world history

G

Geocentrism

Pietro Daniel Omodeo History of astronomy and philosophy, Max Planck Institute for the History of Science, Berlin, Germany

Abstract

“Geocentrism” refers to a cosmological and plan- etary theory, in which the Earth occupies the cen- tral position of the world system. In antiquity and in the Middle Ages, geocentrism was the most common cosmological view, although some astronomers and philosophical schools embraced alternative visions about worldly order. During the Renaissance, debates following Nicolaus Copernicus’s proposal of a heliocentric planetary theory prompted a reexamination of traditional geocentric (and geostatic) arguments (see “▶ Copernicanism” and “▶ Astronomy”). This also led to their reworking and expansion. Aristotle’s and Ptolemy’s arguments were atten- tively reconsidered. Many scholars deemed them conclusive and therefore stuck to terrestrial cen- trality even after parallax computation (in the 1580s, especially Tycho Brahe) and telescopic evidence (after 1610, especially Galileo Galilei) demonstrated the impossibility of geocentric paths for Mars and the inferior planets. Geo-heliocentrism thus emerged as the only via- ble solution. It was a planetary theory according to

which all or some of the planets rotate around the Sun, while the Sun remained Earth centered along with the Moon and the fixed stars. The Inquisition prohibition of Copernican astronomy in 1616 gave new impetus to geocentrism, in its geoheliocentric form, among Catholics.

The Aristotelian Legacy

Aristotle’s arguments in favor of terrestrial cen- trality, especially those in De coelo II 12–13, were particularly influential during the Middle Ages and the Renaissance. They was especially due to Aristotle’s acknowledged authority and to their integration in a systematic vision of nature. In particular, geocentrism was compatible with the elemental theory according to which the four sub- lunary elements – earth, water, air, and fire – are ordered according to a concentric scheme beneath the sphere of the Moon (the first of the celestial bodies). They were thought to have innate tenden- cies to move toward their “natural places.” According to this doctrine, the earth, as the “heaviest” element, strives toward the cosmolog- ical center, which coincides with the center of gravity.

Against this philosophical backdrop an ad hoc explanation had to account for the fact that the orbis terrarum – the three continents, Africa, Asia, and Europe – was not submerged in the water. During the Middle Ages, this explanation was sought in the providential intervention of God

# Springer International Publishing Switzerland 2015 M. Sgarbi (ed.), Encyclopedia of Renaissance Philosophy, DOI 10.1007/978-3-319-02848-4_67-1

at the moment of the Creation. In the sixteenth century, the oceanic explorations and the discov- ery of continents thus far unknown to the Europeans – especially the so-called antipodes – undermined traditional cosmography and proved the fundamental unity of the globus terracquaeus (the earthly watery globe). This new evidence and its theoretical consequences for geography were a mortal blow to medieval cos- mology, as astronomical innovators such as Copernicus stressed. The latter mentioned the epi- stemic discontinuity in geographical knowledge in his first book of De revolutionibus orbium coelestium (I 3) in order to make his heliocentric theory acceptable in spite of its novelty. Coperni- cus claimed that astronomy ought to be emended just like geography.

In spite of Copernicus’s claim, the Aristotelian tradition lived long after him, as witnessed by the countless editions and commentaries of Sacrobosco’s standard textbook, which began with reference to the theory of the elements and the “two-physics” distinction between the sublu- nary realm of corruption and the quintessentially incorruptible heavenly realm. The most authorita- tive Renaissance commentary on this book was composed by the Jesuit mathematician Christoph Clavius. It was widely circulated during the Renaissance, especially as a textbook for the teaching of spherical astronomy at Jesuit colleges.

The Ptolemaic Legacy

By far the most important astronomical defense of geocentrism from antiquity is Ptolemy’s. The Hel- lenistic astronomer, who was still regarded as the “prince of astronomy” during the Renaissance, refutes the eccentricity of the Earth in Almagest I 5 (standard modern numbering). He bases his objection on considerations of how a hypothetical displacement of the Earth in different directions would alter celestial phenomena. He considers in particular the cases of terrestrial eccentricity on the equatorial plane or along the rotational axis. A “third” case, that the Earth is neither on the axis of the daily rotation nor on the equatorial plane, cumulates the disadvantages of both dislocations.

