The Amateur Astronomer’s Introduction to the Celestial Sphere
Presented by William Charles Millar, MA, Professor of Astronomy , Grand Rapids Community College
About the Speaker
Professor Millar is Professor of Astronomy at Grand Rapids Community College and has been teaching the subject for over twenty years. He is very involved with local amateur astronomy groups and belongs to The Planetary Society and the Astronomical Society of the Pacific and has traveled to Europe and South America to observe solar eclipses. In addition to his degree in astronomy, he holds a Masters degree in physics from Western Michigan University. His book ,The Amateur Astronomer’s Introduction to the Celestial Sphere is an introduction to the night sky for amateur astronomers who desire a deeper understanding of the principles and observations of naked- eye astronomy. Professor Millar has taught for 26 years at GRCC; with subjects ranging from mathematics and physics to astronomy and is in the process of garnering his PhD.
About the Event
Minutes
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The next meeting will be on October 11. The topic will be Dr. Franklin’s Medicine; The Medical Legacy of Benjamin Franklin. It will be presented by Stanley Finger, PhD. He is the author of a book by the same title as this presentation and is a Medical Historian and Professor of Psychology in Arts & Sciences at Washington University, St. Louis. We thank FA member, Dr. Robert Collins, for setting this presentation up with his long time friend and colleague.
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The meeting for November 8 will be on the topic: Errors, Contradictions and Fallacies in the Bible and will be presented by C. Dennis McKinsey, author of the book: The Encyclopedia of Biblical Errancy as well as the book: Biblical Errancy, A Reference Guide. Both are published by Prometheus Books. Our meetings are broadcast on GRTV (local cable access channel 25) on Wednesdays at 10:30PM.
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The Michigan Atheists Convention in Livonia, MI will take place on November 17-19 at the Holiday Inn, Livonia West; 17123 Laurel Park Drive in Livonia, Michigan. Among other special guest speakers/presenters, will be the well- known State/Church separation advocate, Dr. Michael Newdow and our own FA member, Dr. Gregory Forbes. For more information: 313-388-9594 , or http://www.www.michiganatheists.org/. The Holiday Inn number is (734) 464-1300. The convention fee, which includes luncheon, is $42.50. One may attend just the convention for $39, or the luncheon only for $17.50. Early registration ends November 6. Hotel reservations may be made directly with the hotel for $89 (plus tax.)
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Presentation
Tonight’s meeting topic was: The Amateur Astronomer’s Introduction to the Celestial Sphere. It was presented by William Charles Millar. He is Professor of Astronomy at Grand Rapids Community College and has been teaching the subject for almost twenty years. Professor Millar is very involved with local amateur astronomy groups and belongs to The Planetary Society and the Astronomical Society of the Pacific and has traveled to Europe and South America to observe solar eclipses. In addition to his degree in astronomy, he holds a Masters degree in physics from Western Michigan University. He has published a book with the same title as tonight’s presentation.
His book is an introduction to the night sky for amateur astronomers who desire a deeper understanding of the principles and observations of naked- eye astronomy. It covers topics such as terrestrial and astronomical coordinate systems, stars and constellations, the relative motions of the sky, sun, moon and Earth leading to an understanding of the seasons, phases of the moon and eclipses. Topics are discussed and compared for observers located in both the northern and southern hemispheres. Written in a conversational style, only addition and subtraction skills are needed to understand the basic principles, while a more advanced mathematical treatment is available in the appendices. Each chapter contains a set of review questions and simple exercises to reinforce the reader’s comprehension of the material. The last chapter is a set of self- contained observation projects to get readers started with making observations about the concepts they have learned.
Professor Millar has taught for 26 years at GRCC; with subjects ranging from mathematics and physics to astronomy and is in the process of garnering his PhD, with his dissertation to regard supernova remnants. The above mentioned book, his first, was released this summer. He has traveled extensively to observe celestial activity from various places on the planet and is a member of the Grand Rapids Astronomical Association, comprised of professionals and amateurs, that meets at the Veen Observatory in GR to educate and enlighten the public.
Professor Millar’s presentation was very well received by this meeting’s attendees. The conversational style that his book was written in was apparent in his lecture as well. In his talk (in which he encouraged feedback and questions during it) he brought in historical events and personages and a highly satisfying survey of how humankind has interpreted the solar system and our place in it over time and then tied it all together with his central theme of the celestial sphere concept. Interestingly, this concept, created- and subscribed to- by the ancients as a very real material manifestation in space, yet abides in our own time as a teaching and observational tool, even as we have long left behind the belief in it as a physically existing structure. The latitude and longitude lines, time zones and even national border lines are some examples of similar conceptual delineations that have utilitarian value while not existing as tangible demarcations.
