Heliocentrism, or heliocentricism, is the astronomical model in which the Earth and planets revolve around the Sun at the center of the Solar System. The word comes from the Greek (ἥλιος helios "sun" and κέντρον kentron "center"). Historically, heliocentrism was opposed to geocentrism, which placed the Earth at the center. The notion that the Earth revolves around the Sun had been proposed as early as the 3rd century BC by Aristarchus of Samos, but at least in the post-ancient world Aristarchus's heliocentrism attracted little attention—possibly because of the loss of scientific works of the Hellenistic Era.
It was not until the 16th century that a geometric mathematical model of a heliocentric system was presented, by the Renaissance mathematician, astronomer, and Catholic cleric Nicolaus Copernicus, leading to the Copernican Revolution. In the following century, Johannes Kepler elaborated upon and expanded this model to include elliptical orbits, and Galileo Galilei presented supporting observations made using a telescope.
With the observations of William Herschel, Friedrich Bessel, and others, astronomers realized that the sun was not the center of the universe as heliocentrists at the time of Copernicus had supposed. Modern thinking is that there is no specific location that is the center of the universe, per Albert Einstein's principle of relativity.
- 1 Early developments
- 2 Copernican revolution
- 2.1 Astronomical model
- 2.2 Religious attitudes to heliocentrism
- 2.2.1 Circulation of Commentariolus (before 1533)
- 2.2.2 Publication of de Revolutionibus (1543)
- 2.2.3 Tycho Brahe's geo-heliocentric system c. 1587
- 2.2.4 Publication of Starry messenger (1610)
- 2.2.5 Publication of Letter to the Grand Duchess (1615)
- 2.2.6 1616 ban against Copernicanism
- 2.2.7 Publication of Epitome astronomia Copernicanae (1617–1621)
- 2.2.8 Publication of Dialogue concerning the two chief world systems
- 2.2.9 Subsequent developments
- 2.2.10 Heliocentrism and Judaism
- 3 The view of modern science
- 4 See also
- 5 Notes
- 6 External links
- 7 References
To anyone who stands and looks up at the sky, it seems that the Earth stays in one place, while everything in the sky rises in the east and sets in the west once a day. However, with more scrutiny one will observe more complicated movements. The positions at which the Sun and moon rise change over the course of a year, some planets and stars do not appear at all for many months, and planets sometimes appear to have moved in the reverse direction for a while, relative to the background stars.
As these motions became better understood, more elaborate descriptions were required, the most famous of which was the geocentric Ptolemaic system, which achieved its full expression in the 2nd century. The Ptolemaic system was a sophisticated astronomical system that managed to calculate the positions for the planets to a fair degree of accuracy. 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. However, he rejected the idea of a spinning earth as absurd as he believed it would create huge winds. His planetary hypotheses were sufficiently real that the distances of moon, sun, planets and stars could be determined by treating orbits' celestial spheres as contiguous realities. This made the stars' distance less than 20 Astronomical Units, a regression, since Aristarchus of Samos's heliocentric scheme had centuries earlier necessarily placed the stars at least two orders of magnitude more distant.
Greek and Hellenistic world
The non-geocentric model of the Universe was proposed by the Pythagorean philosopher Philolaus (d. 390 BC). According to Philolaus, there was at the center of the Universe a "central fire" around which the Earth, Sun, Moon and Planets revolved in uniform circular motion. This system postulated the existence of a counter-earth collinear with the Earth and central fire, with the same period of revolution around the central fire as the Earth. The Sun revolved around the central fire once a year, and the stars were stationary. The Earth maintained the same hidden face towards the central fire, rendering both it and the "counter-earth" invisible from Earth. The Pythagorean concept of uniform circular motion remained unchallenged for approximately the next 2000 years, and it was to the Pythagoreans that Copernicus referred to show that the notion of a moving Earth was neither new nor revolutionary. Kepler gave an alternative explanation of the Pythagoreans' "central fire" as the sun, "as most sects purposely hid[e] their teachings".
Heraclides of Pontus (4th century BC) said that the rotation of the Earth explained the apparent daily motion of the celestial sphere. It used to be thought that he believed Mercury and Venus to revolve around the Sun, which in turn (along with the other planets) revolves around the Earth. Macrobius Ambrosius Theodosius (AD 395–423) later described this as the "Egyptian System," stating that "it did not escape the skill of the Egyptians," though there is no other evidence it was known in ancient Egypt.
- Aristarchus of Samos
The first person known to have proposed 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 wider than the Earth and thus hundreds of times more voluminous. 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. Though the original text has been lost, a reference in Archimedes' book The Sand Reckoner describes another work by Aristarchus in which he advanced an alternative hypothesis of the heliocentric model. Archimedes wrote:
You King Gelon are aware the 'universe' is the name given by most astronomers to the sphere the center of which is the center of the Earth, while its radius is equal to the straight line between the center of the Sun and the center of the Earth. This is the common account as you have heard from astronomers. But Aristarchus has brought out a book consisting of certain hypotheses, wherein it appears, as a consequence of the assumptions made, that the universe is many times greater than the 'universe' just mentioned. His hypotheses are that the fixed stars and the Sun remain unmoved, that the Earth revolves about the Sun on the circumference of a circle, the Sun lying in the middle of the orbit, and that the sphere of fixed stars, situated about the same center as the Sun, is so great that the circle in which he supposes the Earth to revolve bears such a proportion to the distance of the fixed stars as the center of the sphere bears to its surface.
Aristarchus believed the stars to be very far away, and saw this as the reason why there was no visible parallax, that is, an observed movement of the stars relative to each other as the Earth moved around the Sun. The stars are in fact much farther away than the distance that was generally assumed in ancient times, which is why stellar parallax is only detectable with telescopes.
