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Previously, I posted a series of papers on improving the heliocentric model, but due to the lack of direct evidence of heliocentric defects, these papers have not been published.After careful research, direct evidence of the defect in heliocentric theory was finally discovered.&nbsp

The heliocentric theory has been universally accepted, so it is very difficult to believe that heliocentric model has defects. However, there are two simple facts that show that the heliocentric model does have defects. First, the direction of the Big Dipper observed on the earth is changing with the change of seasons. Second, there are always some stars that can be observed on the earth all year round. I try to use an improved model to explain these astronomical phenomena.

There’s a parallelism between the classical geocentric cosmos and the following essentials of life chemistry: the electron octet, the bio-elements, the amino acids, and the genetic code. The introduction contains a short summary of the chemistry of life and the classical geocentric cosmology. The research method compares the classical geocentric cosmos to the investigated essentials of life chemistry. The Earth-Sun (substrate-source of life) opposite and the inner-outer planet opposites correspond to several of these essentials. The twelve zodiac constellations correspond to the twelve macro bio-elements, the twelve polar amino acids and the twelve by doublet codons encoded amino acids. Each of the latter three zodiac chemical representatives shows the typical seven to five ratio of the twelve zodiac constellations: seven animal and five human related constellations. An original genetic code table based on third position synonyms shows the similarities and differences between the vertebrate mitochondrial and the standard genetic codes, and the parallelism with the classical geocentric cosmos. Specific zodiac constellation representatives for the life chemistry essentials are presented.

Zvjezdani glasnik je astronomska rasprava koju je 1610. objavio Galileo Galilei. Galileo je konstruirao teleskop i po prvi puta ga upotrijebio za opažanje astronomskih fenomena. Prikazana su opažanja i analize koja je Galileo objavio u Zvjezdanom glasniku. Prikazana su Galilejeva opažanja i analiza Mjesečeve površine. Dano je Galilejevo otkriće mnoštva, bez optičkih pomagala nevidljivih, zvijezda te rasprava o prividnoj promjeni blistavosti zvijezda ovisnoj o prisutnosti nešto Sunčeve svjetlosti. Ilustrirano je postojanje četiriju velikih mjeseca oko Jupitera koje je Galileo teleskopom opazio. Kratko je diskutiran značaj Galilejevih otkrića za rađanje moderne znanosti te kritike koju su njegova otkrića izazvala. The Starry Messenger is astronomical treatise published in 1610 by Galileo Galilei. Galileo constructed telescope and used it for the first time for observing astronomical phenomena. The observations he presented and discussed in The Starry Messenger are described. Galileo’s analysis of his observation of the Moon's surface are presented. Galileo's discovery of myriads of previously unseen stars and apparent change in their luminosity in presence of some daylight is given. The existence of the four large moons around Jupiter observed by Galileo are illustrated. Significance of Galileo’s discoveries for the birth of modern science as well as critique he faced are briefly discussed.

The Pythagorean Philolaus of Croton (470-390 BCE) created a unique model of the Universe and he placed at its centre a ‘fire’, around which the spheres of the Earth, the Counter-Earth, the five planets, the Sun, the Moon and the outermost sphere of fixed stars, also viewed as fire but of an ‘aethereal’ kind, were revolving. This system has been considered as a step towards the heliocentric model of Aristarchus of Samos (310-230 BCE), the astronomical theory opposed to the geocentric system, which already was the communis opinio at that time and would be so for many centuries to come: but is that really so? In fact, comparing the Greek data with those of other ancient peoples of Indo-European language, it can be assumed that the ‘pyrocentric’ system is the last embodiment of a theological tradition going back to ancient times: Hestia, the central fire, was the descendant of an Indo-European goddess of Hearth placed at the centre of the religious and mythological view of a deified Cosmos where the gods were essentially personifications of atmospheric phenomena and of celestial bodies.

The cosmos that we understand today is composed of innumerable stars, galaxies, and exoplanets, with curious quasars, pulsars, dark matter, and black holes, expanding in all directions into infinite black space. Such a universe did not exist in the Middle Ages. The medieval cosmos was sensibly organized, structured within seven concentric, transparent layers. Each planet had its own sphere and moved in perfect circular motion. The eighth sphere carried the fixed stars, all at the same distance from Earth. Beyond the zone of fixed stars lay the heavenly realm where God, the angels, and the righteous existed in bodily form, waiting for resurrection of the saved to join them after the Apocalypse at the end of time and the Last Judgment. Then the damned would suffer in Hell with Satan, and the saved would live in Heaven at the right hand of God for eternity in everlasting peace.

For thousands of years, humans on Earth across all cultures knew of seven luminaries: The Sun; the Moon; and five planets, Mercury, Venus, Mars, Jupiter, and Saturn, all of which move relative to the fixed stars. The number seven was therefore considered special and sacred (Chap. 10, Vol. 1) and the possibility that there could be more than five planets had never entered anyone’s mind. After Copernicus proposed the heliocentric model, the Solar System was centered around the Sun, which had six planets (including the Earth) revolving around it. The Earth, therefore, became a part of the cosmic structure. Although the positions of the Solar System objects were re-arranged, the total number of celestial objects remained the same. When Galileo began his telescopic observations, he found that Jupiter has four moons similar to the Earth’s Moon (Chap. 20, Vol. 1). So, the Solar System consisted of a total of 11 objects: The Sun, six planets, and five moons. The special significance given to the number seven was therefore no longer secure.

In this chapter, there is discussion of the heaven of the Fixed Stars, which are given over to a sight of the Church Militant, who adorn a triumph of Christ, and who have Mary at their head. Dante is examined on Faith, Hope, and Love, by Peter, James, and John, the apostles of Christ, and he sees Adam. Peter issues a judgment against Rome, defaced by the presence of the contemporary Papacy, and canto 27, the last to be discussed, and the one which takes Dante into the last of the heavens, the Primum Mobile, pronounces several prophecies which imply that a new setting in order awaits the earth. The chapter attempts to read these events in a way which draws out a continuing significance.