Millar showed that as we learned more and developed ever more complex and ultimately accurate descriptions of the relative motions of the night sky and our planet and position within the changing models, the celestial sphere model was modified and grew to accommodate more data, but never really left us. Professor Millar came—aptly—full circle in his presentation, beginning and ending with discussion of the celestial sphere in how humankind has interpreted its place within it. It was amusing to see how much complexity in the sphere model was due to tortured, long- enduring efforts to still keep humanity somehow at the center of universe. Each displacement brought new circles within circles to maintain and make sense of the new information while striving to nudge us back to the center. Besides the centrality issue, the spheres, being of the heavens—the place where the Divine Creator dwells- had to describe perfect circles; ellipses just could not be reconciled with the production of a perfect Being.
Like the biblical firmament, the initial celestial sphere concept of the ancients was viewed as a solid thing, almost within reach of the people. The stars were pinpricks in this solid from which the heavenly light from outside the sphere emanated. The sun and moon rode about on the moving concentric transparent sphere, with our Earth firmly fixed in the center. In the Bible (what Fundamentalist Christians wish to replace science textbooks with) God was a very big male who could step down from heaven, a ladder or tower could be erected to reach heaven, and the sun orbited the Earth as the moon does, and they were considered merely greater and lesser lights.
The modern model of the celestial sphere represents a rotational axis (Professor Millar brought with him such a hand- held celestial globe for our examination) and extends out four light years in radius. It also has a celestial equator and poles. The relative motions of the c. sphere and our Earth may be examined, as the transparent model shows a map of the perimeters of the sphere and what star systems may be observed at different places on Earth at different times. With the advent of computers, coordinates may now be fed in and the celestial cartography to show the area or object in space desired and where it exists and how it travels and behaves, relative to the observer. Eclipses, stellar motion, the appearance of constellations, planetary and cometary motion, etc. may be predicted from this teaching tool. Professor Millar also spoke of the geocentric parallax that occurs when one makes an observation of the night sky from one’s point of reference on the surface of the moving planet, rather than what one would see if one were in the mid-point inside of the Earth itself.
Returning to the vision of the ancient star gazers, Professor Millar spoke of the early idea of the Earth with a vault or domed ceiling; this was reasoned out to be supported by mountains as an opaque tent-like structure. The Earth, in this scheme, was perfectly fixed and the inside of the dome had bumps on the inside. The top of the Earth was where all life was; the bottom was presumably a barren rocky region. As the structure moved around the fixed Earth, the bumps scraped against the base of our planet. This abrasion generated sparks and heat from the friction so that its direction of travel caused the light warmth to rise in the east and cool down again as it traversed to the west, only to be re-heated as it slid and ground against the base of Earth again to repeat the cycle. Even today there still exists a Flat Earth Society. And as recently as the time when Robert Goddard was sending liquid fuel rockets far into the sky, there were people giving dire warnings about this. They were worried that the rockets would break the dome above us, letting all the air out and we would all die as a result. The concept of the universe by the ancients and those still remain willfully ignorant of modern knowledge, was of a very small place indeed. They could not imagine that the pinpricks of light were suns like ours and that not only was there a solar system with other planets besides ours in play, but that it was a heliocentric system and that those suns dotting the night sky could also have planets circling them. They could not have fathomed that these star systems were a tiny part of just one galaxy- where our solar system was indifferently placed in but one spiral arm of it- in a universe containing countless other such formations. Not only was geocentrism within a local system false, but the idea of centrality itself in the universe was also to be found incorrect.
The concept of concentric layers was one based on the idea of the rudest and heaviest of materials being at the core, with lighter, purer and more divine spheres or layers going out further and further. The Earth was, in this model, the heaviest and least perfect part of the construct, going up to the ether and finally heaven. From this we get the arrangement that may still be heard today of Earth, water, wind, fire, air and ether—progressing from the heaviest to the lightest elements before the purest of all… Heaven.
