HELIOCENTRISM

In astronomy, 'heliocentrism' is the theory that the sun is at the centre of the Universe and/or the Solar System. The word is derived from the Greek (''Helios'' = "Sun" and ''kentron'' = "Center"). Historically, heliocentrism is opposed to geocentrism and currently to modern geocentrism, which places the earth at the center. (The distinction between the Solar System and the Universe was not clear until modern times, but extremely important relative to the controversy over cosmology and religion.) Although many early cosmologies speculated about the motion of the Earth around a stationary Sun, it was not until the 16th century that Copernicus presented a fully predictive mathematical model of a heliocentric system, which was later elaborated by Kepler and defended by Galileo, becoming the center of a major religious dispute.

Contents

Development of heliocentrism

Philosophical discussions

Ancient India

Greco-Roman world

Middle East

Medieval Europe

Mathematical astronomy

Medieval India

Middle East

Renaissance Europe

Religious disputes over heliocentrism

The view of modern science

Modern use of ''geocentric'' and ''heliocentric''

See also

Notes

References

Development of heliocentrism

To anyone who stands and looks at the sky, it seems clear that the earth stays in one place while everything in the sky rises and sets or goes around once every day. Observing over a longer time, one sees more complicated movements. The Sun makes a slower circle over the course of a year; the planets have similar motions, but they sometimes turn around and move in the reverse direction for a while (retrograde motion). As these motions became better understood, they required more and more elaborate descriptions, the most famous of which was the Ptolemaic system, formulated in the 2nd century, which, though considered incorrect today, still manages to calculate the correct positions for the planets to a very useful degree of accuracy. It is interesting to note that Ptolemy, himself, in his Almagest points out that any model for describing the motions of the planets is merely a mathematical device, and, since there is no actual way to know which is True, the simplest model that gets the right numbers should be used.

Philosophical discussions

Philosophical arguments on heliocentrism involve general statements that the Sun is at the center of the universe or that some or all of the planets revolve around the Sun, and arguments supporting these claims. These ideas can be found in a range of Sanskrit, Greek, Arabic and Latin texts. Few of these early sources, however, develop techniques to compute any observational consequences of their proposed heliocentric ideas.

Ancient India

The earliest traces of a counter-intuitive idea that it is the Earth that is actually moving and the Sun that is at the centre of the solar system (hence the concept of heliocentrism) is found in several Vedic Sanskrit texts written in ancient India.Teresi (2002).Blavatsky (1877), Part One, Chapter I. Yajnavalkya (c. 9th–8th century BC) recognized that the Earth is spherical and believed that the Sun was "''the centre of the spheres''" as described in the ''Vedas'' at the time. In his astronomical text ''Shatapatha Brahmana'' (8.7.3.10), he states:
He recognized that the Sun was much larger than the Earth, which would have influenced this early heliocentric concept. He also accurately measured the relative distances of the Sun and the Moon from the Earth as 108 times the diameters of these heavenly bodies, close to the modern measurements of 107.6 for the Sun and 110.6 for the Moon. He also described an accurate solar calendar in the ''Shatapatha Brahmana''.Joseph (2000). The ''Aitareya Brahmana'' (2.7) (c. 9th–8th century BC) also states:
Some interpret this to mean that the Sun is stationary, hence the Earth is moving around it, though others are less clear about the meanings of the terms. This would be elaborated in a later commentary ''Vishnu Purana'' (2.8) (c. 1st century BC), which states:

Greco-Roman world

In the 4th century BC, Aristotle wrote that:

Aristarchus's 3rd century BC calculations on the relative sizes of the Earth, Sun and Moon, from a 10th century AD Greek copy