From antiquity to the sixteenth century, observers of the heavens believed the Aristotelian harmony of nature and that the fixed stars in the heavens were constant and unchanging. Algol (Beta Persei) was a notable exception, but more on that later.

In Ptolemaic cosmology, the Universe has a finite size defined by the celestial sphere upon which the fixed stars lie. Within this celestial sphere are the five planets and the Sun revolving around the Earth. Assuming that the interior volume of the celestial sphere is filled by orbits and epicycles of the planets, Ptolemy derived a size of the Universe that is 20,000 times the radius of the Earth (Chap. 15, volume 1). After the development of the heliocentric theory, the hypothesis of the daily rotation of the celestial sphere was replaced by the hypothesis of the rotation of the Earth. This removes the need for the stars to lie at the same distance and rotate together, which in turn opens the possibility that the stars may have different distances from Earth and that the Universe could be infinite in size (Chap. 18, Vol. 1). While Copernicus replaced the Earth with the Sun as the center of the Universe, this cannot be true in an infinite Universe. An infinite Universe has no center, and therefore whether the Universe is finite or infinite has implications for our place in the Universe.

This paper aims to shed light on two different mathematical practices in late eighteenth-century China. For this purpose, we analyze two solutions to the “three problems of the eastward motion of fixed stars” (恒星東行三題) that were given separately by Jiang Sheng (江聲) and Li Rui (李銳), who were both Qian-Jia scholars in the same region of eastern China. By comparing their modes of problem-solving, of reasoning and of computation, we suggest that the mathematical practices they employed represent the recreation of two traditions of mathematical commentaries by Qian-Jia scholars.

Is the De Caelo book one, chapter 9 one of the Aristotelian texts which demonstrate the existence of beings beyond the fixed stars, that is to say beyond the limit of the Heaven? The question was first raised by Fabienne Baghdassarian in her article "De Caelo I, 9: the identity of the beings from there". Our statement will bring to light the problem around the notion of takei (contraction of ta ekei, meaning “the…from there”, “the things from there”) in order to recontextualize in the Aristotelian corpus and to analyse the diverse interpretations, reasonings regarding the meaning of this notion and the passage in which it appears.; Le De Caelo livre I, chapitre 9 est-il un des textes aristotéliciens qui manifestent l’existence d’être se trouvant au-delà de la sphère des fixes, c’est-à-dire au-delà de la limite du ciel ? Cette question a d’abord été posée par Fabienne Baghdassarian dans son article « De Caelo I, 9 : l’identité des êtres de là-bas ». Notre propos consistera à mettre en évidence le problème que pose la notion de takei (contraction de ta ekei qui signifie « les… de là-bas », « les choses de là-bas ») afin de le recontextualiser dans le corpus aristotélicien et d’analyser les diverses interprétations, arguments quant à la signification de cette notion et du passage dans lequel elle apparaît.

Relational mechanics is a gauge theory of classical mechanics whose laws do not govern the motion of individual particles but the evolution of the distances between particles. Its formulation gives a satisfactory answer to Leibniz's and Mach's criticisms of Newton's mechanics: relational mechanics does not rely on the idea of an absolute space. When describing the behavior of small subsystems with respect to the so called "fixed stars", relational mechanics basically agrees with Newtonian mechanics. However, those subsystems having huge angular momenta will deviate from the Newtonian behavior if they are described in the frame of fixed stars. Such subsystems naturally belong to the field of astronomy; they can be used to test the relational theory., 12 pages, 1 figure

Distortion of Scientific Terms by Supposed Modernizing Translations: The Example 'orbis' (sphere)/'orbita' (orbit). The use of modern terminology and thinking hinders to understand historic astronomical and physical texts and often misleads the reader, because between celestial physics from Aristotle and Ptolemy to Copernic on the one side and since Kepler and Newton on the other side a fundamental change of paradigm had taken place. The former started from the assumption that planets are indirectly moved by large equally rotating etherical spheres combined with each other to form every kind of unequally apparent planetary motion as a resultant, whereas the later started from Kepler's idea that every motion of a planet is directly caused by two forces moulding his (naturally unequal) 'orbit'. 'orbita' was Kepler's new specific term for the way of the planet coined in late 1604; in contrast, the Latin term of the elder paradigm has been 'orbis' ('sphere'), on the one hand as concentric 'orbis totalis' of a planet (or the fixed stars), on the other hand as non-concentric 'orbes particulares' (of the eccenters and epicycles) within the space of an 'orbis totalis'. These terms were interpreted and translated in accordance with modern dynamic (as the supposed 'true') thinking as if they were 'orbits' (German: 'Bahn'). But you cannot bring the two paradigms into line. As a result, the texts of seemingly 'modern' translations become incomprehensible, absurd and wrong. The study shows this on thinking (1st ) about Aristotelian physics of former times using terms and ideas of modern dynamics, and on thinking (2nd ) about the former explanation of apparent motions of heavenly bodies using these dynamics and ignoring the different special Aristotelian and Ptolemaic physics of 'orbes' (spheres).