Professor Millar spoke to us about how we approached our view of Nature changed at about 600 BCE in Ionia. The Greek Empire’s town of Miletus, an ancient place on the western coast of Anatolia became one of the 12 Ionian cities of Asia Minor and an important center of philosophy and science. Magnesia, in central Greece, was the place for the discovery of lode stones. As a humorous aside, our presenter said that rather than think of Milk of Magnesia, one, in this case, ought to think of magnets from Magnesia. The word magnet, in fact, is derived from magnitis lithos, or magnesian stone. Magnesia was also one of the first places in Greece to be inhabited. It became an area where there was not only a healthy trade of goods but also of ideas. There was an openness to freethinking, where the role of the gods was diminished and natural forces and their effects upon the natural world started becoming apparent. This helped foster a need for a better way to conceptualize the world and develop a language—mathematics- to better render the concepts into a comprehensible format. Experiment and hypothesis ensued to test ideas, instead of thinking that it was all beyond humankind’s potential to investigate the world around them.
The professor next discussed Pythagorean Theorum (developed eponymously by Pythagoras)- dealing with the relation in Euclidean geometry among the three sides of a right triangle. Pythagoras lived on the Samos Island and found geometric proof for the theoretical constructs that had been around for a long time. Euclidean geometry, gets its name from Euclid of Alexandria, who was the first to show how earlier propositions could be fitted together into a comprehensive deductive system. Pythagoras’ school of philosophy helped nudge into existence an early solar system model, but instead of the sun at the center, there was a central hearth, and Earth had a counter- Earth also in orbit, which was thought to help with the eclipses. The sun itself was one of the orbiting bodies in this scheme, and in fact, the sun and moon, in the ancient world, were thought of as other planets. And because of the love of numerology, where certain number combinations related to certain words and powers, the number of celestial bodies in this system was set up to sum to a number pleasing to the people of the time.
Western astrology was developed out of the idea that what was happening in the skies directly impacted what occurred on Earth. The zodiac is derived from the idea of a circle of animals. Even when astrology is taken into times where people know of the heliocentric system we are a part of, it still places the significance of sky patterns into a format that can only be interpreted from an earthly vantage point—thereby making humankind of central importance and the Earth the sole planetary body of significance. From any other angle, the seemingly flat stellar depictions and starry journeys lose the morphologies seen from Earth. Astrology still harkens back to the flat dome or solid sphere that celestial patterns are writ upon for the benefit of human observers, influencing only them.
We still find in the names of the days of the week, the planet names (remember, the ancients saw the sun and moon as planets), such as Sun day, Moon day (Monday) and Saturn day (Saturday). Tuesday- Friday reflect the Saxon influence, but in the romance languages, the connection remains more apparent, with Mars day, Venus day, Mercury day, etc. being represented. These days of the week were named after the cycles of the gods, as it was believed that through their influence the growing seasons and other important changes occurred on Earth. While they may have been errant as to the actual causal effects, they did note the correlations between pattern changes in the night sky and what could be predicted to occur at those times—seasonal changes.
For two millennia the apparent retrograde motions of the constellations was vexing for the human observers. They detected a looping motion with the movement casting backwards. This was difficult to reconcile with the concept of the celestial sphere, where transparent solid globes held all the observed bodies on fixed tracks. But as more was learned, the celestial spheres grew larger and larger. Plato’s version saw a motionless Earth held in equilibrium by natural forces inside the sphere. This nullified any role for an Atlas or the back of a gigantic elephant, stack of tortoises, etc. to hold the Earth aloft. The universe expanded and took into account natural forces. As Dr. Forbes has noted in a couple of his presentations to the FA, the more that was comprehended of the natural workings of the world, the longer the lines became for the unemployment offices of the gods. Their own sphere of influence has steadily decreased for any operations in the natural world. Only by leaving them to their own devices in the supernatural realm—which is still undisturbed by knowledge of natural laws and actions- may they yet have abundant things to do with their infinite time.
The conceptual framework noted above was later revised into an Aristotelean one where sets of spheres were nestled together with a different celestial grouping on each sphere. More spheres allowed for the addition of different angles and rotations to carry the sky elements around the Earth. More spheres were also required to restore the aberrations in motion seen to the perfection longed for; this rose eventually to a model containing over fifty crystalline spheres altogether, moving one inside another.
This worked out for a time, until comets potentially threw a monkey wrench into the cosmic machine. These rebels seemed to iconoclastically burst through the spheres. All the ancients could do with this (to still preserve the idea of the crystalline spheres) was to attribute the cometary presence to atmospheric events.