Archimedes says that Aristarchus made the stars' distance larger, suggesting that he was answering the natural objection that heliocentrism requires stellar parallactic oscillations. He apparently agreed to the point but placed the stars so distant as to make the parallactic motion invisibly minuscule. Thus heliocentrism opened the way for realization that the universe was larger than the geocentrists taught.
- Seleucus of Seleucia
Since Plutarch mentions the "followers of Aristarchus" in passing, it is likely that there were other astronomers in the Classical period who also espoused heliocentrism, but whose work was lost. The only other astronomer from antiquity known by name who is known to have supported Aristarchus' heliocentric model was Seleucus of Seleucia (b. 190 BC), a Hellenistic astronomer who flourished a century after Aristarchus in the Seleucid empire. Seleucus adopted the heliocentric system of Aristarchus and is said to have proved the heliocentric theory. According to Bartel Leendert van der Waerden, Seleucus may have proved the heliocentric theory by determining the constants of a geometric model for the heliocentric theory and by developing methods to compute planetary positions using this model. He may have used early trigonometric methods that were available in his time, as he was a contemporary of Hipparchus. A fragment of a work by Seleucus has survived in Arabic translation, which was referred to by Rhazes (b. 865).
Alternatively, his explanation may have involved the phenomenon of tides, which he supposedly theorized to be caused by the attraction to the Moon and by the revolution of the Earth around the Earth-Moon 'center of mass'.
There were occasional speculations about heliocentrism in Europe before Copernicus. In Roman Carthage, the pagan Martianus Capella (5th century A.D.) expressed the opinion that the planets Venus and Mercury did not go about the Earth but instead circled the Sun. Capella's model was discussed in the Early Middle Ages by various anonymous 9th-century commentators and Copernicus mentions him as an influence on his own work.
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."
Aryabhata (476–550), in his magnum opus Aryabhatiya (499), propounded 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. 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.[page needed][page needed] Early followers of Aryabhata's model included Varahamihira, Brahmagupta, and Bhaskara II.
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. In the Tantrasangraha (1500), he further revised his planetary system, which was mathematically more accurate at predicting the heliocentric orbits of the interior planets than both the Tychonic and Copernican models, but like Indian astronomy in general fell short of proposing models of the universe. Nilakantha's planetary system also incorporated the Earth's rotation on its axis. Most astronomers of the Kerala school of astronomy and mathematics seem to have accepted his planetary model.
Medieval Islamic world
Muslim astronomers generally accepted the Ptolemaic system and the geocentric model, but by the 10th century texts appeared regularly whose subject matter was doubts concerning Ptolemy (shukūk). Several Muslim scholars questioned the Earth's apparent immobility and centrality within the universe. Some accepted that the Earth rotates around its axis, such as the 10th-century astronomer Abu Sa'id al-Sijzi (d. circa 1020). According to al-Biruni, Sijzi invented an astrolabe called al-zūraqī based on a belief held by some of his contemporaries "that the motion we see is due to the Earth's movement and not to that of the sky." The prevalence of this view is further confirmed by a reference from the 13th century which states:
According to the geometers [or engineers] (muhandisīn), the earth is in constant circular motion, and what appears to be the motion of the heavens is actually due to the motion of the earth and not the stars.
Early in the 11th century Alhazen wrote a scathing critique of Ptolemy's model in his Doubts on Ptolemy (c. 1028), which some have interpreted to imply he was criticizing Ptolemy's geocentrism, but most agree that he was actually criticizing the details of Ptolemy's model rather than his geocentrism. By the end of the 12th century, some Islamic astronomers developed complete alternatives to the Ptolemaic system (although not heliocentric), such as Nur ad-Din al-Bitruji who considered the Ptolemaic model as totally not real.
Abu Rayhan Biruni (b. 973) discussed the possibility of whether the Earth rotated about its own axis and around the Sun, but in his Masudic Canon, he set forth the principles that the Earth is at the center of the universe and that it has no motion of its own. He was aware that if the Earth rotated on its axis, this would be consistent with his astronomical parameters, but he considered this a problem of natural philosophy rather than mathematics. Qutb al-Din Shirazi (b. 1236) also discussed the possibility of heliocentrism, but rejected it. At the Maragha and Samarkand observatories, the Earth's rotation was discussed by al-Kātibī (d. 1277), Tusi (b. 1201) and Qushji (b. 1403). The arguments and evidence used by Tusi and Qushji resemble those used by Copernicus to support the Earth's motion.
However, it remains a fact that the Maragha school never made the big leap to heliocentrism. Some historians maintain that the thought of the Maragha school influenced Copernicus, in particular the mathematical devices known as the Urdi lemma and the Tusi couple. Copernicus used such devices in the same planetary models as found in Arabic sources. Furthermore, the exact replacement of the equant by two epicycles used by Copernicus in the Commentariolus was found in an earlier work by Ibn al-Shatir (d. c. 1375) of Damascus. Ibn al-Shatir's lunar and Mercury models are also identical to those of Copernicus. However, this remains speculative as no researcher has yet proven that Copernicus knew about Ibn al-Shatir's work or the Maragha school. It has been argued that Copernicus could have independently discovered the Tusi couple or took the idea from Proclus's Commentary on the First Book of Euclid, who Copernicus cited. Another possible source for Copernicus's knowledge of this mathematical device is the Questiones de Spera of Nicole Oresme, who described how a reciprocating linear motion of a celestial body could be produced by a combination of circular motions similar to those proposed by al-Tusi. A recent study adds further proof[clarification needed] that there is actually very little evidence that Copernicus knew or was influenced by the Maragha or other late-Islamic astronomical schools. Nevertheless, Copernicus mentions some of the early-Islamic astronomers whose theories and observations he used in De Revolutionibus, namely al-Battani, Thabit ibn Qurra, al-Zarqali, Ibn Rushd, and al-Bitruji.