Setting Aside All Authority: Giovanni Battista Riccioli and the Science against Copernicus in the Age of Galileo. By Christopher M. Graney. (Notre Dame: University of Notre Dame Press. 2015. Pp. xv, 270. $29.00 paperback. ISBN 978-0-26802988-3.)The "Copernican Revolution" is the transition from the ancient worldview, claiming that the earth stands still at the center of the universe, to the modern worldview asserting that the earth is a planet rotating daily around its own axis and revolving annually around the sun. The transition was a long and difficult process taking about 150 years, roughly from Copernicus's On the Revolutions of the Heavenly Spheres (1543) to Newton's Mathematical Principles of Natural Philosophy (1687). The difficulties stemmed from the fact that there were many strong arguments against the earth's motion: they were not merely biblical and religious, philosophical and epistemological, but also observational, astronomical, and mechanical. For example, if the earth revolved, then we should observe an annual parallax in the apparent position of fixed stars, but no one could; and if the earth rotated, then freely falling bodies should deviate from the vertical, and gunshots in opposite directions should not behave equally. The transition was also gradual insofar as such objections had to be answered piecemeal and new confirming evidence had to be found piecemeal. A significant step was the invention of the telescope and Galileo's discovery by its means of the moon's mountains, Jupiter's satellites, Venus's phases, and sunspots (in 1609-13). However, these telescopic discoveries did not resolve the issue; they merely refuted some anti-Copernican arguments and confirmed some aspects of Copernicanism. Another important step was Galileo's Dialogue on the Two Chief World Systems, Ptolemaic and Copernican (1632), which provided a critical examination of all arguments on both sides (save the religious ones), including a critique of the mechanical objections; this book showed that the scientific and philosophical evidence favored the earth's motion, which thus became more probable than the geostatic alternative; but, as Galileo realized, the case for the earth's motion was still not conclusive, since, for example, the stellar parallax objection could not be refuted.The sketch just given represents a consensus of recent scholarship. However, despite such scholarly consensus, there is at least one popular myth about the Copernican revolution that continues to be widespread: that conclusive proof of the earth's motion was provided by Copernicus himself, or the telescope, or Galileo's Dialogue, and that only religious superstition or ecclesiastic authoritarianism prevented the acceptance of Copernicanism.The aim of this book is to criticize this popular myth. It does so by examining the writings of the leading anti-Copernicans of the period and showing that they contained many good scientific arguments against the earth's motion. The principal author is, as the book's subtitle indicates, Giovanni Battista Riccioli, an Italian Jesuit who published the ambitious Almagestum novum (1651); a key topic was the critical examination of 126 arguments on both sides. Riccioli was building on the work of an earlier anti-Copernican, the Danish astronomer Tycho Brahe who, before the telescope, collected a mass of observational data that were unprecedented in quantity and quality; moreover, Tycho devised a "hybrid" worldview according to which the planets revolve around the sun, but the whole solar system and the fixed stars move around the central, motionless earth. A third author discussed by Graney is the Italian priest Francesco Ingoli, who in 1616 compiled an essay summarizing the astronomical, mechanical, and theological arguments against the earth's motion; this essay provided the basis for a decree by the Con- gregation of the Index declaring the earth's motion scientifically false and theologically contrary to scripture, and prohibiting Copernicus's book. …

The dial at the center of the front face of the Antikythera Mechanism was surrounded by two scales, one representing the zodiac, the other the Egyptian calendar year. The Zodiac Scale was inscribed with the names of the zodiacal signs as well as series of index letters in alphabetic order, while the Egyptian Calendar Scale was inscribed with the Greek names of the Egyptian months. In addition, two rectangular plates, the remains of which survived displaced from their original positions, bore an inscription, called the Parapegma Inscription, comprising an alphabetically indexed list of annually repeating astronomical events relating to the Sun and to fixed stars. This paper gives transcriptions and translations of the inscriptions on the dial scales and the Parapegma Inscription, and deduces the original structure, layout, and location of the Parapegma Inscription. A provisional astronomical analysis of the data in the Parapegma Inscription and tentative restorations of some of its damaged and missing line...

Among the characteristic features of Georg Peurbach's influential Theoricae novae planetarum (1454) was a model of the motion of the fixed stars, based on the Alfonsine Tables, that involved both an eighth sphere undergoing trepidation and a ninth sphere subject to linear precession. Instead of being an innovation on Peurbach's part, the model in question can be shown to have been derived from an obscure treatise De triplici motu octave spere written in 1450 by the Paduan astrologer Nicolo Conti (d. 1468). The main purpose of this article is to highlight relevant parallels between the two works, especially in their use of diagrams, and to present evidence of personal ties between Conti and Peurbach, which explain how the model in question was transmitted from Padua to Vienna. In addition, it discusses the astrological impetus behind Conti's physical model, which was based on the notion that the slow motion of the fixed stars influences the course of history.

Despite the exiguity of the remains, it appears that one can determine the focus of Dikaiarchos' work on geography. In this brief survey of the sherds, It tries to summarize his interests and accomplishments in a synoptic way, placing them in their proper historical context. Dikaiarchos seems to me to have made use of a newly-developed scientific method by which for the first time ever the heights of the mountains could be accurately determined. However he did it, his method seems to have tended to generate some sort of systematic error and in fact the values recorded are ca. 1/6 high. Aristotle in fact uses just the argument that Dikaiarchos later did: that the fixed stars visible to an observer moving north or south on the Earth change. Fritz Wehrli argues that Dikaiarchos referred to the difference in rising times apparent to one going east or west.

In this essay I shall propose to those who study Nature great objects to be seen and admired. I define them great both for the excellence of the topic, the unprecedented novelty, and the instrument through which I could observe them. It is indeed important to add to the great number of fixed stars which we have been able to see with our own eyes, countless other stars, never seen before, and display them in a number which is more than ten times the number of the known stars.

An examination of the preserved Arabic copies of the Islāḥ al-Majisṭī (12th century AD) has revealed an unnoticed before appendix preserved in MS Escorial ár. 930. The appendix contains in Arabic a portion of a larger passage which was known from (presumably) Gerard of Cremona’s Latin translation of the Iṣlāḥ al-Majisṭī but which had not been found in Arabic copies of the work. The passage pertains to Book VI of the Iṣlāḥ al-Majisṭī, on the fixed stars, and relates particularly to the Milky Way, the Solid Globe and the configurations of the fixed stars. In this article the chapters preserved in the appendix will be located in the context of Book VI of the Iṣlāḥ. It is further examined how far the newly found appendix helps to determine whether the passage known from the Latin formed an original part of Jābir ibn Aflaḥ’s work or was supplemented later, in particular based on the Arabic translations of the Almagest that were available in twelfthcentury al-Andalus

The fact that the Sun and stars do not rotate around the Earth at the same rate implied that the Sun is moving through the background of fixed stars. Over the course of a year, the Sun goes around the 12 zodiac constellations along the ecliptic. Curiously, the path of the ecliptic is inclined at an angle with respect to the celestial equator. This inclination gives us the seasons.