Claudius Ptolemy was the next figure to be discussed. He was a Roman citizen of Greek descent living in Egypt from 100- 160 CE. The last name we know him by was a mistake. Professor Millar explained that during the conquest of Egypt by Alexander the Great, a general of that conquest had the last name Ptolemy. The surnames of the last five rulers of Egypt all were known by the surname Ptolemy. During his conquest, Alexander set up libraries everywhere. At any rate the Ptolemy under discussion came up with a new, non-Aristotelean system that incorporated deferents and epicycles where smaller circles rode around the Earth on larger ones, which, in the manner it was portrayed, helped to make sense of that previously mentioned problem of retrograde motion and restore perfect motion to the heavenly construction of the universe. However, a new challenge arose—the only way this model could work was if the Earth was somewhat (heaven forfend!) out of the center of the universe. The calculations had to now include an additional planet and more deferents to help reconcile the problem. This model, in revised version, held for over 1,000 years.
God became ever more inscrutable—why would he build such a universe? This is sort of like trying to make sense of the myriad of non-optimal designs and even design flaws seen in living organisms, if they had been planned and implemented by a divine Designer (with a capital D [or G, if the believer in such a Designer is being honest]). The spheres once again became further and further away, permitting an expanding cosmos. As the Dark Ages were drawing to a close, there emerged the figure of Nicolei Kopernic (Copernicus; 1473-1543). While this time of unimpeded religiosity brought in its wake the destruction of libraries, universities and books in general, some books survived by being copied, and learning once again could start to gain a foothold.
In an effort to get the Earth back to its proper place in the middle of all that is, a dizzying array of new circles upon circles had to be installed into the celestial shere model. But this scheme was beginning to break down and eventually a new model would need to be implemented. Universities were still under the control of the Church and were mostly in the business of training up the next batch of the faithful for the clergy. Such was the view of the time that the priest was considered at the top of the heap of pursuits available then, with doctors and lawyers falling below. The university was a corporation of masters and students and this is where Copernicus found himself when he developed the heretical heliocentric system. When the new bishop came in, he got rid of the the bold Copernicus and his troublesome model. But this only freed up the mostly autodidactic Copernicus to further develop his ideas.
Even while excising the Earth from its vaunted position in the center, the heliocentrist still retained the idea of spheres; only now they were transformed somewhat so that one might think of them as containing tracks or belts that moved at different speeds. Just as someone, in modern times, in a vehicle that is moving forward faster than the vehicle next to her experiences the sensation of the other car as if it is moving backwards- the racetrack system that Copernicus developed could, in a similar fashion, explain the retrograde movement problem. Earth, in this scheme, was on a track that viewed bodies moving in one direction on a slower track until it caught up and past it; thus seeming to loop those bodies back in a reverse direction in space. He used this model to order the planets according to their relative speeds. Although his geocentric model was seen as the height of heresy, Copernicus himself was not to demolish all the theologically based concepts of the day; he still believed in the perfection of heaven and in perfect spheres (no elliptical orbits and no celestial bodies diverging from their tracks). Retention of these divine perfect circles, however, had the unfortunate outcome of bringing the epicycles back into the system, thus undermining the model- even though it was based on more correct ideas up to that point. So, once again, the number of spheres had to be increased and there was no stellar parallax due to the relative position of the surface of the Earth to following layers of the interior of the spheres presented to the surface-dwelling humans.
Publication, then, was delayed for two reasons: the system still had its flaws and challenges, and it thrust Earth out of its God’s- special- creation centrality. A German astronomer tried to get the work published, however. This was a time of the Reformation, so some independent thought and writing was beginning to leak out. It was with the darkest of humor that one notes that when Copernicus’ heliocentric model was eventually brought to light, a caveat was insinuated into it that it was only a model; not something depicting actual reality. It is sad to think that religiously inspired opposition to evolution theory is even now—in the 21st century—still no further along in its method of attempting to blunt the findings of biological science than those in the time of Copernicus were in blunting his heliocentric model. We still see obligatory disclaimers posted inside biology textbooks that say that the ideas on evolution presented are not to be seen as factual, but are only a theory. Sigh. In any event, Copernicus died at the time of publication.