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, 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—in reality it did not predict the planets' positions any better than the Ptolemaic system. 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 attitudes to heliocentrism
Heliocentrism had been in conflict with religion before Copernicus. One of the few pieces of information we have about the reception of Aristarchus's heliocentric system comes from a passage in Plutarch's dialogue, Concerning the Face which Appears in the Orb of the Moon. According to one of Plutarch's characters in the dialogue, the philosopher Cleanthes had held that Aristarchus should be charged with impiety for "moving the hearth of the world".
Circulation of Commentariolus (before 1533)
The first information about the heliocentric views of Nicolaus Copernicus was circulated in manuscript. Although only in manuscript, Copernicus' ideas were well known among astronomers and others. His ideas contradicted the then-prevailing understanding of the Bible. In the King James Bible First Chronicles 16:30 state that "the world also shall be stable, that it be not moved." Psalm 104:5 says, "[the Lord] Who laid the foundations of the earth, that it should not be removed for ever." Ecclesiastes 1:5 states that "The sun also ariseth, and the sun goeth down, and hasteth to his place where he arose."
Nonetheless, in 1533, Johann Albrecht Widmannstetter delivered in Rome a series of lectures outlining Copernicus' theory. The lectures were heard with interest by Pope Clement VII and several Catholic cardinals. On November 1, 1536, Archbishop of Capua Nikolaus von Schönberg wrote a letter to Copernicus from Rome encouraging him to publish a full version of his theory.
However, in 1539, Martin Luther said:
"There is talk of a new astrologer who wants to prove that the earth moves and goes around instead of the sky, the sun, the moon, just as if somebody were moving in a carriage or ship might hold that he was sitting still and at rest while the earth and the trees walked and moved. But that is how things are nowadays: when a man wishes to be clever he must . . . invent something special, and the way he does it must needs be the best! The fool wants to turn the whole art of astronomy upside-down. However, as Holy Scripture tells us, so did Joshua bid the sun to stand still and not the earth."
Publication of de Revolutionibus (1543)
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 defending the system and arguing that it was useful for computation even if its hypotheses were not necessarily true. 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 of heliocentrism should be banned, but nothing came of it at the time.
Some years after the publication of De Revolutionibus John Calvin preached a sermon in which he denounced those who "pervert the course of nature" by saying that "the sun does not move and that it is the earth that revolves and that it turns".
On the other hand, Calvin is not responsible for another famous quotation which has often been misattributed to him: "Who will venture to place the authority of Copernicus above that of the Holy Spirit?" It has long been established that this line cannot be found in any of Calvin's works. It has been suggested that the quotation was originally sourced from the works of Lutheran theologian Abraham Calovius.
Tycho Brahe's geo-heliocentric system c. 1587
Prior to the publication of De Revolutionibus, the most widely accepted system had been proposed by Ptolemy, in which the Earth was the center of the universe and all celestial bodies orbited it. Tycho Brahe, arguably the most accomplished astronomer of his time, advocated against Copernicus's heliocentric system and for an alternative to the Ptolemaic geocentric system: a geo-heliocentric system now known as the Tychonic system in which the five then known planets orbit the sun, while the sun and the moon orbit the earth.
Tycho appreciated the Copernican system, but objected to the idea of a moving Earth on the basis of physics, astronomy, and religion. The Aristotelian physics of the time (modern Newtonian physics was still a century away) offered no physical explanation for the motion of a massive body like Earth, whereas it could easily explain the motion of heavenly bodies by postulating that they were made of a different sort substance called aether that moved naturally. So Tycho said that the Copernican system "... expertly and completely circumvents all that is superfluous or discordant in the system of Ptolemy. On no point does it offend the principle of mathematics. Yet it ascribes to the Earth, that hulking, lazy body, unfit for motion, a motion as quick as that of the aethereal torches, and a triple motion at that." Likewise, Tycho took issue with the vast distances to the stars that Aristarchus and Copernicus had assumed in order to explain the lack of any visible parallax. Tycho had measured the apparent sizes of stars (now known to be illusory – see stellar magnitude), and used geometry to calculate that in order to both have those apparent sizes and be as far away as heliocentrism required, stars would have to be huge (much larger than the sun; the size of Earth's orbit or larger). Regarding this Tycho wrote, "Deduce these things geometrically if you like, and you will see how many absurdities (not to mention others) accompany this assumption [of the motion of the earth] by inference." He also cited the Copernican system's "opposition to the authority of Sacred Scripture in more than one place" as a reason why one might wish to reject it, and observed that his own geoheliocentric alternative "offended neither the principles of physics nor Holy Scripture".
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." However, after the advent of the telescope showed problems with some geocentric models (by demonstrating that Venus circles the sun, for example), the Tychonic system and variations on that system became very popular among geocentrists, and the Jesuit astronomer Giovanni Battista Riccioli would continue Tycho's use of physics, stellar astronomy (now with a telescope), and religion to argue against heliocentrism and for Tycho's system well into the seventeenth century (see Riccioli).
Publication of Starry messenger (1610)
Galileo was able to look at the night sky with the newly invented telescope. Then he published his discoveries in Sidereus Nuncius including (among other things) the moons of Jupiter and that Venus exhibited a full range of phases. These discoveries were not consistent with the Ptolemeic model of the solar system. As the Jesuit astronomers confirmed Galileo's observations, the Jesuits moved toward Tycho's teachings.