The model of Ptolemy treated the celestial bodies as mathematical points and their trajectories as lines and curves. Aristotle gave the description of the physical structure of the Universe, proposing that the Earth was made of earth, water, air and fire and the celestial objects were made of ether. The rise of Christianity led to the marriage of the world views of the Bible with those of Aristotle and Ptolemy, producing a consistent hierarchy of the structure of the Universe from Hell at the center of the Earth to Heaven beyond the sphere of fixed stars.

The study explores vagueness area of the crowd concept and points the identification of nodal points. By means of some descriptive, comparative and meta-analytical methods are examining crowds abstract idea limits and are found meaningful convergent paths. It is ascertained that the crowd is not an uniform ideaful construction homogeneous and centripetal, but a multi-layered and multi-structured, heterogeneous and centrifuge. The released conclusion is that, despite the disorder within the concept of crowd, inside of it can delineated three fixed stars, three symbolic meaningful figures of crowds: the citizen, the militant and the worker.

Previous research on the origins of double star astronomy in the early nineteenth century emphasized the role mathematical methods and instrumentation played in motivating early observations of these objects. The work of the British astronomer John Herschel, however, shows that questions regarding the physical nature of double stars were also important. In particular, an analysis of John Herschel's early work on double stars illustrates the way in which speculations regarding these objects were shaped by assumptions of the properties of stars themselves. For Herschel, a major consideration in double star astronomy was distinguishing between types of double stars. Optical doubles were useful in determining parallax while binary doubles were not. In practice, classification of a specific double star pair into one of these categories was based on the assumption that stars were of approximately the same luminosity and thus differences in relative brightness between stars were caused by difference in distances. Such assumptions, though ultimately abandoned, would lead Herschel in the 1830s to advance the possibility that the dim companion stars in certain double star pairs were not stars at all but in fact planets.

Notes: items in bold in curly brackets are the original marginal notes; items in square brackets are our interpolations; capitals are as in the original; cross-references in the footnotes are to the end-notes of Part 1.AN IDYLL BY THE RIGHT WORSHIPFUL JOHANN BAPTIST HEBENSTREIT ON THE KEPLERIAN STAR-SPANGLED TOWER, SHOWING DEPICTED THE BIRTH AND PROGRESS OF ASTRONOMY UP TO OURAGEAND THE QUITE NEW, LONG-DESIRED AND INCOMPARABLE WORK OF THE TABLES[first version]1 Tell, Urania,2 Divine Chief of the Aonian3 sisters, you who derive your name from heaven itself, what sort of Apellean4 composition stands at the threshold of MR KEPLER'S5 BOOK?[second version] Tell, Urania, Divine Chief of the Aonian sisters, you who derive your name from heaven itself, what sort of Apellean composition stands at the threshold of this splendid book?[final version] Tell, Urania, Divine Chief of the Clarian6 sisters, you who derive your exalted name from heaven itself, what sort of Apellean composition stands at the threshold of this splendid book?In as much as you value so highly those sublime realms that the gentle throng of the Gods inhabits, whence comes to suffering mortals every vicissitude in their travails,7 let it be no shame to show in precise forms the image of such great matters. And lo! You who marvel so much at the earth and the heavenly sphere, do you not see, arising with a new refinement, the temples of the Gods, which the diverse labours of the first men brought forth and left to be polished in our age? If perhaps these things seem too marvellous and you are transfixed, struck dumb at a single glance, I shall now (with the help of the Goddess) explain them. If you will lend me your ears, you will see all that is obscure become clear as if by the torches of Phoebus.8 Do you not see how the roof shines, held up by twelve Columns, distinguished by as many figures; and how bases adorned with five plaques support the columns? "Yes", you say, "I see that, but what is the point of this topsy-turvy arrangement? {Why are the Fixed Stars placed at the bottom?} It seems that all the lights fixed in the heavenly Vault, elsewhere placed in the highest position, are by that device now inscribed on the floor.9 Is the sky confounded with the ground? Has the upper air abandoned its realm?" Whoever you are, asking these things: [I reply that] Heaven remains immutable, but by the genius of the Seers and the guidance of the skilled Apelles, and by the law of the Astronomer, these thresholds underlie the lofty columns like the foundations of the sacred art of rulers. Thus the base shows you the stars, an area strewn with the twelve Signs.10 In scarcely any other way could vigilant eyes draw down Olympus [the heavens] or with skilled examination trace the wondrous paths and conjunctions of the seven Wanderers [the planets]. {Because they serve as the basis for Observations.} Happy souls, whose unrelenting labour has divided the starry Orb and the blazing stars themselves by rank, and depicted the sundry forms of things and men." {The armiilary sphere of Aratus.}12 Among these [souls], why, Aratus, do you lurk round the back of the Column?13 Is it not enough that you are praised in Pierian14 song for having distinguished the zones of Heaven, and for having enclosed rings within rings? Has fortune not favoured your work? {Hipparchus's sphere of the Fixed Stars.} Surely the might of Hipparchus toiled more on the Pharian shores?15 We are not all allotted the same tasks. A thousand are the kinds of men; their industry is not all of the same stamp;16 the very law of fate is fickle; nor do the highest powers of intellect arise at any one time. Just as Hipparchus surpassed Aratus17 (both of them Greeks), so he in turn has suffered the appearance of a DANE, who was even better, heir to the works begun. Behold his posture! {Tycho completed a Catalogue of the fixed stars.} Whoever in later times would lay better foundations, let him draw on the tables approved by the Gods. …