Copernicus, as Professor Millar explained, was not the first to develop a heliocentric system. Aristarchus of Samos, a couple hundred years BCE, is considered the Copernicus of antiquity for creating a celestial sphere model with the sun at the center and an orbiting Earth back in his time. Moreover, he also saw the sphere as a more immense structure than had ever before been imagined. He made major breakthroughs, too, in finding correct distances to objects in the visible universe and devising measurements that stand the test of time as to the relative distances between many celestial bodies. He understood, as well, that the moon orbits the Earth and receives (and reflects) its light from the sun. As might be expected, Aristarchus was imprisoned for impiety but died before tasting the flames of the stake. Copernicus himself credited Aristarchus in his tome but it was crossed out before publication.
Professor Millar sprinkled his presentation with various interesting asides regarding the historical personalities that he brought to light for us. This served to put more flesh on the bones of the early contributors to astronomical science. In the case of Tycho Brahe (1546- 1601), it was not just the flesh but gold that added to his physiognomy; Brahe sported a golden nose to replace his natural one lost in a fight with a classmate over who was the better mathematician. Tyge (Latinized as Tycho) Brahe observed new stars in the constellation Cassiopeia and wrote books such as On the New and Never Previously Seen Star; Concerning the New Phenomena in the Ethereal World; and Instruments for the Restored Astronomy.
Pertinent to this discussion, he witnessed a supernova and saw how this amazing phenomenon could simply not be tied in any way to the designation of mere atmospheric activity. Other observations he made, including those of how parallax was negated, showed him how this and other deeper phenomena had to be occurring in space—beyond any celestial sphere. Since, from antiquity on, the notion of perfection was so bound up in the idea of perfect circles, his observations shattered not only those sublime crystalline spheres but the very idea of a supremely organized divine engineering project. Brahe was given an island by the King of Denmark, from which the astronomer observed space. He was a skilled and natural builder of large scale astronomical instruments. So well- constructed were these devices that even today they remain among the most accurate for gaining resolution in naked eye observations.
Tycho Brahe attempted to combine the models previously constructed into a sensible unity; one featuring a heliocentric system but where the other bodies still circled the Earth. To assert a personal opinion at this time, this Secretary will suggest here that perhaps the innate and deep- seated desire of humankind to place itself at the center of the universe—resisting strenuously every bit of displacing data until the bitter end, may not be exclusively a result of our collective ego and sense of exceptionalism. Perhaps also we might consider how strongly we sense our own personhood and truest self to be a localized thing within us, leading to the homunculus idea or that we are essentially something within our heads or that a separate soul pulls the strings inside us. Even those who know better still feel this sensation mightily. It is only with sheer force of well informed will that we can begin to comprehend the unity of our bodies and brains, with all our systems, hormonal excretions, environmental releasing factors, staggering physio-neurological processes acting and reacting at numerous levels of conscious and unconscious activity—that culminate to create what we call our self. In cosmology- all stellar phenomena are linked through time and space as surely as all life forms are via evolution. But we are wired up to see a singular fixed site from which all else emanates—a central or controlling hub that all else is peripheral to. The idea of a universe that is connected all the way back to when spacetime began, at the Big Bang, but where there is no center, no top nor bottom, no comprehensible temporal beginning nor end, no edges- well, this is simply too foreign to our innate sensibilities and takes considerable effort to emotionally, as well as intellectually, accept.
Johannes Kepler (1571- 1630) next steps onto the stage. This German astronomer was influenced from his student days by Copernican teachings. His book, Mysterium Cosmographicum, opened the door for a friendly interchange of ideas with Galileo and Tycho Brahe. He became an assistant at Tycho’s observatory near Prague. Mars was considered a special problem for existing celestial concepts since its motion disagreed the most with what should be observed under those models. In 1609, Kepler published Tycho’s calculations of the orbits of Mars and in this publication first promoted what became known as Kepler’s Laws. Kepler understood that the planets orbited the sun and that the sun exerted some compelling force upon them, but extended this to incorporate the idea of elliptical orbits and developed his laws relating to relative speeds of planets in their orbits, according to their distance, in their elliptical orbit, from the sun. When the planet is closer to the sun, its speed increases; when further out in space, its speed decreases. If one imagines pie slices between the sun and a given orbiting planet, where the edges of the wedge are defined by given time frames, one will note that the slices are short and fat at closer orbiting distances and thinner but elongated at greater distances. Kepler’s laws predict that the area swept out within equal amounts of time are the same at all points of the orbit (think of a shorter squatter vessel of water and a taller but thinner one that each hold the same quantity of fluid).