The reasons for this placement were philosophic based on the classical elements rather than scientific; fire was more precious than earth in the opinion of the Pythagoreans, and for this reason the fire should be central. However, the central fire is not the Sun. The Pythagoreans believed the Sun orbited the central fire along with everything else. Aristotle dismissed this argument and advocated geocentrism.
Heraclides of Pontus (4th century BC) explained the apparent daily motion of the celestial sphere through the rotation of the Earth. The first person to present an argument for a heliocentric system, however, was Aristarchus of Samos (c. 270 BC). Like Eratosthenes, Aristarchus calculated the size of the earth, and measured the size and distance of the Moon and Sun, in a treatise which has survived. From his estimates, he concluded that the Sun was six to seven times larger than the Earth. His writings on the heliocentric system are lost, but some information is known from surviving descriptions and critical commentary by his contemporaries, such as Archimedes. Some have suggested that his calculation of the relative size of the Earth and Sun led Aristarchus to conclude that it made more sense for the Earth to be moving than for the huge Sun to be moving around it. As Aristarchus' original work on heliocentrism has not survived it is uncertain whether these arguments were his own. It should be noted that Plutarch mentions the 'followers of Aristarchus' in passing, so it is likely that there are other astronomers in the Classical period who also espoused heliocentrism whose work is now lost to us.
In Roman Carthage, Martianus Capella (5th century) expressed the opinion that the planets Venus and Mercury did not go about the Earth but instead circled the Sun.^[1] Copernicus mentioned him as an influence on his own work.^[2]

Middle East

Qutb al-Din, 13th century AD, discussed whether heliocentrism was a possibility

In Mesopotamia, the Babylonian astronomer Seleucus of Seleucia (b. 190 BC) adopted the heliocentric system of Aristarchus, and according to Plutarch, may have even proved it. His proposed proof may have been related to his observations of the phenomenon of tides. Indeed Seleucus correctly theorized that tides were caused by the Moon, although he believed that the interaction was mediated by the Earth's atmosphere. He noted that the tides varied in time and strength in different parts of the world.
In the medieval Islamic civilization, due to the scientific dominance of the Ptolemaic system in early Islamic astronomy, most Muslim astronomers accepted the geocentric model.^[3] However, several Muslim scholars had discussions on whether the Earth moved and tried to explain how this might be possible. Alhacen (c. 1000 AD) wrote a scathing critique of Ptolemy's model, which some interpret to imply he was criticizing Ptolemy's geocentrism,Qadir (1989), p. 5-10. but many agree that he was actually criticizing the details of Ptolemy's model rather than his geocentrism.^[4]
In 1030, Biruni discussed the Indian astronomical theories of Aryabhata, Brahmagupta and Varahamihira in his ''Indica''. Biruni agreed with the Earth's rotation about its own axis, and while he was initially neutral regarding the heliocentric and geocentric models,^[5] he noted that heliocentrism was a philosophical problem, rather than a mathematical problem.Saliba (1999). Abu Said Sinjari, a contemporary of Biruni, suggested the possible movement of the Earth around the Sun, which Biruni did not reject. Qutb al-Din (b. 1236), in his ''The Limit of Accomplishment concerning Knowledge of the Heavens'', also discussed whether heliocentrism was a possibility.A. Baker, L. Chapter (2002).

Nicholas of Cusa, 15th century, asked whether there was any reason to assert heliocentrism

Medieval Europe

Heliocentric ideas were known in Europe before Copernicus. Explorers and traders were increasingly venturing out beyond Europe and introducing the West to the Indian heliocentric traditions as detailed above (cf. the Silk Road and Muslim commentators). Scholars were also aware of the arguments of Aristarchus and Philolaus, as well as several other thinkers who had proposed (or were alleged to have proposed) heliocentric or quasi-heliocentric views, such as Hicetas, Heraclides Ponticus, and Martianus Capella.
During the Late Middle Ages, Bishop Nicole Oresme discussed the possibility that the Earth rotated on its axis, while Cardinal Nicholas of Cusa in his ''Learned Ignorance'' asked whether there was any reason to assert that the Sun (or any other point) was the center of the universe. In parallel to a mystical definition of God, Cusa wrote that "Thus the fabric of the world (''machina mundi'') will ''quasi'' have its center everywhere and circumference nowhere."^[6]

Mathematical astronomy

In mathematical astronomy, computational models of heliocentrism involve mathematical computational systems that are tied to a heliocentric model and where positions of the planets can be computed. The first computational system explicitly tied to a heliocentric model was the Copernican model described by Copernicus, but there were earlier computational systems that may have implied some form of heliocentricity, notably Aryabhata's model, which has astronomical parameters which some have interpreted to imply a form of heliocentricity. Several Muslim astronomers also developed computational systems with astronomical parameters compatible with heliocentricity, as stated by Biruni, but the concept of heliocentrism was considered a philosophical problem rather than a mathematical problem. Their astronomical parameters, however, were later adapted in the Copernican model in a heliocentric context.