Publication of Letter to the Grand Duchess (1615)
In a Letter to the Grand Duchess Christina, Galileo defended heliocentrism, and claimed it was not contrary to Scriptures (see Galileo affair). He took Augustine's position on Scripture: not to take every passage literally 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.
1616 ban against Copernicanism
In February 1615, prominent Dominicans including Thomaso Caccini and Niccolò Lorini brought Galileo's writings on heliocentrism to the attention of the Inquisition, because they appeared to violate Holy Scripture and the decrees of the Council of Trent. Cardinal and Inquisitor Robert Bellarmine was called upon to adjudicate, and wrote in April that treating heliocentrism as a real phenomenon would be "a very dangerous thing," irritating philosophers and theologians, and harming "the Holy Faith by rendering Holy Scripture as false."
In January 1616 Msgr. Francesco Ingoli addressed an essay to Galileo disputing the Copernican system. Galileo later stated that he believed this essay to have been instrumental in the ban against Copernicanism that followed in February. According to Maurice Finocchiaro, Ingoli had probably been commissioned by the Inquisition to write an expert opinion on the controversy, and the essay provided the "chief direct basis" for the ban. The essay focused on eighteen physical and mathematical arguments against heliocentrism. It borrowed primarily from the arguments of Tycho Brahe, and it notedly mentioned the problem that heliocentrism requires the stars to be much larger than the sun. Ingoli wrote that the great distance to the stars in the heliocentric theory "clearly proves ... the fixed stars to be of such size, as they may surpass or equal the size of the orbit circle of the Earth itself." Ingoli included four theological arguments in the essay, but suggested to Galileo that he focus on the physical and mathematical arguments. Galileo did not write a response to Ingoli until 1624.
In February 1616, the Inquisition assembled a committee of theologians, known as qualifiers, who delivered their unanimous report condemning heliocentrism as "foolish and absurd in philosophy, and formally heretical since it explicitly contradicts in many places the sense of Holy Scripture." The Inquisition also determined that the Earth's motion "receives the same judgement in philosophy and ... in regard to theological truth it is at least erroneous in faith." Bellarmine personally ordered Galileo
"to abstain completely from teaching or defending this doctrine and opinion or from discussing it... to abandon completely... the opinion that the sun stands still at the center of the world and the earth moves, and henceforth not to hold, teach, or defend it in any way whatever, either orally or in writing."—Bellarmine and the Inquisition's injunction against Galileo, 1616
In March, after the Inquisition's injunction against Galileo, the papal Master of the Sacred Palace, Congregation of the Index, and Pope banned all books and letters advocating the Copernican system, which they called "the false Pythagorean doctrine, altogether contrary to Holy Scripture." In 1618 the Holy Office recommended that a modified version of Copernicus' De Revolutionibus be allowed for use in calendric calculations, though the original publication remained forbidden until 1758.
Publication of Epitome astronomia Copernicanae (1617–1621)
In Astronomia nova (1609), Johannes Kepler had used an elliptical orbit to explain the motion of Mars. In Epitome astronomiae Copernicanae he developed a heliocentric model of the solar system in which all the planets have elliptical orbits. This provided significantly increased accuracy in predicting the position of the planets. Kepler's ideas were not immediately accepted. Galileo for example completely ignored Kepler's work. Kepler proposed heliocentrism as a physical description of the solar system and Epitome astronomia Copernicanae was placed on the index of prohibited books despite Kepler being a Protestant.
Publication of Dialogue concerning the two chief world systems
Pope Urban VIII encouraged Galileo to publish the pros and cons of Heliocentrism. Galileo's response, Dialogue concerning the two chief world systems, clearly advocated heliocentrism, despite his declaration in the preface that
I will endeavour to show that all experiments that can be made upon the Earth are insufficient means to conclude for its mobility but are indifferently applicable to the Earth, movable or immovable...
and his straightforward statement,
I might very rationally put it in dispute, whether there be any such centre in nature, or no; being that neither you nor any one else hath ever proved, whether the World be finite and figurate, or else infinite and interminate; yet nevertheless granting you, for the present, that it is finite, and of a terminate Spherical Figure, and that thereupon it hath its centre...
Some ecclesiastics also interpreted the book as characterizing the Pope as a simpleton, since his viewpoint in the dialogue was advocated by the character Simplicio. Urban VIII became hostile to Galileo and he was again summoned to Rome. Galileo's trial in 1633 involved making fine distinctions between "teaching" and "holding and defending as true". For advancing heliocentric theory Galileo was forced to recant Copernicanism and was put under house arrest for the last few years of his life.
According to J. L. Heilbron, informed contemporaries of Galileo's:
"appreciated that the reference to heresy in connection with Galileo or Copernicus had no general or theological significance."
René Descartes postponed, and ultimately never finished, his treatise The World, which included a heliocentric model. But ultimately the Galileo affair did little to slow the spread of heliocentrism across Europe, as Kepler's Epitome of Copernican Astronomy became increasingly influential in the coming decades. By 1686 the model was well enough established that the general public was reading about it in Conversations on the Plurality of Worlds, published in France by Bernard le Bovier de Fontenelle and translated into English and other languages in the coming years. It has been called "one of the first great popularizations of science."
In 1687, Isaac Newton published Philosophiæ Naturalis Principia Mathematica, which provided an explanation for Kepler's laws in terms of universal gravitation and what came to be known as Newton's laws of motion. This placed heliocentrism on a firm theoretical foundation, although Newton's heliocentrism was of a somewhat modern kind. Already in the mid-1680s he recognized the "deviation of the Sun" from the centre of gravity of the solar system. For Newton it was not precisely the centre of the Sun or any other body that could be considered at rest, but "the common centre of gravity of the Earth, the Sun and all the Planets is to be esteem'd the Centre of the World", and this centre of gravity "either is at rest or moves uniformly forward in a right line". Newton adopted the "at rest" alternative in view of common consent that the centre, wherever it was, was at rest.