Therefore Ptolemy only mentions it but does not treat it extensively.

Concerning the first case, Ptolemy argues,

If we imagined [the Earth] removed towards the zenith or the nadir of some observer then, if he were at sphaera recta [at the equator], he would never experience equinox, since the horizon would always divide the heavens into two unequal parts, one above and one below the Earth; if he were at sphaera obliqua [at an arbitrary latitude], either, again, equinox would never occur at all, or [if it did occur], it would not be at a position halfway between summer and winter solstices, since these intervals would necessarily be unequal, because the equator, which is the greatest of all parallel circles drawn about the poles of the [daily] motion, would no longer be bisected by the horizon; instead [the horizon would bisect] one of the circles parallel to the equator, either to the north or to the south of it. (Toomer 1984, p. 41)

Ptolemy additionally observes that, if the Earth were “removed towards the east or west of some observer,” the sizes and the distances of the stars would be different at eastern and western hori- zons. Moreover, the time intervals between rising and culmination and between culmination and setting would be unequal.

In the second case – that the Earth is displaced along the axis toward the north or the south – the plane of the horizon would divide the heavens into unequal parts for any observer (at the equator or at any other latitude). Furthermore, the shadows of sundials would be altered. At equinoxes the shadows of a gnomon at sunrise and at sunset would not form a straight line in a plane parallel to the horizon.

These were the main Ptolemaic arguments for geocentrism based on geometrical reasoning and empirical evidence. According to Ptolemy a dis- placement of the Earth from the center would not be compatible with the heavenly phenomena. Copernicus and the supporters of the heliocentric system solved these inconveniences by simply assuming that the dimensions of the annual “orbit” of the Earth around the Sun are negligible relative to the distance of the starry heaven, as stated in De revolutionibus I 5.

Copernicus’s claim about the immensitas of the heavens persuaded only a few among his contem- porary and immediate followers. Particularly

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revealing of the post-Copernican endurance of geocentrism is Erasmus Reinhold’s edition with commentary of the first book of the Almagest (15491). This was a textbook directed to Witten- berg students. In it, Reinhold not only explained and illustrated the Ptolemaic arguments but also expanded and strengthened them. He appreciated Copernicus’s mathematics but not his violation of acknowledged physical principles.

Ancient and Medieval Alternative Systems Reassessed

Ancient and medieval scholars also produced cos- mologies that were neither geocentric nor geostatic. In De coelo II 13, Aristotle reported the Pythagoreans’ worldview as one such case. According to them, a “fire” occupies the center of the cosmos. Based on this reference, there was a tendency in the early reception of Copernicus to ascribe his system to Pythagorean forerunners. However, there was no compelling evidence that their “central fire” corresponded to the Sun nor that the terrestrial rotation around the center referred to the annual revolution. Aristotle only reported that the Pythagorean model could account for the same celestial phenomena as geocentrism:

Most of those who hold that the whole Universe is finite say that it lies at its center, but this is contradicted by the thinkers of the Italian school called Pythagorean. These affirm that the center is occupied by fire, and that the Earth is one of the stars, and creates night and day as it travels in a circle about the center. . . . Since the Earth’s surface is not in any case the centre, they [the Pythagoreans] do not feel any difficulty in supposing that the phenomena are the same although we do not occupy the centre as they would be if the Earth were in the middle. For even in the current view [that is, geocentrism] there is nothing to show that we are distant from the center by half the Earth’s diameter. (Aristotle 1986, p. 217)

A proper heliocentric theory had to wait until the third century BC, when Aristarchus of Samos developed and defended it as a viable astronomi- cal thesis. Archimedes referred to it in The Sand Reckoner. He asserted that he could express the number of grains of sand encompassed by

Aristarchus’s cosmos in a handy manner through a new numerical system solving the major short- comings of Greek mathematical symbolism. This reference to Aristarchus’s cosmos is a hint at the conspicuous enlargement of the world implied by the passage from a geocentric to a heliocentric theory, as a consequence of the fact that terrestrial revolution produces no observable stellar paral- lax. Several Renaissance scholars perceived this difficulty as insurmountable. In particular, the “useless” vastness of the space between Saturn and the fixed stars looked impossible to critics of heliocentrism such as Brahe, and this formed part of their criticism against heliocentrism.