Medieval India

Aryabhata, 5th century, developed a computational planetary model which has been interpreted as heliocentric

Aryabhata (476–550), in his magnum opus ''Aryabhatiya'', propounded a computational system based on a planetary model in which the Earth was taken to be spinning on its axis and the periods of the planets were given with respect to the Sun. Some have interpreted this to be a heliocentric model,^[7][8][9]
but this view has been disputed by others.^[10][11][12]
He was also the first to discover that the light from the Moon and the planets was reflected from the Sun, and that the planets follow elliptical orbits, on which he accurately calculated many astronomical constants, such as the periods of the planets, times of the solar and lunar eclipses, and the instantaneous motion of the Moon (expressed as a differential equation).^[13]Teresi, et al. (2002). Early followers of Aryabhata's model included Varahamihira, Brahmagupta, and Bhaskara II. Arabic translations of Aryabhata's ''Aryabhatiya'' were available from the 8th century, while Latin translations were available from the 13th century, before Copernicus had written ''De revolutionibus orbium coelestium'', so it is possible that Aryabhata's work had an influence on Copernicus' ideas.
Nilakantha Somayaji (1444-1544), in his ''Aryabhatiyabhasya'', a commentary on Aryabhata's ''Aryabhatiya'', developed a computational system for a partially heliocentric planetary model, in which the planets orbit the Sun, which in turn orbits the Earth, similar to the Tychonic system later proposed by Tycho Brahe in the late 16th century. Nilakantha's system, however, was mathematically more effient than the Tychonic sytem, due to correctly taking into account the equation of the centre and latitudinal motion of Mercury and Venus. Most astronomers of the Kerala school of astronomy and mathematics who followed him accepted his planetary model.^[14][15]

Middle East

Biruni, 11th century, suggested that if the Earth rotated on its axis this would be consistent with astronomical theory. He discussed heliocentrism but considered it a philosophical problem.

Although al-Biruni discussed the possibility that the Earth rotated about its own axis, in his ''Masudic Canon'', in which he set forth the principles that the Earth is at the center of the universe and that it has no motion of its own.^[16] He was aware that if the Earth rotated on its axis and around the Sun, this would be consistent with his astronomical parameters,Khwarizm, Foundation for Science Technology and Civilisation.^[17] but he considered this a philosophical problem rather than a mathematical problem.
Nasir al-Din al-Tusi (b. 1201) resolved significant problems in the Ptolemaic system by developing the Tusi-couple as an alternative to the physically problematic equant introduced by Ptolemy.M. Gill (2005). 'Umar al-Katibi al-Qazwini (d. 1277), who also worked at the Maragheh observatory, in his ''Hikmat al-'Ain'', wrote an argument for a heliocentric model, but later abandoned the model. Ibn al-Shatir (b. 1304) eliminated the need for an equant, proposing a system that was only approximately geocentric, rather than exactly so, having demonstrated trigonometrically that the Earth was not the exact center of the universe. His rectification was later used in the Copernican model, along with the earlier Tusi-couple and the Urdi lemma of Mo'ayyeduddin Urdi. Their theorems played an important role in the Copernican model of heliocentrism, which was achieved by reversing the direction of the last vector connecting the Earth to the Sun. In the published version of his masterwork, Copernicus also cites the theories of Albategni, Arzachel and Averroes as influences,Covington (2007). while the works of Alhacen and Biruni were also known in Europe at the time.

