce variations in speed, stationary points, and retrograde motions characterize the planets.Aristotlethe celestial bodies like planets should be viewed as proceeding in constant and uniform motions. Plato’s great myth of the lost Atlantis

                                           Myth of Atlantis

            In Plato’s time, thinkers were influenced by certain Egyptian ideas about longrange cosmic irregularities, ideas which Solon brought back to Greece. In Plato’s Timaeus, Critias recounts  Atlantis swallowed up by the sea.  9000 years ago modern historians suppose is a mistaken chronology likely, the tale about Atlantis’ destruction referred back to the volcanic eruptions on the island of Santarini, some 900 years earlier, now dated to the mid-15th century BCE.

When Solon was visiting the Egyptian Delta he encountered a priest who said to him: “You [Greeks] are all young in mind, you have no belief rooted in old tradition and no knowledge hoary with age.” The priest talked of many destructive calamities by fire or floodreferred to the Greek legend of Phaethon, “child of the sun.” Phaethon was said to have harnessed his father’s chariot but was not able to keep it from going off course, because, said the pries “… [this] is a mythical version of the truth that at long intervals avariation in the course of the heavenly bodies and a consequence of widespread destruction by fire of things on earth”34035)

Solar Theory of Hipparchus and Ptolemy

(According to Bertrand Russell, Hipparchus “flourished” from 161-126 BCE and Claudius Ptolemy from 127-151 CE)

The following observations on the importance of the theories of Hipparchus and Ptolemy are taken from Professor Alexander Jones’ classroom teachings on ancient Greek astronomyWhat fascinated me at the time was  the Greeks’ conception of the Great Celestial Wheel with its many arcs of planetary and stellar circles rotating round and round in an orderly fashion. there underlying concern that the heavenly bodies might depart at times from such regularity?

Professor Jones (Lecture February 25, 2002) introduced early Greek astronomy by describing how they viewed the heavens as a huge globe that was divided down the middle by the “ecliptic” (not the same as the terrestrial equator). This immensity of celestial wonders was pictured as surrounding the earth situated at the center of the globe. They viewed the multitudes of stars, sun, moon and planets moving in their respective circles through this “Great Circle” as they called the heavens around us. They would look for stars and star groupings rising above the earthly horizon – then descending below the horizon for a time – just as the sun disappears below the horizon during the hours of darkness at night. Some stars appeared to them not to move, but to spin in circular movements around the northern pole of the vault of the sky.

The Greeks saw that the sun shifts back and forth between its most northerly limit at summer solstice and its most southerly limit at winter solstice. They viewed the sun moving through the twelve zodiacal constellations of the Great Circle of the heavens, borrowing from their predecessors, the Babylonians, the design of a circle set at 360 degrees. Each constellation was assigned 30 degrees of the greater circle. But by their fairly exact knowledge of the number of days in the solar year, they had to fit these different dimensions together.

In 432 BCE, at Athens, two early Greek astronomers, Meton and Euctemon observed the time of the summer solstice as exactly as possible by the shadow-stick standing upright at the exact time when the sun’s shadow was no longer visible. According to Evans (1998:20) Meton’s name was applied to the nineteen year lunar eclipse cycle, which earlier had been discovered by the Babylonians. The Greek astronomer Hipparchus, acquainted with Babylonian data, was able to estimate the length of the lunar month with an error of less than one second, according to Bertrand Russell (1945:215).

Hipparchus, as Jones said to us, was trying to deal with the problem of measuring as accurately as possible the equinoctial points of the solar year, the beginnings of spring and autumn. At this time, the sun would intersect the ecliptic that divides the Great Circle. By their circular design of the 360 degrees of the Great Circle of the heavens, the equinoctial points of equal hours of daylight and darkness should have stood at right angles to the north-south solstices by observations of particular equinoxes Hipparchus found that the number of days from spring equinox to summer solstice did not match exactly the number of days between summer solstice and autumn equinox.

What this meant to a geometrically-minded Greek astronomer like Hipparchus was that the sun’s circular orbit over the course of the year could not be divided down into equal-sized quarters of a circle. Knowing of the Babylonians’ 19 solar years of lunar eclipses, Hipparchus did not suppose that the days of the solar year could vary from one year to anotherfigure of 365 days and a quarter minus 1-300th to the solar yearalways remain the same.

a print-out on the “Solar Theory of Hipparchus and Ptolemy Professor Jonespoints out that the time interval from spring equinox to summer solstice is approximately 94 and a half days. Yet, from summer solstice to autumn equinox it is approximately 92 and one half days.  the Greeks did to resolve this quandary was to situate the earth at a slightly different point from the centre of the sun’s circular orbit. Jones refers to this as “a simple eccentric model.” He says that they used trigonometry, as Hipparchus customarily did in order to measure specific angles. They could calculate the direction from the earth (a little off-center) to the centre of the sun’s orbit, and find the ratio of the distance between the earth and the sun’s orbit centre – to obtain the radius of the sun’s orbit. This complicated mathematical construction of angular relationships enabled Hipparchus to obtain a mathematical result that was less than one degree off.  Ptolemycreated solar tables based on “the simple eccentric model,” using Hipparchus’ observations of two equinoxes and a solstice.

                             Hipparchus on the Shifting of the Stars

      Hipparchus discovered that a star called Spica, which earlier astronomers, Timocharis and Aristyllos (ca. 290 BCE in Alexandria), had seen lying at 8 degrees west of the autumn equinox, 6 degrees west. According to Evans (1998:248), Hipparchus, working on the Island of Rhodes, could not be sure if this backward motion of one star was common to all star movements. Hipparchus’ book, On the Change of the Tropic and Equinoctial Points, was lost, but Ptolemy discussed Hipparchus’ finding regarding Spica. Ptolemy supposed it had been difficult for Hipparchus to generalize to other stars for lack of reliable longterm observationsother than Timocharis and Aristyllos.

Hipparchus’ discovery of the Precession of the Equinoxes, as it came to be known, was unsettling to leading thinkers in ancient civilizations. The Roman historian Pliny wrote that the appearance of “a new star” (nova stella) suggested, in Evans’ words (1998:247), “at least one startling change in the heavens.” Eventually, it became known that the equinoctial points shift backwards through the zodiac over time, by one degree every 72 years according to the theory of the Precession of the Equinoxes.

Ptolemy utilized the armillary sphere to assign coordinates for many stars. He realized he had to find a way to account for the retrograde motions of planets like Mars, stopping, slowing and going backwards for a period. He used the “Epicycle” model, attaching a little circle to the edge of the Great Circle (called the Deferent) to show that the planet often would go in an opposite direction. As Ptolemy did his calculations, he dispensed with the classical principle (Aristotle’s dictm) of constant motion. He resorted to constructing constant angles and achieved credible results for the movements of a planet such as Venus. According to Evans, Ptolemy’s idea of using constant angles enabled Kepler to undertake calculations for the elliptical order of the planet Mars Kepler’s great discovery. ompelled by the documented evidence of planetary observations to abandon the classical model of perfectly circular orbits.  his new geometric model of the “elliptically shaped  orbit,” he inscribed within this slightly altered circle the angular relationships devised by Ptolemy in Roman antiquity.