Meanwhile, the Church remained opposed to heliocentrism as a literal description, but this 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 (Index of Prohibited Books, published by order of Alexander VII, P.M.) which included all previous condemnations of heliocentric books.
In the mid-eighteenth century the Church's opposition began to fade. An annotated copy of Newton's Principia 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. In 1758 the Catholic Church dropped the general prohibition of books advocating heliocentrism from the Index of Forbidden Books. Pope Pius VII approved a decree in 1822 by the Sacred Congregation of the Inquisition to allow the printing of heliocentric books in Rome.
The Roman Catholic Church currently operates the Vatican Observatory, home to multiple award winning scholars, showing their ultimate acceptance of heliocentrism by furthering the field.
Heliocentrism and Judaism
Already in the Talmud, Greek philosophy and science under general name "Greek wisdom" were considered dangerous. They were put under ban then and later for some periods. For example, in 13-5 a beit din (rabbinical court) in Barcelona forbade men younger than 25 from studying secular philosophy or the natural sciences (although an exception was made for those who studied medicine). Possibly due to this the system of Nicolaus Copernicus did not cause furious resistance, although it was found to be contradicting verses of Tanakh (Jewish Bible).
The first to mention the new system was Maharal of Prague, although he did not mention Copernicus, the author of the system. In his book "Be'er ha-Golah", in 1593 Maharal used the appearance of the new system to show that scientific theories are not reliable enough – even astronomy was turned upside-down.
Copernicus is mentioned for the first time in Hebrew in the books of David Gans (1541–1613), who worked with Tycho Brahe and Johannes Kepler. Gans wrote two books on astronomy: a short one "Magen David" (1612) and a full one "Nehmad veNaim" (published only in 1743). He described objectively three systems: Ptolemy, Copernicus and of Tycho Brahe without taking sides.
In 1629 a new Hebrew book "Elim" by Joseph Solomon Delmedigo (1591–1655) appeared. The author says that the arguments of Copernicus are so strong, that only an imbecile will not accept them. Delmedigo studied at Padua and was acquainted with Galileo.
The following wave of Hebrew literature on the subject is from the 18th century. Most of its authors were for Copernicus, although David Nieto and Tobias Cohn were exceptions. These two authors gave the same reason for opposing heliocentrism—namely, contradiction of the Bible—although Nieto merely rejected the new system on those grounds without much passion, whereas Hacohen went so far as to call Copernicus "a first-born of Satan". Hacohen also mentions the fact that the Sages of Talmud derived the Hebrew name of Earth from the verb "run".
In the 20th century R. M.M. Schneerson suggested that the theory of relativity makes the question obsolete, as he writes; "on the basis of the presently accepted scientific view (in accordance with the theory of Relativity) that where two bodies in space are in motion relative to one another, it is impossible scientifically to ascertain which revolves around which, or which is stationary and the other in motion. Therefore, to say that there is, or can be, "scientific proof" that the earth revolves around the sun is quite an unscientific and uncritical statement." 
The view of modern science
Kepler's laws of planetary motion were used as arguments in favor of the heliocentric hypothesis. Three apparent proofs of the heliocentric hypothesis were provided in 1727 by James Bradley, in 1838 by Friedrich Wilhelm Bessel and in 1851 by Foucault. Bessel proved that the parallax of a star was greater than zero by measuring the parallax of 0.314 arcseconds of a star named 61 Cygni. In the same year Friedrich Georg Wilhelm Struve and Thomas Henderson measured the parallaxes of other stars, Vega and Alpha Centauri.
The thinking 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. 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.
The concept of an absolute velocity, including being "at rest" as a particular case, is ruled out by the principle of relativity, also eliminating any obvious "center" of the universe as a natural origin of coordinates. Some forms of Mach's principle consider the frame at rest with respect to the distant masses in the universe to have special properties.
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 approximately 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 small "wobble" in the Sun's motion.
Modern use of geocentric and heliocentric
In modern calculations the terms "geocentric" and "heliocentric" are often used to refer to reference frames. In such systems the origin in the center of mass of the Earth, of the Earth–Moon system, of the Sun, of the Sun plus the major planets, or of the entire solar system can be selected; see center-of-mass frame. Right Ascension and Declination are examples of geocentric coordinates, used in Earth-based observations, while the heliocentric latitude and longitude are used for orbital calculations. This leads to such terms as "heliocentric velocity" and "heliocentric angular momentum". In this heliocentric picture, any planet of the Solar System can be used as a source of mechanical energy because it moves relatively to the Sun. A smaller body (either artificial or natural) may gain heliocentric velocity due to gravity assist – this effect can change the body's mechanical energy in heliocentric reference frame (although it will not changed in the planetary one). However, such selection of "geocentric" or "heliocentric" frames is merely a matter of computation. It does not have philosophical implications and does not constitute a distinct physical or scientific model. From the point of view of General Relativity, inertial reference frames do not exist at all, and any practical reference frame is only an approximation to the actual space-time, which can have higher or lower precision.
- The Shorter Oxford English Dictionary (6th ed., 2007)
- Dreyer (1953), pp.135–48; Linton (2004), pp.38–9). The work of Aristarchus's in which he proposed his heliocentric system has not survived. We only know of it now from a brief passage in Archimedes's The Sand Reckoner.