Renaissance Europe

Main articles: Copernican heliocentrism

Nicolaus Copernicus, 16th century, described the first computational system explicitly tied to a heliocentric model

In the 16th century, Nicolaus Copernicus's ''De revolutionibus'' presented a full discussion of a heliocentric model of the universe in much the same way as Ptolemy's ''Almagest'' had presented his geocentric model in the 2nd century. Copernicus discussed the philosophical implications of his proposed system, elaborated it in full geometrical detail, used selected astronomical observations to derive the parameters of his model from a series of astronomical observations, and wrote astronomical tables which enabled one to compute the past and future positions of the stars and planets. In doing so, Copernicus moved heliocentrism from philosophical speculation to predictive geometrical astronomy. This theory resolved the issue of planetary retrograde motion by arguing that such motion was only perceived and apparent, rather than real: it was a parallax effect, as a car that one is passing seems to move backwards against the horizon. This issue was also resolved in the geocentric Tychonic system; the latter, however, while eliminating the major epicycles, retained as a physical reality the irregular back-and-forth motion of the planets, which Kepler characterized as a "pretzel."
Copernicus cited Aristarchus in an early (unpublished) manuscript of ''De Revolutionibus'' (which still survives) so he was clearly aware of at least one previous proponent of the heliocentric thesis. However, in the published version he restricts himself to noting that in works by Cicero he had found an account of the theories of Hicetas and that Plutarch had provided him with an account of the Pythagoreans Heraclides Ponticus, Philolaus, and Ecphantus. These authors had proposed a moving earth, which did not, however, revolve around a central sun.

Religious disputes over heliocentrism

Psalm 93:1, Psalm 96:10, and Chronicles 16:30 state that "the world is firmly established, it cannot be moved." Psalm 104:5 says, "[the LORD] set the earth on its foundations; it can never be moved." Ecclesiastes 1:5 states that "the sun rises and the sun sets, and hurries back to where it rises."
Galileo defended heliocentrism, and claimed it was not contrary to those Scripture passages. He took Augustine's position on Scripture: not to take every passage literally, particularly when the scripture in question is a book of poetry and songs, not a book of instructions or history. The writers of the Scripture wrote from the perspective of the terrestrial world, and from that vantage point the sun does rise and set. In fact, it is the earth's rotation which gives the impression of the sun in motion across the sky.
As early as the time of Aristarchus, the heliocentric idea was denounced as being against religion in Europe. The issue did not assume any importance, however, for nearly 2,000 years.
Nicolaus Copernicus published the definitive statement of his system in ''De Revolutionibus'' in 1543. Copernicus began to write it in 1506 and finished it in 1530, but did not publish it until the year of his death. Although he was in good standing with the Church and had dedicated the book to Pope Paul III, the published form contained an unsigned preface by Osiander stating that the system was a pure mathematical device and was not supposed to represent reality. Possibly because of that preface, the work of Copernicus inspired very little debate on whether it might be heretical during the next 60 years.
There was an early suggestion among Dominicans that the teaching should be banned, but nothing came of it at the time. Some Protestants, however, voiced strong opinions during the 16th century. Martin Luther once said:
This was reported in the context of dinner-table conversation and not a formal statement of faith. Melanchthon, however, opposed the doctrine over a period of years.
A famous quotation, often mis-attributed to John Calvin, reads: It has long been established that the line cannot be found in the works of Calvin ^[18] (see also ^[19] and ^[20]). It has been suggested ^[21] that the quotation was originally sourced from the works of Lutheran theologian Abraham Calovius.
Over time, however, the Catholic Church began to become more adamant about protecting the geocentric view. Pope Urban VIII, who had approved the idea of Galileo's publishing a work on the two theories of the world, became hostile to Galileo. Over time, the Catholic Church became the primary opposition to the Heliocentric view.
The favored system had been that of Ptolemy, in which the Earth was the center of the universe and all celestial bodies orbited it. A geocentric compromise was available in the Tychonic system, in which the Sun orbited the Earth, while the planets orbited the Sun as in the Copernican model. The Jesuit astronomers in Rome were at first unreceptive to Tycho's system; the most prominent, Clavius, commented that Tycho was "confusing all of astronomy, because he wants to have Mars lower than the Sun." (Fantoli, 2003, p. 109) But as the controversy progressed and the Church took a harder line toward Copernican ideas after 1616, the Jesuits moved toward Tycho's teachings; after 1633, the use of this system was almost mandatory. For advancing heliocentric theory Galileo was put under house arrest for the last several years of his life.
Theologian and pastor Thomas Schirrmacher, however, has argued:
Catholic scientists also:

In the 17th century AD Galileo Galilei opposed the Roman Catholic Church by his strong support for heliocentrism