It should be stressed that the thesis of the motion of the Earth is not incompatible with geocentrism. Among others, Plato defended geokinetic geocentrism: in Timaios 40b–c, he ascribed to the Earth the axial rotation as the cause of the succession of days and nights. In the fifteenth century, Nicholas Cusanus argued for terrestrial motion in the second book of De docta ignorantia. In the following centuries, the thesis of terrestrial centrality-cum-mobility was endorsed by several scholars, among whom were the imperial mathematician Nicolaus Raimarus Ursus in Fundamentum astronomicum (1588), the Brandenburg mathematician David Origanus in his ephemerides and Brahe’s pupil Christian Longomontanus in Astronomia Danica (1622).

During the Middle Ages geocentrism was never cast into doubt. It was linked to theological conceptions of divine Providence and Creation, as witnessed in Dante Alighieri’s synthesis of late- medieval thought in the Divina Commedia. The Earth rested at the center as the place of change and corruption, encircled by the ethereal perfec- tion of the heavenly spheres surrounded by the empyrean heaven, which was the abode of the blessed souls and the contemplating God. Plane- tary order was less standardized. In the twelfth century Andalusia al-Bitruji argued for the sublu- nary location of Mercury and the superlunary of Venus in his work of homocentric astronomy, Book on Astronomy, which had large dissemina- tion among Jewish and Latin philosophers. Medi- eval commentaries on Macrobius, Pliny the Elder, Martianus Capella, and Calcidus also displayed

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qualitative heavenly diagrams in which planetary motions are not perfectly circular or the two infe- rior planets encircle the Sun instead of the Earth. The latter model (geocentrism with heliocentric paths for Mercury and Venus), ascribed in antiq- uity to Herakleides of Pontus, became known as the Capellan system. Copernicus would refer to the diverging opinions of his ancient and medieval forerunners in the beginning of De revolutionibus to claim his right to an independent and innova- tive inquiry into this matter:

Therefore, having obtained the opportunity from these sources, I too began to consider the mobility of the Earth. And even though the idea seemed absurd, nevertheless I knew that others before me had been granted the freedom to imagine any circles whatever for the purpose of explaining the heavenly phenomena. Hence I thought that I too would be readily permitted to ascertain whether explanations sounder than those of my predecessors could be found for the revolution of the celestial spheres on the assumption of some motion of the Earth. (Copernicus 1978)

Post-Copernican Geocentrists

The mathematical reception of Copernicus never implied adherence to heliocentrism as a physical reality. At Wittenberg, one of the most important irradiating centers of his astronomical work, the leading intellectuals opposed this realist option. Martin Luther is reported to have reacted with skepticism to the new system because it was in contrast with the Bible. Philip Melanchthon condemned Copernicus’s hypotheses on the basis of natural-philosophical considerations. In his and the philosopher Paul Eber’s introduction to physics, Initia doctrinae physicae (Introduction to Physics, 1549), the Copernican theory was rejected and its teaching was prohibited.

The Wittenberg mathematician Reinhold was enthusiastic about Copernicus’s geometrical models, for they respected the so-called astronom- ical axiom (celestial motions are circular and uni- form about their centers). In his manuscript commentary on Copernicus, Commentarius in opus Revolutionum Copernici, he hinted at the possibility of accepting his devices without

renouncing geocentrism. However, he could not complete his geocentric revision of Copernican astronomy due to an untimely death.