His model eliminated the deferents and epicycles from all previous constructs. Previously, each body was a special case (and often required its own sphere to travel upon) but now the Kepler’s laws could be extended generally throughout the heliocentric system. Some slight deviations within his model that have since been discovered are explained by the small forces that the orbiting bodies exert upon each other. Kepler, the first real astrophysicist, had, with his model, assigned the perfection of the heavens to the circular file. This writer would note the oddness I have always seen between the stated wonder of theological concepts in being beautiful harmonizing ones that make one feel more connected with something larger. Religion is, in this writer’s opinion, the great divider- not unifier:religious sect and denomination from other ones; man from woman; humankind from all other life forms, with each kind of organism from all others; a separate essence (soul) from the body (creating the errant mind/body dualism belief); the Earth from all other planetary bodies and sun and moon as distinct from all other stars and orbiting moons; a separate realm for rewards and punishment (heaven and hell), etc.
Perfection had been seen with a system where each group of celestial bodies was separate from others, on distinct spheres, and where none had any influence upon the others and none had been born out of each other but separately created and arranged and where the idea of stellar evolution—the supreme connection idea throughout the universe—was as unimaginable as the comprehension that each of our bodies contain the stuff of stars in a galaxy—one among countless others- that have been born and died- expelling their nuclear-forged elements in their death throes. Talk about being created from the forces from above and our oneness with the universe! Everything, in the informed scientific way of examining the natural world, involves perturbations and influences shot through every particle of all that is—-from vibrating Superstrings to planetary influences upon the wobble of their gravitationally tethering stars to the actions and reactions of genes and environment. The greatest of unifying, supremely glorious epic tales is told by nature as discovered by science; not from the musings of supernatural agency as dreamed up by theologians.
Science, also, is the great explainer of observations and makes predictions that may be tested. It does not always say what we wish it to (humans having evolved from a common ancestor with the apes!? Heaven forbid!). The more data that can be brought together in an explanatory model, the more robust the theory that is constructed. The Copernican model, as Professor Millar noted, predicts (for instance) that Venus should have phases. And this is so. While the prophesies of religious writings have predicted nothing that can be shown to have any real direct link with reality, we know to the second when the next cometary appearance will take place, for but one example of science’s predictive efficacy. When the date for the return of Jesus comes and goes without any appearance of the Nazarene, the faithful soldier on, with not a whit of diminution of their faith in religious prophesy. But when a scientific prediction fails, the model must be scrapped for a new one that works.
The development of telescopes showed that it was space itself that was under examination (not merely more spheres concentrically rippling outward further and further) with the revelation of faint stars that are part of a galaxy—the Milky Way- filled with an almost incomprehensible number of other systems such as ours; our own being in but one unremarkable spiral arm. Not only were we not at the center of our local system, we were not centrally or significantly located within the Milky Way; which itself has no location of special placement or importance among the countless other galaxies in the universe. As a final blow to perfect- sphere thinking, our galaxy is disc shaped.
Science will also sometimes lead to counter-intuitive outcomes, but is evidence led, rather than by what is wished or assumed to be the case. Just one example Professor Millar gave of this was that the Earth is actually further from the sun in the summer and closer in the winter. Earth’s tilt explains the seasonal changes.
As mentioned near the beginning of this presentation summary, Professor Millar came full circle and embedded this conceptual circle within the sphere again; yes, the celestial sphere. The modern use of the celestial sphere model as generated by computers and informed by cutting edge knowledge, is a far cry from the ancient concepts, and is free from the distractions of trying to reconcile its representation with outmoded beliefs in being fashioned along the lines of perfect circular perfection by divine agency that constructed it all for one branch of primates on one planet at the center of it all. Yet the modern version of the celestial sphere is still useful as a tool and a way of showing the correct relationships of stellar and planetary motion within a given system in space. It allows us, Millar explained, to comprehend the rotation of the whole and perceive eclipses and take in larger themes. This reminds this writer of how Big History (another presentation the FA was treated to) displays larger patterns and events by taking a long view perspective. In both cases, one sees the forest, rather than getting caught up in a tangle of sylvan undergrowth (so to say). The modern celestial sphere model gives one a virtual god’s eye view of our solar system, whereby astrometric measurements and relationships may be made, orientations between bodies in motion may be visualized and our real, correct place in this glorious system may be better comprehended.
Secretary: Charles LaRue.