- according to Lucio Russo, the heliocentric view was expounded in Hipparchus's work on gravity. (source: Lucio Rosso, The Forgotten Revolution, How Science was Born in 300BC and Why it had to be Reborn, pp 293-296)
- Debus, Allen G. (1987), Man and nature in the Renaissance, Cambridge University Press, p. 76, ISBN 0-521-29328-6, Chapter V, page 76
- In Book 1 section 7 he admits that a model in which the earth revolves with respect to the stars would be simpler but doesn't go as far as considering a heliocentric system.
- Dennis Duke, Ptolemy's Universe
- Boyer, C. A History of Mathematics. Wiley, p. 54.
- Johannes Kepler (1618–21), Epitome of Copernican Astronomy, Book IV, Part 1.2
- Eastwood, B. S. (November 1, 1992), "Heraclides and Heliocentrism – Texts Diagrams and Interpretations", Journal for the History of Astronomy 23: 233, Bibcode:1992JHA....23..233E
- Otto E. Neugebauer (1975), A history of ancient mathematical astronomy, Berlin/Heidelberg/New York: Springer, p. 695, ISBN 3-540-06995-X
- Rufus, W. Carl (1923), "The astronomical system of Copernicus", Popular Astronomy 31: 510–521 , Bibcode:1923PA.....31..510R, at pp. 511-512
- Arenarius, I., 4–7
- D.Rawlins, Aristarchus's vast universe: ancient vision, contends that all of Aristarchus's huge astronomical estimates of distance were based upon his gauging the limit of human visual discrimination to be approximately a ten thousandth of a radian which is about right.
- Murdin, Paul, Murdin, Paul, ed., Seleucus of Seleucia (c. 190 BC-?), Adsabs.harvard.edu, doi:10.1888/0333750888, ISBN 0-333-75088-8, retrieved 2009-08-08
- Index of Ancient Greek Philosophers-Scientists, Ics.forth.gr, retrieved 2009-08-08
- Bartel, B. L. (1987), "The Heliocentric System in Greek, Persian and Hindu Astronomy", Annals of the New York Academy of Sciences 500 (1): 525–545 [527–529], Bibcode:1987NYASA.500..525V, doi:10.1111/j.1749-6632.1987.tb37224.x.
- Shlomo Pines (1986), Studies in Arabic versions of Greek texts and in mediaeval science 2, Brill Publishers, pp. viii & 201–17, ISBN 965-223-626-8
- Lucio Russo, Flussi e riflussi, Feltrinelli, Milano, 2003, ISBN 88-07-10349-4.
- 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
- Eastwood, Bruce S. (2007), Ordering the Heavens: Roman Astronomy and Cosmology in the Carolingian Renaissance, Leiden: Brill, pp. 244–259, ISBN 978-90-04-16186-3
- Eastwood, Bruce S. (1982), "Kepler as Historian of Science: Precursors of Copernican Heliocentrism according to De revolutionibus I, 10", Proceedings of the American Philosophical Society 126: 367–394.
- Nicholas of Cusa, De docta ignorantia, 2.12, p. 103, cited in Koyré (1957), p. 17.
- Joseph (2000).
- Thurston (1994).
- Ramasubramanian, K. (1998), "Model of planetary motion in the works of Kerala astronomers", Bulletin of the Astronomical Society of India 26: 11–31 [23–4], Bibcode:1998BASI...26...11R
- K. Ramasubramanian, et al. (1994), p. 788
- Amartya Kumar Dutta (May 2006), "Āryabhata and axial rotation of earth", Resonance (Springer) 11 (5): 58–72 [70–1], doi:10.1007/BF02839373, ISSN 0973-712X
- George G. Joseph (2000), p. 408.
- Ramasubramanian, K.; Srinivas, M. D.; Sriram, M. S. (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: 784–790.
- 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:
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.
- Hoskin, Michael (1999-03-18). The Cambridge Concise History of Astronomy. Cambridge University Press. p. 60. ISBN 9780521576000.
- Ragep, F. Jamil (2001a), "Tusi and Copernicus: The Earth's Motion in Context", Science in Context (Cambridge University Press) 14 (1–2): 145–163, doi:10.1017/s0269889701000060
- Ragep, F. Jamil; Al-Qushji, Ali (2001b), "Freeing Astronomy from Philosophy: An Aspect of Islamic Influence on Science", Osiris, 2nd Series 16 (Science in Theistic Contexts: Cognitive Dimensions): 49–64 & 66–71, Bibcode:2001Osir...16...49R, doi:10.1086/649338
- Adi Setia (2004), "Fakhr Al-Din Al-Razi on Physics and the Nature of the Physical World: A Preliminary Survey", Islam & Science 2, retrieved 2010-03-02
- Alessandro Bausani (1973). "Cosmology and Religion in Islam". Scientia/Rivista di Scienza 108 (67): 762.
- Young, M. J. L., ed. (2006-11-02). Religion, Learning and Science in the 'Abbasid Period. Cambridge University Press. p. 413. ISBN 9780521028875.
- Nasr, Seyyed Hossein (1993-01-01). An Introduction to Islamic Cosmological Doctrines. SUNY Press. p. 135. ISBN 9781438414195.
- Qadir (1989), p. 5–10.
- Nicolaus Copernicus, Stanford Encyclopedia of Philosophy (2004).
- Samsó, Julio (2007). "Biṭrūjī: Nūr al‐Dīn Abū Isḥāq [Abū Jaʿfar] Ibrāhīm ibn Yūsuf al‐Biṭrūjī". In Thomas Hockey et al. The Biographical Encyclopedia of Astronomers. New York: Springer. pp. 133–4. ISBN 978-0-387-31022-0. (PDF version)
- 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.
- 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.
- Saliba (1999).
- A. Baker, L. Chapter (2002).