How did a Copernican deal with the 'star size' objection to the Copernican theory articulated by Tycho Brahe (1546-1601)? According to Giovanni Battista Riccioli (1598-1671), a Copernican did so by appealing to divine power: an infinite and omnipotent God can make stars as large as He desires; such stars are nothing compared to God. A fascinating illustration of this approach to the Copernican theory's 'star size' problem can be found in the work of the Dutch Copernican Philips Lansbergen (1561-1632).Tycho's 'star size' objection was straightforward. Fixed stars appear to the naked eye to have measurable sizes. Tycho measured first magnitude stars to be about two arc minutes in apparent diameter, and lesser stars to be progressively smaller - values that generally agreed with earlier measurements.1 By geometry, the more distant an object of a given apparent size is, the physically larger it must be. Therefore, the great Copernican distance to the fixed stars, required in that theory to explain the lack of observable annual stellar parallax, translated into large physical sizes. Tycho's measurements and calculations indicated even a third magnitude Copernican star to be as physically large as the orbit of the Earth - dwarfing even the Sun. By contrast, in Tycho's geo-heliocentric theory, the stars lay just beyond Saturn (Figure 1), and had reasonable physical sizes (consistent with the other celestial bodies - Figure 2).Here was a weighty anti-Copernican argument. As Albert van Helden has put it: 'Tycho's logic was impeccable; his measurements above reproach. A Copernican simply had to accept the results of this argument."2 The telescope is often said to have dissolved this argument, because the telescope "made necessary a re-estimation of the true diameter of the fixed stars, which were now known to be far smaller than they appear to the naked eye".3 However, early telescopes produced images of stars that had the appearance of distinct disks, whose spurious nature was not understood at the time.4 The telescope did reveal stars to have smaller diameters than those Tycho measured non-telescopically, but it also increased the Copernican theory's sensitivity to parallax. The net result was that Tycho's objection remained. Simon Marius, Riccioli, and even the Copernican Martinus Hortensius all noted the problem that telescopically measured star diameters posed for the Copernican theory; even Galileo's telescopic star observations challenged the Copernican theory, although Galileo did not address this.5How could a Copernican respond to Tycho's objection? According to Riccioli, by appeal to the power of God.6 Indeed, the English Copernican Thomas Digges wrote in 1576 of the starry heaven with its stars "far excelling our sun" as being "the palace of felicity" and the "habitacle of the elect". The German Copernican Christoph Rothmann defended giant stars to Tycho in 1590 by invoking imagery of a palace of God and claiming that size was irrelevant to an infinite creator.7 Responding to Rothmann, Tycho had rejected such reasoning:On what is such an assertion based? Where in nature do we see the Will of God acting in an irregular or disorderly manner? In nature where all things are wellordered in all ways of time, measure, and weight? In nature where there is nothing empty, nothing irrational, nothing disproportionate or inharmonious. Consider 700,000 or more Earth semidiameters being between Saturn and the fixed stars in the Copernican hypothesis. Consider those same fixed stars each being as large as the whole Orbit of Earth (and some larger still) and thus dwarfing the Sun, the luminary and centre of motion for all the planets. These are the same fixed stars which are noted as the least of the heavenly lights in the account of the Creation of the World. This is empty, irrational, disproportionate and inharmonious. Is such a disproportionate universe reasonable?8Tycho went on to say that by Divine providence such an ageometrical, asymmetrical, disorderly, and most unworthy method of philosophizing will go away. …

Plato’s ‘Myth of Er’ in the Republic gives an account of the World Spindle, the Axis mundi, operated by the goddess Necessity and her three daughters, the Fates. The afterlife vision of the soldier Er, who died previously in battle and was resurrected, suggests image of a Platonic geocentric universe of eight celestial whorls standing for planetary spheres, the sun, the moon, and the sphere of the fixed stars, each sphere in a different color. A hundred years before Plato classical Greek sources reported on the Persian city of Ecbatana, the capital of the Median King Deiokes, as having seven concentric walls, with battlements colored in accordance to their corresponding walls. It has been pointed out elsewhere that the seven walls of Ecbatana conspicuously match the orbits or spheres of the planets, the sun and the moon. There is thus an apparent parallel between the colored battlements of the seven walls of Ecbatana and the colored world whorls in the ‘Myth of Er’. There also appears to be a match between the concentric plan of Ecbatana, and the concentric plan of Atlantis, inferred in past studies.

The problems of spherical trigonometry concern the sizes of circular arcs or angles on the surface of a sphere, and their relationships to each other. In applications, the sphere was either the celestial sphere or the earth, the former being a sphere that was thought to contain the fixed stars and to have such a large radius that, in relation to it, the earth was no more than a dot.

The paper is proposing several examples of the use of Stellarium, an open source free software planetarium, for simulating the astronomical landscapes of the ancient stargazers. Here we will focus on the motion of the stars, in particular with respect to the precession of Equinoxes. Usually, we consider that this precession was discovered by Hipparchus of Nicaea (c. 190 – c. 120 BC), Greek astronomer and mathematician, who measured it comparing the positions of the stars that he observed to the data recorded a hundred of years before. In fact, Hipparchus gave us the first historical record of the precession but probably he was not the first to observe this motion of the heaven of the fixed stars. We can argue this possibility from the simulation of the sky seen by the ancient stargazers.

I propose an analysis of one of the principal steps in the formation of the concept of cosmic space at the very beginning of classical science. Following the Copernican reversal, the apparent movement of the sky became pure illusion, while even the existence of the sphere of fixed stars lost its self-evident character. From there, the ancient argument in favor of the finitude of the universe (according to which it is impossible that an infinite thing turn) lost all credibility and the question of whether the universe was infinite came to be asked anew. The infinitization of the universe achieved by Giordano Bruno made necessary a reworking of the concept of cosmic space. Thanks to his new conception of infinite, cosmic space (profoundly inspired by John Philoponus and Francesco Patrizi), Bruno was pleased to have escaped from the traditional difficulties of finitude. Paradoxically, it is this new concept of cosmic space that comes to counterbalance the dominant peripatetic cosmology. It constitutes a philosophical transition between perceptive space (qualified, heterogeneous, discontinuous, limited) and the space of classical science (homogenous, infinite, continuous) that would later be developed by Gassendi, Morus, Charleton and Newton.