Reinhold’s follower as a professor of mathe- matics in Wittenberg and Melanchthon’s son-in- law, Caspar Peucer continued his “translation” of the Copernican models by showing that his model for the precession and the trepidation of the starry heaven could easily be adapted to a geocentric frame. Far from a conventionalist approach to astronomy, that is to say, an approach only inter- ested in “saving the phenomena” without any consideration about the physical tenability of the models employed by the astronomers, his and his master’s efforts bear witness to a shared desire to reconcile physics and mathematical astronomy. Peucer’s astronomical hypotheses, or “hypotyposes,” published anonymously in Stras- bourg in 1568 (as Hypothyposes) and then with the author’s name in Wittenberg in 1571 (Hypotheses astronomicae, seu Theoriae planetarum), exerted a conspicuous influence on the cosmological and philosophical post- Copernican debate at the end of the century. The Strasbourg mathematician Conrad Dasypodius carried out the first anonymous edition. In the preface he ascribed this work to Reinhold reinforcing the conviction, among learned scholars, that the author of the Prutenicae tabulae was also the designer of a geocentric revision of Copernicus, the details of which had not yet been developed.

Among those who reworked De revolutionibus with a geocentric perspective, the Silesian mathe- matician Paul Wittich occupies a special place. In two preserved copies of De revolutionibus, he developed geometrically equivalent planetary models, which varied Copernicus’s theory. In these diagrams he illustrated how to pass from Sun-centered models to equivalent Earth-centered ones. Those displaying the “theory of the three superior [planets] accorded with the immobility of the Earth” are accompanied by a claim for author- ship: “I found this new genre of hypotheses on 13 February 1579.” Wittich also accommodated the inferior planets within a geocentric (and geostatic) framework, remarking that “[. . .] Copernicus’s theory of the two inferior [planets]

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can be in agreement with the immobility of the Earth, in accordance with Ptolemy’s words.”

Wittich’s geometrical considerations acquired a strong physical meaning a decade later when geoheliocentric systems proliferated, following the seminal publications by Ursus and Brahe, who were both acquainted with the ideas of the talented Silesian mathematician. However Ursus’s and Brahe’s models were slightly differ- ent. The former maintained that the central Earth rotates producing the apparent daily rotation of the heavens. In Brahe’s system, the solar and Martian “orbits” intersected. The reason he gave for this intersection was the alleged observation, in 1582, of a Martian parallax larger than that of the Sun. This demonstrated that the planet is closer to the Earth in opposition. Ptolemy could not explain this proximity, as Brahe explained in a writing, Apologia de cometis (Apology on [My Theory of] Comets), directed to the Scottish mathematician John Craig (1589). He added that only two systems could account for it, namely the Copernican or a geoheliocentric one. The latter, however, presupposed that the heavens are fluid. Hence, Brahe attached great importance to the observation of comets demonstrating that celestial bodies freely traverse cosmic space:

Hence, there is no doubt that Mars is closer to the Earth in opposition than the Sun can ever be. Thus, the ancient Ptolemaic hypotheses, which were accepted up to present, can never agree with reality. By necessity, either the Earth accomplishes an annual revolution and the Sun is immobile at the center of the universe, as Copernicus asserted with conviction in modern times; or—if this appears to be absurd, as it is—there remains no other possible system (hypothesium conformatio) than that which we have introduced. [. . .] From these consider- ations it is sufficiently clear that I did not reject the reality of the [celestial] spheres with temerity. In fact, if the Earth has to be immobile, [the parallax of] Mars implies this consequence [i.e., the rejec- tion of the solid spheres], so that no impossible penetration of the Solar sphere occurs. (Brahe 1972, p. 475)

These publications of the late 1580s triggered off a polemic over the priority in the “discovery” of geoheliocentrism that lasted more than one decade. Even Kepler was co-opted by Brahe in his struggle for the recognition of his priority.

Brahe required him to write against Ursus as a condition for his appointment in Prague as his assistant in 1600. Brahe was notoriously jealous of his theory and deemed other scholars dealing with it without appropriate reference to his author- ship to be plagiarizers. For instance, in 1591, after he was informed that the Scottish mathematician Duncan Liddel was teaching his theory to Rostock and Helmstedt students, he accused him of unduly appropriating his doctrines, as emerges in his cor- respondence with Kepler (2001, pp. 91-92.).