- Hikmat al-'Ain, p. 78
- Toby E.Huff(1993):The rise of early modern science: Islam, China, and the West
- Roberts, V.; Kennedy, E. S. (1959). "The Planetary Theory of Ibn al-Shatir". Isis 50: 232–234. doi:10.1086/348774.
- Guessoum, N. (June 2008), "Copernicus and Ibn Al-Shatir: does the Copernican revolution have Islamic roots?", The Observatory 128: 231–239 , Bibcode:2008Obs...128..231G
- A. I. Sabra (1998).
- E. S. Kennedy (Autumn 1966), "Late Medieval Planetary Theory", Isis (University of Chicago Press) 57 (3): 365–378 , doi:10.1086/350144, JSTOR 228366
- Saliba, George (1995-07-01). A History of Arabic Astronomy: Planetary Theories During the Golden Age of Islam. NYU Press. ISBN 9780814780237.
- Swerdlow, Noel M. (1973-12-31). "The Derivation and First Draft of Copernicus's Planetary Theory: A Translation of the Commentariolus with Commentary". Proceedings of the American Philosophical Society 117 (6): 424. ISSN 0003-049X. JSTOR 986461.
- King, David A. (2007). "Ibn al‐Shāṭir: ʿAlāʾ al‐Dīn ʿAlī ibn Ibrāhīm". In Thomas Hockey et al. The Biographical Encyclopedia of Astronomers. New York: Springer. pp. 569–70. ISBN 978-0-387-31022-0. (PDF version)
- N.K. Singh, M. Zaki Kirmani,Encyclopaedia of Islamic science and scientists
- Veselovsky, I. N. (1973), "Copernicus and Nasir al-Din al-Tusi", Journal for the History of Astronomy 4: 128–30, Bibcode:1973JHA.....4..128V.
- Neugebauer, Otto (1975), A History of Ancient Mathematical Astronomy 2, Berlin / Heidelberg / New York: Springer-Verlag, p. 1035, ISBN 0-387-06995-X
- Kren, Claudia (1971), "The Rolling Device of Naṣir al-Dīn al-Ṭūsī in the De spera of Nicole Oresme", Isis 62 (4): 490–498, doi:10.1086/350791.
- Viktor Blåsjö, "A Critique of the Arguments for Maragha Influence on Copernicus", Journal for the History of Astronomy, 45 (2014), 183-195 ADS.
- Freely, John (2015-03-30). Light from the East: How the Science of Medieval Islam Helped to Shape the Western World. I.B.Tauris. p. 179. ISBN 9781784531386.
- Henry, John (2001). Moving heaven and earth : Copernicus and the solar system. Cambridge: Icon. p. 87. ISBN 978-1-84046-251-7.
- Owen Gingerich, The Book Nobody Read (Heinman, 2004, p. 51)
- Dreyer (1953, p.138); Plutarch (1957, p.55) (on-line copy available). According to a footnote in the latter reference, Diogenes Laertius listed a work of Cleanthes' (apparently now lost) with the title Against Aristarchus (Plutarch, 1957, p.54).
- Speller (2008, p.51)
- Melanchthon, Elements of Physics, 1st. edition, 1549
- Revolution in Science, I. Bernard Cohen, page 497.
- Rosen (1995, p.159). Rosen disputes the earlier conclusion of another scholar that this was referring specifically to Copernicus's theory. According to Rosen, Calvin had very likely never heard of Copernicus and was referring instead to "the traditional geokinetic cosmology".
- 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 (1995, pp.161–171).
- Gingerich, Owen (2004), The Book Nobody Read. New York: Walker and Co.
- Hooykaas, R. (1973). Religion and the rise of modern science. Reprint, Edinburgh: Scottish Academic Press, 1977.
- 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.
- Owen Gingerich, The eye of heaven: Ptolemy, Copernicus, Kepler, New York: American Institute of Physics, 1993, 181, ISBN 0-88318-863-5
- Blair, Ann, "Tycho Brahe's critique of Copernicus and the Copernican system", Journal of the History of Ideas, 51, 1990, 364.
- Gingerich, O. & Voelkel, J. R., J. Hist. Astron., Vol. 29, 1998, page 1, 24
- Fantoli, 2003, p. 109
- Arthur Koestler, The Sleepwalkers (Penguin Arkana, 1989 p. 433)
- Langford (1992), p.56-57
- Drake (1978, p.240), Sharratt (1994, pp.110−111), Favaro (1907, 19:297−298) (Italian).
- Sharratt (1994, pp.110−115)
- Graney (2015, pp. 68-69) Ingoli's essay was published in English translation for the first time in 2015.
- Finocchiaro (2010, pp. 72)
- Graney (2015, pp. 71)
- Graney (2015, pp. 66-76, 164-175, 187-195)
- Favaro (1907, 19:320), Domínguez (2014); arXiv:1402.6168 Original text of the decision
- Heilbron (2010), p.218
- Finochiario, Maurice (2007). Retrying Galileo. University of California Press.
- The Systeme of the World: in Four Dialogues (1661) Thomas Salusbury translation of Dialogo sopra i Due Massi Sistemi del Mondo (1632)
- Arthur Koestler, The Sleepwalkers (Penguin Arkana, 1989 p. 491)
- Heilbronn (1999, p.203)
- Weintraub, David A. Is Pluto a Planet, p. 66, Princeton University Press, 2007
- "Kepler's Laws of Planetary Motion: 1609–1666", J. L. Russell, British Journal for the History of Science, Vol. 2, No. 1, June 1964
- Curtis Wilson, "The Newtonian achievement in astronomy", pages 233–274 in R Taton & C Wilson (eds) (1989), The General History of Astronomy, Volume 2A, at page 233
- (text quotations from 1729 translation of Newton Principia, Book 3 (1729 vol.2) at pages 232–233).