Cardinal Robert Bellarmine himself considered that Galileo's model made "excellent good sense" on the ground of mathematical simplicity; that is, as a ''hypothesis'' (see above). And he said:
Therefore, he supported a ban on the teaching of the idea as anything but hypothesis. In 1616 he delivered to Galileo the papal command not to "hold or defend" the heliocentric idea. In the discussions leading to the ban, he was a moderate, as the Dominican party wished to forbid teaching heliocentrism in any way whatever. Galileo's heresy trial in 1633 involved making fine distinctions between "teaching" and "holding and defending as true".
The official opposition of the Church to heliocentrism did not by any means imply opposition to all astronomy; indeed, it needed observational data to maintain its calendar. In support of this effort it allowed the cathedrals themselves to be used as solar observatories called ''meridiane''; i.e., they were turned into "reverse sundials", or gigantic pinhole cameras, where the Sun's image was projected from a hole in a window in the cathedral's lantern onto a meridian line.
In 1664, Pope Alexander VII published his ''Index Librorum Prohibitorum Alexandri VII Pontificis Maximi jussu editus'' which included all previous condemnations of geocentric books. An annotated copy of Principia by Isaac Newton was published in 1742 by Fathers le Seur and Jacquier of the Franciscan Minims, two Catholic mathematicians with a preface stating that the author's work assumed heliocentrism and could not be explained without the theory. Pope Benedict XIV suspended the ban on heliocentric works on April 16, 1757 based on Isaac Newton's work. Pope Pius VII approved a decree in 1822 by the Sacred Congregation of the Inquisition to allow the printing of heliocentric books in Rome.
More recently, in May of 2007, a blog dedicated to promoting the candidacy of Senator Sam Brownback decried the "non-debate over an issue that rational Americans have foolishly conceded to the secular among us: the issue of Heliocentrism, or the idea that the Earth revolves around the Sun." [3]

The view of modern science

The realization that the heliocentric view was also not true in a strict sense was achieved in steps. That the Sun was not the center of the universe, but one of innumerable stars, was strongly advocated by the mystic Giordano Bruno; Galileo made the same point, but said very little on the matter, perhaps not wishing to incur the church's wrath. Over the course of the 18th and 19th centuries, the status of the Sun as merely one star among many became increasingly obvious. By the 20th century, even before the discovery that there are many galaxies, it was no longer an issue.
Even if the discussion is limited to the solar system, the sun is not at the geometric center of any planet's orbit, but rather at one focus of the elliptical orbit. Furthermore, to the extent that a planet's mass cannot be neglected in comparison to the Sun's mass, the center of gravity of the solar system is displaced slightly away from the center of the Sun. (The masses of the planets, mostly Jupiter, amount to 0.14% of that of the Sun.) Therefore a hypothetical astronomer on an extrasolar planet would observe a "wobble".
Giving up the whole concept of being "at rest" is related to the principle of relativity. While, assuming an unbounded universe, it was clear there is no privileged ''position'' in space, until postulation of the special theory of relativity by Albert Einstein, at least the existence of a privileged class of inertial systems absolutely ''at rest'' was assumed, in particular in the form of the hypothesis of the luminiferous aether. Some forms of Mach's principle consider the frame at rest with respect to the masses in the universe to have special properties.

Modern use of ''geocentric'' and ''heliocentric''

In modern calculations, the origin and orientation of a coordinate system often have to be selected. For practical reasons, systems with their origin in the mass, solar mass or in the center of mass of solar system are frequently selected. The adjectives may be used in this context. However, such selection of coordinates has no philosophical or physical implications.