In the eighteenth century French comet hunter Charles Messier completed the first catalogue of nebulous objects in the sky. Seen through a small telescope, these hazy cloudlets look much like a comet. They gave Messier much trouble in his hunt for comets, so he decided to once and for all make a list of them such that they could no longer confuse him. An object in his catalogue is indicated by capital letter M followed by a number. M1 is the Crab Nebula in the constellation Taurus: the remnant of a supernova (an exploding star), and M42 is the Orion Nebula, a gaseous nebula in this constellation. One also finds in this catalogue globular star clusters, such as M3, M4, M5, M10, M13, M15 and M92, and open star clusters such as M6, M18, M21 and M67. Some of the “nebulae” in Messier’s catalogue have, seen through a larger telescope, a spiral shape, for example M31 in the constellation Andromeda (Fig. 6.1), M33 in the Triangle and M51 in Canes Venatici (Fig. 6.3a). The Andromeda Nebula M31 is the only spiral nebula visible to the naked eye. The first one to mention this hazy object, in the year 964 in his “Book of the fixed stars” was Persian astronomer Abd-al Rahman Al Sufi, who described the nebula as a little cloud. This “little cloud” is the very central bright part of the nebula, and one must have good eyes to see it. It is the most distant object visible to the naked eye.

There is an obvious paradox in any attempt to map the topography of Paradise, for Paradise, theologians assure us, is outside of space as well as time. Yet mapping Paradise is what Dante's poem, the Paradiso, attempts to do. For the two preceding realms of the afterlife, hell and purgatory, Dante provides numerous finely articulated descriptions of rigorously ordered regions. And again for Paradise, the variegated states of the souls making up the spiritual order of the realm are expressed very precisely by a topographical scheme, one in this case based on Ptolemy's system of the heavens. The seven planetary spheres are followed by the sphere of the fixed stars and the primum mobile, the whole finally bordering on the completely nonspatial heaven of the Empyrean. But this last “sphere” alone is Paradise in the full and strict sense. As Dante has Beatrice explain in canto 4.28–48, the whole poem attempts to describe this totally nonspatial order in terms of the array of the nine physical heavens as metapho...

The stars in the Chinese star catalogue, Yixiangkaocheng, which were edited by the Jesuit astronomer Kogler in ad 1744 and published in ad 1756, are identified with their counterparts in the Hipparcos catalogue. The equinox of the catalogue is confirmed to be J1744.0. By considering the precession of equinox, proper motions and nutation, the star closest to the location of each star in Yixiangkaocheng, having a proper magnitude, is selected as the corresponding identified star. I identified 2848 stars and 13 nebulosities out of 3083 objects in Yixiangkaocheng, and so the identification rate reached 92.80 per cent. I find that the magnitude classification system in Yixiangkaocheng agrees with the modern magnitude system. The catalogue includes dim stars, whose visual magnitudes are larger than 7, but most of these stars have Flamsteed designations. I find that the stars whose declination is lower than −30° have relatively larger offsets and different systematic behaviour from other stars. This indicates that there might be two different sources of stars in Yixiangkaocheng. In particular, I find that μ1 Sco and γ1 Sgr approximately mark the boundary between two different source catalogues. The observer’s location, as estimated from these facts, agrees with the latitude of Greenwich where Flamsteed made his observations. The positional offsets between the Yixiangkaocheng stars and the Hipparcos stars are 0.6 arcmin, which implies that the source catalogue of stars with δ > −30° must have come from telescopic observations. Nebulosities in Yixiangkaocheng are identified with a few double stars, o Cet (the variable star, Mira), the Andromeda galaxy, ω Cen and NGC6231. These entities are associated with listings in Halley’s Catalogue of the Southern Stars of ad 1679 as well as Flamsteed’s catalogue of ad 1690.

PTOLEMY IN PERSPECTIVE Ptolemy in Perspective: Use and Criticism of his Work from Antiquity to the Nineteenth Century. Edited by Alexander Jones Archimedes, xxiii; Springer, Berlin, 2010). Pp. xvi + 229. $189. ISBN 978-90-481-2787-0.Here we have a collection of research articles by eight authors, all well known professionals. The subject is Ptolemy and his legacy in astronomy, geography and astrology. One theme that runs through a number of articles is the way in which Ptolemy's so-called observations of the equinoxes posed insoluble problems for all the later theories of precession.The volume opens with a report by Anne Tihon of a newly discovered and exciting text, written by an anonymous contemporary of Ptolemy. This is a report of work in progress, as we await with great interest the eventual edition by Tihon and her colleague, the papyrologist Jean-Luc Fournet. The text presents not only a calculation of the Sun in A.D. 130 according to both sidereal and tropical theories, but also testifies to a hitherto unknown observation by Hipparchus of the summer solstice of -157 June 26. Although brief and disturbed by some lacunae, the text is fairly clear and deepens our understanding of tropical and sidereal coordinates and precession, since we are given precise values for the sidereal and tropical motions of the Sun, as well as an implied apogee of the Sun in the sidereal frame.The second study in the collection, by Alexander Jones, is an ambitious study of the use of sidereal coordinates in a number of Greek horoscopes and other Greek texts. A famous passage in Theon's Small commentary on the Handy tables presents a model of precession used by astrologers of his time. Jones compares the solar andlunar longitudes in a good number of horoscopes (mainly those gathered by Neugebauer and van Hoesen) from which he subtracts the Ptolemaic tropical longitude. In spite of the inevitable scatter in the values he finds a fair clustering around Theon's precession, and concludes that the majority of astrologers obtained sidereal coordinates in this way. This is however a purely statistical argument, based on horoscopes where positions are given in degrees only, without minutes. Those horoscopes where the minutes are given are so close to the year 483, when that precession vanishes, that they add little to the argument; Jones argues in any case that after about the year 350 astrologers no longer corrected for precession. This is not the first time that this point has been made about such calculations in the Greek horoscopes, not least by Jones himself, but here the context of the discussion is much wider and includes the Standard Model of the Moon, Vettius Valens, and the Stobart tablets (not that the latter two add anything very convincing to the argument). As to the Standard Model, it is shown here that the mean moon differed from that of the Handy tables by precisely Theon's precession. The difficulty with these horoscopes is that recalculation from Ptolemy's parameters never yields complete agreement with the text, and this makes it hard to be sure whether the Almagest or the Handy tables had been used, since these yield practically the same results. Beyond such questions bearing on the usage of the sidereal frame there is the as yet unanswered question as to just what is 'sidereal' about the sidereal longitude, that is, How is it anchored to the fixed stars? Jones is content to remark that the astrologers who used sidereal rather than tropical longitudes were hardly aware of the scientific distinction, but surely there is more to it than that.Florian Mittenhuber discusses the origin of the maps in Ptolemy's Geography. The earliest extant maps are of the thirteenth and fourteenth centuries, and it has been argued that these were reconstructed from the text by Planudes in the thirteenth century. Now Mittenhuber, who was one of the team in Switzerland who produced the new edition of the Geography (Basel, 2006), argues that the maps designated U, K, F (Vatican, Istanbul, Copenhagen) have a hypothetical common ancestor in a group designed ? …