- "The Pontifical Decrees Against the Doctrine of the Earth's Movement, and the Ultramontane Defence of Them", Rev. William Roberts, 1885, London
- John L.Heilbron, Censorship of Astronomy in Italy after Galileo (in McMullin, Ernan ed., The Church and Galileo, University of Notre Dame Press, Notre Dame, 2005, p. 307, IN. ISBN 0-268-03483-4)
- Noah J. Efron. Jewish Thought and Scientific Discovery in Early Modern Europe. Journal of the History of Ideas, Vol. 58, No. 4 (Oct., 1997), pp. 719–732
- Sefer Elim, Amsterdam, 1629, стр. 304
- Copernicus in the Hebraic Literature from the Sixteenth to the Eighteenth Century Journal of the History of Ideas, vol. 38, No. 2 (Apr. – Jun., 1977), pp. 211–226. (André Neher)
- "Shvut Yakov" 3:20 (r. Y. Reisner from Prague 1710–1789)
- Hatam Sopher (1762–1839) "Kovetz Tshuvot", 26
- ""Igrot Kodesh" v. 7, p.134, letter number 1996". Otzar770.com. Retrieved 2012-12-04.
- Does Heliocentrism Mean That the Sun is Stationary?
- Heliocentric Pantheon
- The Copernican Model: a Sun Centered Solar System
- Baker, A. and Chapter, L. (2002), "Part 4: The Sciences". In M. M. Sharif, "A History of Muslim Philosophy", Philosophia Islamica.
- Drake, Stillman (1978). Galileo At Work. Chicago: University of Chicago Press. ISBN 0-226-16226-5.
- Dreyer, J.L.E. (1953), A History of Astronomy from Thales to Kepler, New York, NY: Dover Publications, ISBN 0-486-60079-3
- 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.
- Favaro, Antonio, ed. (1890–1909). Le Opere di Galileo Galilei, Edizione Nazionale [The Works of Galileo Galilei, National Edition] (in Italian). Florence: Barbera. ISBN 88-09-20881-1. A searchable online copy is available on the Institute and Museum of the History of Science, Florence, and a brief overview of Le Opere is available at Finn's fine books, and here.
- Finocchiaro, Maurice (2010), Defending Copernicus and Galileo: Critical Reasoning in the two Affairs, Springer, ISBN 978-9048132003
- Graney, Christopher M. (2015), Setting Aside All Authority: Giovanni Battista Riccioli and the Science against Copernicus in the Age of Galileo, University of Notre Dame Press, ISBN 978-0268029883
- 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, John L. (1999), The Sun in the Church: Cathedrals as Solar Observatories, Cambridge, MA: Harvard University Press, ISBN 0674005368
- Heilbron, John L. (2005). "Censorship of Astronomy in Italy after Galileo". In McMullin, Ernan. The Church and Galileo. University of Notre Dame Press, Notre Dame. ISBN 0-268-03483-4.
- Heilbron, John L. (2010). "Biography of Galileo". Galileo. Oxford University Press, Oxford.
- Joseph, George G. (2000). The Crest of the Peacock: Non-European Roots of Mathematics, 2nd edition. Penguin Books, London. ISBN 0-691-00659-8.
- Koestler, Arthur, (1959) The Sleepwalkers: A History of Man's Changing Vision of the Universe, Penguin Books; 1986 edition: ISBN 0-14-055212-X, 1990 reprint: ISBN 0-14-019246-8
- Koyré, Alexandre (1957). From the Closed World to the Infinite Universe. Baltimore: Johns Hopkins Univ. Pr.
- Langford, Jerome K., O.P. (1998) . Galileo, Science and the Church (third ed.). St. Augustine's Press. ISBN 1-890318-25-6.. Original edition by Desclee (New York, NY, 1966)
- Linton, Christopher M. (2004), From Eudoxus to Einstein—A History of Mathematical Astronomy, Cambridge: Cambridge University Press, ISBN 978-0-521-82750-8
- Plutarch (1957), Plutarch's Moralia in Fifteen Volumes, XII, Loeb Classical Library edition, translated by Harold Cherniss and William C. Helmbold, London: William Heinemann
- Qadir, Asghar (1989). Relativity: An Introduction to the Special Theory. World Scientific. ISBN 9971-5-0612-2.
- Rosen, Edward (1995), Copernicus and his Successors, London: Hambledon Press, ISBN 1-85285-071-X
- Sabra, A. I. (1998), "Configuring the Universe: Aporetic, Problem Solving, and Kinematic Modeling as Themes of Arabic Astronomy", Perspectives on Science 6: 288–330.
- Saliba, George (1999). Whose Science is Arabic Science in Renaissance Europe? Columbia University.
- The Shorter Oxford English Dictionary (6th ed.), Oxford, UK: Oxford University Press, 2007, ISBN 978-0-199-20687-2
- Sharratt, Michael (1994). Galileo: Decisive Innovator. Cambridge: Cambridge University Press. ISBN 0-521-56671-1.
- Speller, Jules (2008), Galileo's Inquisition Trial Revisited, Frankfurt am Main: Peter Lang, ISBN 978-3-631-56229-1
- Taton, René; Wilson, Curtis, eds. (1989), Planetary astronomy from the Renaissance to the rise of astrophysics Part A: Tycho Brahe to Newton, Cambridge: Cambridge University Press, ISBN 0-521-24254-1, retrieved 2009-11-06
- Thurston, Hugh (1994). Early Astronomy. Springer-Verlag, New York. ISBN 0-387-94107-X.