The geo-heliocentric theory was long lived. In northern Europe, Brahe’s pupils picked it up, in particular Longomontanus who proved one of the most strenuous opponents to Kepler’s heliocentric-and-elliptical planetary theory. After the Inquisition prohibited heliocentrism, geoheliocentrism remained the only system a Catholic astronomer could adhere to. Students of Jesuit Colleges were taught the details of this theory alongside anti-Copernican arguments. A telling document of this anti-heliocentric resis- tance is the extensive refutation of the Copernican system in the second volume of Giovanni Battista Riccioli’s Almagestum novum (New Almagest, 1651). The author embraced a hybrid system. According to this Jesuit astronomer, the two infe- rior planets plus Mars encircle the Earth while the Sun, the Moon, Jupiter, Saturn, and the sphere of the fixed stars turn about the cosmologically cen- tral Earth.

References

Primary Literature Aristotle. 1986. On the heavens, 217. London/Cambridge,

MA: Harvard UP. Brahe, Tycho. 1972. Apologia de cometis. In Opera

omnia, ed. John Louis Emil Dreyer (Havniae: Libraria Gyldendaliana, 1913–1929, repr. 1972), Vol. 4, pp. 415–476.

Brahe to Kepler (Benatek, 9. December 1599). In Gesammelte Werke, Johannes Kepler, Vol. 14 (M€unchen: Beck, 2001), pp. 89–98.

Copernicus, Nicolaus. 1978. On the revolutions, ed. Jerzy Dobrzycki, transl. and comm. by Edward Rosen. Bal- timore/London: The Johns Hopkins University Press.

Toomer, G.J. 1984. Ptolemy’s Almagest, 41. London: Duckworth.

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Secondary Literature On Ancient cosmological models, see Michel-Pierre Ler-

ner, Le monde des sphères (Paris: Les Belles Lettres, 2008) and Otto Neugebauer, A history of ancient math- ematical astronomy (Berlin: Springer, 1975).

On Aristotle’s geocentric arguments, see Pietro-Daniel Omodeo and Irina Tupikova, Aristotle and Ptolemy on geocentrism: diverging argumentative strategies and epistemologies (Berlin: Max-Planck-Institut f€ur Wissenschaftsgeschichte, 2012), Preprint 422.

On the impact of the idea of an earthly-watery globe and its meaning for Copernican astronomy, see Klaus Vogel, “Das Problem der relativen Lage von Erd- und Wassersphäre im Mittelalter und die kosmographische Revolution,” Mitteilungen der Österreichischen Gesellschaft f€ur Wissenschaftsgeschichte 13 (1993): pp. 103–143 and, by the same author, “Cosmography,” in The Cambridge History of Science, vol. 3, Early Modern Science, ed. by Karin Park and Lorraine Daston (Cambridge, 2006), pp. 469–96.

On Sacrobosco and his commentators in the Middle Ages and the Renaissance, see Lynn Thorndike, The Sphere of Sacrobosco and Its Commentators (Chicago: UP, 1949), James M. Lattis, Between Copernicus and Gali- leo. Christoph Clavius and the Collapse of Ptolemaic Cosmology (Chicago: UP, 1994) and Isabelle Pantin, “Francesco Giuntini et les nouveautés célestes,” in Dario Tessicini and Patrick Boner, Celestial Novelties on the Eve of the Scientific Revolution, 1540–1630 (Florence: Olschki, 2013), pp. 85–104.

On Ptolemy’s astronomy and its the Renaissance reception, see Olaf Pedersen, A Survey of the Almagest (Odense: Odense Press, 1974), Liba Chaia Taub, Ptolemy’s Uni- verse: the Natural, Philosophical and Ethical Founda- tions of Ptolemy’s Astronomy (Chicago: Open Court, 1993), and Pietro Daniel Omodeo and Irina Tupikova, “Post-Copernican Reception of Ptolemy: Erasmus Reinhold’s Commented Edition of the Almagest, Book One (Wittenberg, 1549)”, Journal for the History of Astronomy (2013): pp. 235–256.