We describe the theory, design, and construction of simple electromechanical devices that automatically and continually track celestial objects. As Earth rotates and revolves, a star tracker always points at a star or other objects fixed to the celestial sphere, such as the center of the Milky Way galaxy. A planet tracker can fixate on any celestial object including the planets, the Sun, or the Moon. A sidereal clock mechanism drives the star tracker, and software that encodes astronomical algorithms controls an inexpensive robot that drives the planet tracker. The star tracker acts like a gyroscope, rigidly oriented in space, despite Earth’s motion. Both trackers indicate the passing of time just like clocks and calendars. The resulting lecture, hallway, or museum displays promote awareness of and excitement about our place in the universe.

This paper is the third of a multi-part examination of the Babylonian mathematical lunar theories known as Systems A and B. Part I (Britton, AHES 61:83–145, 2007) addressed the development of the empirical elements needed to separate the effects of lunar and solar anomaly on the intervals between syzygies, accomplished in the construction of the System A lunar theory early in the fourth century B.C. Part II (Britton, AHES 63:357–431, 2009) examines the accomplishment of this separation by the construction of a successful theory depicting the variations due to lunar anomaly in System A and its subsequent adaptation in System B. The present paper examines the introduction of the uniform zodiac, necessary for any theory depicting variations depending on the position of syzygy. It addresses three questions: (1) In light of all available evidence, what is the magnitude of the constant term in the expression Δλ* = C − 1.3828°Y, describing the difference between the Babylonian sidereal longitudes and modern tropical longitudes? (2) What considerations governed the placement of the Babylonian sidereal zodiac relative to the fixed stars? (3) When was the uniform zodiac introduced? To the first question it finds C = 3.20° ± 0.1°, scarcely different from Huber’s (Centaurus 5:192–208, 1958) estimate of 3.08°, essentially confirming Huber’s result obtained from much less data. For the second it shows that accommodating the three asterisms comprising Taurus limited the placement of the zodiac to within 3°, while the prominence of half sign multiples among the measured intervals between prominent Normal Stars led irresistibly to the choice adopted. Finally, it finds that the zodiac was introduced between −408 and −397 and probably within a very few years of −400.

In January 1729 a paper written by James Bradley was read at two meetings of the Royal Society. On a newly discovered motion of the fixed stars, later described as the theory of the aberration of light, it was to transform the science of astrometry. The paper appeared as a narrative of a programme of observation first begun at Kew and finalized at Wanstead, but it was, in reality, a careful reconstruction devised to enhance his reputation in response to a recognition that the programme was initially conducted in terms that were inimical to what he conceived to be his interest. The planned attempt to repeat Robert Hooke's celebrated experiment by James Pound, Samuel Molyneux and George Graham was set up at Molyneux's residence in Kew with James Bradley replacing Pound after his untimely and sudden demise. The unexpected and counterintuitive behaviour of the object star γ Draconis and the eradication of any suspicion of instrumental or systemic error led to the abandonment of the attempt to measure annual parallax and the initiation of new conjectures. An annual nutation was proposed but after the observation of a control star, 35 Camelopardalis, this conjecture was abandoned. Unknown to Bradley and Graham a premature approach was made by Molyneux to Newton claiming that the ‘nutation’ negated the whole of Newton's system. In the abandonment of the nutation yet another conjecture opposed to Newtonian theory was proposed and abandoned. Bradley determined to use his own instrument designed on different principles by Graham to observe the phenomenon in Wanstead. At Wanstead Bradley observed many stars to determine the parameters of the phenomenon. With the law of the motion described, Bradley proposed a hypothesis to explain it. Drawn from his earlier work on the ephemerides of Jupiter's satellites his hypothesis of the ‘new-discovered motion’ was quickly presented to the Royal Society as Bradley was working on a later and more definitive version of his paper. It is this later, third, unpublished version that is commonly referred to throughout this essay. It issued a challenge to ‘anti-Copernicans’ to offer an explanation of the observed phenomenon in geostatic terms. One such astronomer, Eustachio Manfredi, had examined the phenomenon of ‘aberrations’ in detail, the term being his. It was Bradley who first applied the term to the ‘new-discovered motion’ and within a short time ‘aberration’ was being applied by astronomers in the reduction of their observations. Annual aberration was widely accepted as evidence of the motion of the Earth. The paper enhanced Bradley's reputation and projected him into the forefront of European astronomers.