See also

★ Geocentrism

★ Nicolaus Copernicus

★ Johannes Kepler

★ History of astronomy

★ Aristarchus of Samos

Notes

1. William Stahl, trans., ''Martianus Capella and the Seven Liberal Arts'', vol. 2, ''The Marriage of Philology and Mercury'', 854, 857, (New York: Columbia Univ. Pr, 1977, pp. 332-3
2. Bruce S. Eastwood, "Kepler as Historian of Science: Precursors of Copernican Heliocentrism according to ''De revolutionibus'' I, 10", ''Proceedings of the American Philosophical Society'', 126 (1982): 367-394.
3. "All Islamic astronomers from Thabit ibn Qurra in the ninth century to Ibn al-Shatir in the fourteenth, and all natural philosophers from al-Kindi to Averroes and later, are known to have accepted ... the Greek picture of the world as consisting of two spheres of which one, the celestial sphere ... concentrically envelops the other." A. I. Sabra, "Configuring the Universe: Aporetic, Problem Solving, and Kinematic Modeling as Themes of Arabic Astronomy," ''Perspectives on Science'' 6.3 (1998): 288-330, at pp. 317-18
4. Nicolaus Copernicus, Stanford Encyclopedia of Philosophy (2004).
5. Michael E. Marmura (1965). "''An Introduction to Islamic Cosmological Doctrines. Conceptions of Nature and Methods Used for Its Study by the Ikhwan Al-Safa'an, Al-Biruni, and Ibn Sina'' by Seyyed Hossein Nasr", ''Speculum'' '40' (4), p. 744-746.
6. Nicholas of Cusa, ''De docta ignorantia'', 2.12, p. 103, cited in Koyré (1957), p. 17.
7. B. L. van der Waerden (1970), ''Das heliozentrische System in der griechischen,persischen und indischen Astronomie,'' Naturforschenden Gesellschaft in Zürich, Zürich: Kommissionsverlag Leeman AG. (cf. Noel Swerdlow (June 1973), "Review: A Lost Monument of Indian Astronomy", ''Isis'' '64' (2), p. 239-243.)

B. L. van der Waerden (1987), "The heliocentric system in greek, persian, and indian astronomy", in "From deferent to equant: a volume of studies in the history of science in the ancient and medieval near east in honor of E. S. Kennedy", ''New York Academy of Sciences'' '500', p. 525-546. (cf. Dennis Duke (2005), "The Equant in India: The Mathematical Basis of Ancient Indian Planetary Models", ''Archive for History of Exact Sciences'' '59', p. 563–576.).
8. Thurston (1994), p. 188.

9. Lucio Russo (2004), ''The Forgotten Revolution: How Science Was Born in 300 BC and Why It Had To Be Reborn'', Springer, Berlin, ISBN 978-3-540-20396-4. (cf. Dennis Duke (2005), "The Equant in India: The Mathematical Basis of Ancient Indian Planetary Models", ''Archive for History of Exact Sciences'' '59', p. 563–576.)
10. Noel Swerdlow (June 1973), "Review: A Lost Monument of Indian Astronomy" [review of B. L. van der Waerden, ''Das heliozentrische System in der griechischen, persischen und indischen Astronomie''], ''Isis'' '64' (2), p. 239-243.

11. David Pingree (1973), "The Greek Influence on Early Islamic Mathematical Astronomy", ''Journal of the American Oriental Society'' '93' (1), p. 32.

12. Dennis Duke (2005), "The Equant in India: The Mathematical Basis of Ancient Indian Planetary Models", ''Archive for History of Exact Sciences'' '59', p. 563–576 [1].

13. Thurston (1994).
14. George G. Joseph (2000), p. 408.
15. K. Ramasubramanian, M. D. Srinivas, M. S. Sriram (1994). "Modification of the earlier Indian planetary theory by the Kerala astronomers (c. 1500 AD) and the implied heliocentric picture of planetary motion", ''Current Science'' '66', p. 784-790.
16. E. S. Kennedy, "Al-Bīrūnī's Masudic Canon", ''Al-Abhath'', 24 (1971): 59-81; reprinted in David A. King and Mary Helen Kennedy, ed., ''Studies in the Islamic Exact Sciences,'' Beirut, 1983, pp. 573-595.
17. G. Wiet, V. Elisseeff, P. Wolff, J. Naudu (1975). ''History of Mankind, Vol 3: The Great medieval Civilisations'', p. 649. George Allen & Unwin Ltd, UNESCO.
18. Rosen, Edward (1960), ''Calvin’s attitude toward Copernicus'' in ''Journal of the History of Ideas'', volume 21, no. 3, July, pp.431-441. Reprinted in, Rosen, Edward (1995). ''Copernicus and his successors''. London: Hambledon Press. pp.161-171
19. Gingerich, Owen (2004), ''The Book Nobody Read''. New York: Walker and Co.
20. Hooykaas, R. (1973). ''Religion and the rise of modern science''. Reprint, Edinburgh: Scottish Academic Press, 1977.
21. Bye, Dan J. (2007). ''McGrath vs Russell on Calvin vs Copernicus: a case of the pot calling the kettle black?'' in '' The Freethinker'', volume 127, no. 6, June, pp.8-10. Available online here.