On ancient and medieval cosmological views alternative to geocentrism, see Giovanni Virginio Schiaperelli, I precursori di Copernico nell’antichità (Milano: U. Hoepli, 1873), Thomas Little Heath, Aristarchus of Samos, the Ancient Copernicus: a History of Greek Astronomy to Aristarchus (Oxford: Clarendon Press, 1913), D’Alverny, Marie-Thérèse: “Survivances du ‘système d’Héraclide’ au Moyen Age,” in Semaine de Synthèse, Avant, avec, après Copernic (Paris: Blanchard, 1975), pp. 39–50 and Bruce S. Eastwood, Ordering the Heavens: Roman Astronomy and Cosmol- ogy in the Carolingian Renaissance (Leiden: Brill, 2007).

The Wittenberg School of astronomy has been studied by Robert S. Westman, “The Melanchthon Circle, Rheticus and the Wittenberg Interpretation of the Copernican Theory,” Isis 66 (1975): pp. 163–93 and

idem, “Three Responses to the Copernican Theory: Johannes Praetorius, Tycho Brahe and Michael Maestlin,” in The Copernican Achievement (Berkeley: University of California Press, 1975) pp. 285–345); Owen Gingerich, “Erasmus Reinhold and the Dissem- ination of Copernican Theory,” in The Eye of Heaven: Ptolemy, Copernicus, Kepler (New York: American Inst. of Physics, 1993), pp. 221–251, and idem, “Reinhold, Erasmus,” Dictionary of Scientific Biogra- phy 11 (1975): pp. 365–367; and Walter Th€uringer, “Paul Eber (1511–1569): Meanchthons Physik und seine Stellung zu Copernicus,” in Melanchthon in seinen Sch€ulern, ed. Heinz Scheible (Wiesbaden: Harrassowitz, 1997), pp. 285–321. Reinhold manu- script commentary of Copernicus has been published in Nicolaus Copernicus, Gesamtausgabe, vol. VIII/1, Receptio Copernicana (Berlin: Akademie Verlag, 2002), pp. 189–358. On Puecer and Dasypodius, see Peter Barker, “The Hypotyposes orbium coelestium (Strasbourg, 1568),” in Nouveau ciel nouvelle terre: La révolution copernicienne dans l’Allemagne de la Réforme (1530–1630), ed. Miguel Angel Granada and Edouard Mehl (Paris: Les Belles Lettre, 2009), pp. 85–108.

For Wittich, cfr. Owen Gingerich and Robert S. Westman, “The Wittich Connection: Conflict and Priority in Late Sixteenth-Century Cosmology,” Transactions of the American Philosophical Society 78/7 (1988). On the controversies over the priority of the geo-heliocentric system, see Nicholas Jardine, The Birth of the History and Philosophy of Science: Kepler’s A Defence of Tycho against Ursus with Essays on its Provenance and Significance (Cambridge: UP, 1984); Edward Rosen, Three Imperial Mathematicians: Kepler Trapped between Tycho Brahe and Ursus (New York: Abaris Books, 1986); Miguel Angel Granada, El debate cosmológico en 1588: Bruno, Brahe, Rothmann, Ursus, Röslin (Naples: Bibiopolis, 1996); and Nicholas Jardine and Alain Segonds, La guerre des astronomes: La querelle au sujet de l’origine du système géo-héliocentrique à la fin du XVIe siècle (Paris, 2008), 2. vol. On the triangulation Brahe- Liddel-Craig, see Adam Mosley, “Tycho Brahe and John Craig: The Dynamic of a Dispute,” in Tycho Brahe and Prague: Crossroads of European Science, ed. John Robert et al. (Frankfurt am Main: Deutsch, 2002), pp. 70–83 and Pietro Daniel Omodeo, “L’iter europeo del matematico e medico scozzese Duncan Liddel,” (Berlin: Max-Planck-Institut f€ur Wissenschaftsgeschichte, 2013), Preprint 438 (2013).

On the reasons for the Jesuit adhesion to geoheliocentrism, see “L’entrée de Tycho Brahe chez les jésuites ou le chant du cygne de Clavius,” in Luce Giard, Les jésuites à la Renaissance: Système éducative et production du savoir (Paris: Presses Universitaires de France, 1995), pp. 145–186.

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