The composition of the astronomical-and-astrological treatise known as the Libro de la ochava esfera involved several translators and compilers. They produced oral and written versions of aṣ-Ṣufī’s Book of the Figures of the Fixed Stars (itself based on a translation of Ptolemy’s star-catalog), and they consulted previous Arabic and Latin versions of these works. This article follows the traces that the collaborative-translation process left in the treatise’s many multilingual phrases, which combine alternative names for the constellations in Castilian, Latin, Arabic, and Greek. It argues that this translation practice worked as a conceptual model for the type of knowledge(s) ( saberes ) the treatise offered. The analysis and argument are inscribed in a discussion of the paradoxical place that the Libro de la ochava esfera occupies in the history of Spanish literature, and they offer a formal ground for challenging dominant conceptualizations of textual production and interpretation, which are based on a monolingual model.

Having reached the borders of the solar system, there is bound to be a desire to lean on the fence, even if there is no one out there, and to look outwards, and, while having a look around, to wonder what might lay beyond. After all, this is the first time we have arrived at this spot.

This paper 1 studies the different conceptions of both centrality and the principle or starting point of motion in the Universe held by Aristotle and later on by Copernicanism until Kepler and Bruno. According to Aristotle, the true centre of the Universe is the sphere of the fixed stars. This is also the starting point of motion. From this point of view, the diurnal motion is the fundamental one. Our analysis gives pride of place to De caelo II, 10, a chapter of Aristotle’s text which curiously allows an ‘Alpetragian’ reading of the transmission of motion. In Copernicus and the Copernicans, natural centrality is identified with the geometrical centre and, therefore, the Sun is acknowledged as the body through which the Deity acts on the world and it also plays the role of the principle and starting point of cosmic motion. This motion, however, is no longer diurnal motion, but the annual periodical motion of the planets. Within this context, we pose the question of to what extent it is possible to think that, before Kepler, there is a tacit attribution of a dynamic or motive role to the Sun by Copernicus, Rheticus, and Digges. For Bruno, since the Universe is infinite and homogeneous and the relationship of the Deity with it is one of indifferent presence everywhere, the Universe has no absolute centre, for any point is a centre. By the same token, there is no place that enjoys the prerogative of being—as being the seat of God—the motionless principle and starting point of motion.

Quarum causas in orbibus sub suppremo collocatis indagantes, in suppremo enim uniformitas semper cernitur, exploratum habuerunt id prouenire ex motibus giratiuis lulabinis appellatis, factis quidem a permistione motus orbis super suis polis cum motu eiusdem super polis alterius, itaque ex multis motibus simul collectis unus fit motus. Quae quidem theorica phisicis conformis rationibus cunctis ueteribus ad Aristotelem philosophorum principem usque uigebat, quin immo sui summi acie ingenii eam 2 de coelo textu commentario 35 teste Auerroe innuere non desinit. Qalo Qalonymos

INSIGHTS INTO DE CAELO New Perspectives on Aristotle's De caelo. Edited by Alan C. Bowen and Christian Wildberg. (Philosophia Antiqua, cxvii; Brill, Leiden, 2009). Pp. vi + 320. euro103. ISBN 978-90-04-17376-7."Familiarity with the main doctrines of the De caelo is a prerequisite for an understanding of much of the thought and culture of Antiquity and the Middle Ages", as Alan C. Bowen and Christian Wildberg state in the Preface to their edited volume of essays on Aristotle's work. Some readers of this journal may be attracted to this volume because of the influence of De cae Io on cosmological thought through to the time of Galileo and Kepler, for, as Bowen and Wildberg note, the work "helped to shape the way in which Western civilization imagined its natural environment and place at the center of the universe"; others will be interested in considering particular issues in De caelo.The contributors to the volume are highly regarded specialists in ancient Greek philosophy; their papers aim to offer philosophically sound readings of difficult passages or topics in De caelo, with the goal of deepening our understanding of Aristotle's cosmology. As the editors explain in their Introduction, the Greek title Peri ouranou and the Latin De caelo indicate that the subject of the work is the entire universe; the English title On the heavens may suggest that the sublunary region is excluded. However, the work is concerned not only with the nature and movement of the sphere of the fixed stars and with planetary movements as well as other phenomena in the region between the sphere of the fixed stars and the Moon, but also considers the universe as a whole (including the Earth) and the natural motion of all the elementary bodies therein. The contributions here reflect the breadth of Aristotle's enquiry; several authors focus on issues relating to scientific method. In some instances the work of one contributor relates closely to and reinforces the arguments of another; in others, contributors disagree about particular questions.A list of the chapter titles gives a good indication of the contents. In the first essay, "From Plato's Timaeus to Aristotle's De caelo: The case of the missing world soul", Thomas K. Johansen considers the title of Aristotle's work, noting that Aristotle himself discussed the different meanings oiouranos (heaven; at 278b9-21). Comparing topics treated in the Timaeus and the De caelo, Johansen argues that there is no world soul in De caelo, nor is there an explicit cosmic teleology, such as that found in the Timaeus. While the astronomy of the Timaeus provides a divine template for living ethically, in the De caelo Aristotle is not concerned with ethics. Several other contributors consider Aristotle's work in relation to that of Plato, including Sarah Broadie, who (in 'The possibilities of being and not-being in De caelo 1. …

A revolution of the line of nodes with respect to the fixed stars takes 6,793 days (see Chap. 17); a revolution of the line of apsides with respect to the fixed stars takes 3,233 days (see Chap. 19). The former is retrograde, the latter is direct: their opposite motions add up one to the other.

'Abd al-Raḥmān al-Ṣūfī (AD 903–986) is justly famous for his Book of the Fixed Stars. This is an outstanding Medieval treatise on astronomy that was written in AD 964. This work was developed from Ptolemy’s Almagest, but was based upon al-Ṣūfī’s own stellar observations. The Book of the Fixed Stars has been copied down through the ages, and currently 35 copies are known to exist in various archival repositories around the world.