References

★ Ajram, K. (1992). ''Miracle of Islamic Science'', Appendix B. Knowledge House Publishers. ISBN 0911119434. ★ Baker, A. and Chapter, L. (2002), "Part 4: The Sciences". In M. M. Sharif, "A History of Muslim Philosophy", ''Philosophia Islamica''. ★ Blavatsky, Helena P. (1877). ''Isis Unveiled''. Theosophical University Press. ISBN 0-911500-03-0. ★ Covington, Richard (May-June 2007). "Rediscovering Arabic science", ''Saudi Aramco World'', p. 2-16. ★ Fantoli, Annibale (2003). ''Galileo—For Copernicanism and the Church'', 3rd English edition, ''tr.'' George V. Coyne, SJ. Vatican Observatory Publications, Notre Dame, IN. ISBN 88-209-7427-4. ★ Gill, M. (2005). Was Muslim Astronomy the Harbinger of Copernicanism? ★ Haug, Martin (1863). ''The Aitareya Brahmanam of the Rigveda, Containing the Earliest Speculations of the Brahmans on the Meaning of the Sacrifical Prayers''. ISBN 0-404-57848-9. ★ Heath, T.L. (1913). ''Aristarchus of Samos, the ancient Copernicus: a history of Greek astronomy to Aristarchus'', Oxford, Clarendon. ISBN 0-486-24188-2 (1981 Dover reprint). ★ Heilbron, J. L. (1999). ''The Sun in the Church: Cathedrals as Solar Observatories''. Harvard University Press, Cambridge, MA. ISBN 0-674-85433-0. ★ Hoyle, Sir Fred (1973). ''Nicolaus Copernicus''. Heinemann Educational Books Ltd., London. ISBN 0-435-54425-X. ★ Joseph, George G. (2000). ''The Crest of the Peacock: Non-European Roots of Mathematics'', 2nd edition. Penguin Books, London. ISBN 0691006598.

★ Koyré, Alexandre (1957). ''From the Closed World to the Infinite Universe''. Baltimore: Johns Hopkins Univ. Pr. ★ Kuhn, Thomas S. (1957). ''The Copernican Revolution''. Cambridge: Harvard Univ. Pr. ISBN 0-674-17103-9 ★ Kak, Subhash C. (2000). 'Birth and Early Development of Indian Astronomy'. In Selin, Helaine (2000). ''Astronomy Across Cultures: The History of Non-Western Astronomy'' (303-340). Boston: Kluwer. ISBN 0-7923-6363-9. ★ Koestler, Arthur (1959). ''The Sleepwalkers: a history of man's changing vision of the universe''. Hutchinson, London. ISBN 0-14-020972-7 (1977 Penguin reprint). ★ Qadir, Asghar (1989). ''Relativity: An Introduction to the Special Theory''. World Scientific. ISBN 9971506122. ★ Sabra, A. I. (1998). "Configuring the Universe: Aporetic, Problem Solving, and Kinematic Modeling as Themes of Arabic Astronomy," ''Perspectives on Science'' '6', p. 288-330. ★ Saliba, George (1999). Whose Science is Arabic Science in Renaissance Europe? Columbia University. ★ Teresi, Dick (2002). ''Lost Discoveries: The Ancient Roots of Modern Science - from the Babylonians to the Maya''. Simon & Schuster, New York. ISBN 0-684-83718-8. ★ Roger Hart, Jamil Ragep, Dick Teresi (2002). \"Ancient Roots of Modern Science\", ''Talk of the Nation'' (NPR discussion of intercultural scientific contacts; astronomy is discussed in the first fifteen-minute segment). ★ Thurston, Hugh (1994). ''Early Astronomy''. Springer-Verlag, New York. ISBN 0-387-94107-X. ★ Walker, Christopher, ed. (1996). ''Astronomy before the telescope''. London: British Museum Press. ISBN 0-7141-1746-3