Heliocentrism, or heliocentricism, is the astronomical theory that the Earth and planets revolve around the Sun and that the Sun is stationary and at the center of the universe. 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 was first proposed in the 3rd century BC by Aristarchus of Samos. However, it was not until the 16th century that a fully predictive mathematical model of a heliocentric system was presented, by the Renaissance mathematician and astronomer Nicolaus Copernicus, leading to the Copernican Revolution. In the following century, this model was elaborated and expanded by Johannes Kepler and supporting observations made using a telescope were presented by Galileo Galilei.
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 once a 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 move in the reverse direction for a while (retrograde motion).
As these motions became better understood, more elaborate descriptions were required, the most famous of which was the geocentric Ptolemaic system, formulated in the 2nd century. Though incorrect, the Ptolemaic system manages to calculate the correct positions for the planets to a moderate degree of accuracy, though Ptolemy's demand that epicycles not be eccentric caused needless problems for the motions of Mars and especially Mercury. 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 himself chose the epicyclic geocentric model and in his ultimate work, Planetary Hypotheses, treated his models as 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 clear regression, since Aristarchus's heliocentric scheme had centuries earlier necessarily placed the stars at least two orders of magnitude more distant.
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 Greek, Arabic and Latin texts. These early sources, however, do not provide techniques to compute any observational consequences of their proposed heliocentric ideas.
In the 4th century BC, Aristotle wrote that:
"At the center, they [the Pythagoreans] say, is fire, and the Earth is one of the stars, creating night and day by its circular motion about the center."
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. 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. Ambrosius Theodosius Macrobius (395–423 AD) 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.
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 thus 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.
It should be noted that since Plutarch mentions the 'followers of Aristarchus' in passing, there were likely other astronomers in the Classical period who also espoused heliocentrism, but whose work is now lost to us. 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 hellenized Babylonian 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.
There were occasional speculations about heliocentrism in Europe before Copernicus. In Roman Carthage, 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 ninth-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."
In mathematical astronomy, models of heliocentrism involve mathematical computational systems that are tied to a heliocentric model and where positions of the planets can be derived. 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 were later adapted in the Copernican model in a heliocentric context.
Aryabhata (476–550), in his magnum opus Aryabhatiya (499), 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, but this view has been disputed by others. 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. 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 elliptic orbits and the Earth's rotation on its axis. Most astronomers of the Kerala school of astronomy and mathematics seem to have accepted his planetary model.
However, several Muslim scholars questioned the Earth's apparent immobility and centrality within the universe. A fragment of a work by Seleucus of Seleucia, who supported the Greek heliocentric model in the 2nd century BC, has survived in Arabic translation, which was referred to by Rhazes (b. 865). In the 9th century, Abu Ma'shar developed a planetary model which has been interpreted as a heliocentric model, due to the orbital revolutions of the planets being given as heliocentric revolutions rather than geocentric revolutions, and the only known planetary theory in which this occurs is in the heliocentric theory. His work on planetary theory has not survived, but his astronomical data were later recorded by al-Hashimi and Biruni. Alhazen wrote a scathing critique of Ptolemy's model in his Doubts on Ptolemy (c. 1028), which some interpret 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. Alhazen did, however, later propose the Earth's rotation on its axis in The Model of the Motions (c. 1038).
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 and around the Sun, this would be consistent with his astronomical parameters, but he considered this a philosophical problem rather than a mathematical one. Fakhr al-Din al-Razi (b. 1149) rejected the Aristotelian and Avicennian notion of the Earth's centrality within the universe, but instead argues that there are more than "a thousand thousand worlds beyond this world such that each one of those worlds be bigger and more massive than this world as well as having the like of what this world has." At the Maragha observatory, Najm al-Dīn al-Qazwīnī al-Kātibī (d. 1277), in his Hikmat al-'Ain, wrote an argument for a heliocentric model, but later abandoned the model. Qotb al-Din Shirazi (b. 1236) also discussed the possibility of heliocentrism, but rejected it. Ibn al-Shatir (b. 1304) developed a geocentric system that employed mathematical techniques, such as the Tusi-couple and Urdi lemma, that were almost identical to those Nicolaus Copernicus later employed in his heliocentric system, implying that its mathematical model was influenced by the Maragha school. At the Maragha and Samarkand observatories, the Earth's rotation was discussed by al-Tusi and Ali Qushji (b. 1403); the arguments and evidence they used resemble those used by Copernicus to support the Earth's motion.
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. 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.
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". In fact, however, Aristarchus's heliocentrism appears to have attracted little attention, religious or otherwise, until Copernicus revived and elaborated it.
The first information about the heliocentric views of Nicolaus Copernicus were 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 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 1 November 1536, Archbishop of Capua Nicholas 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."
This was reported in the context of a conversation at the dinner table and not a formal statement of faith. Melanchthon, however, opposed the doctrine over a period of 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 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.
Prior to the publication of De Revolutionibus, the widely accepted system had been that which was proposed by Ptolemy, in which the Earth was the center of the universe and all celestial bodies orbited it. Tycho Brahe advocated 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. 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." 
Galileo was able to look at the night sky with the newly invented telescope. 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.
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.
The Letter to the Grand Duchess Christina prompted the papal authorities to decide whether heliocentrism was acceptable. Galileo was summoned to Rome to defend his position. The Church accepted the use of heliocentrism as a calculating device, but opposed it as a literal description of the solar system. 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:
"If there were a real proof that the Sun is in the center of the universe, that the Earth is in the third sphere, and that the Sun does not go round the Earth but the Earth round the Sun, then we should have to proceed with great circumspection in explaining passages of Scripture which appear to teach the contrary, and we should rather have to say that we did not understand them than declare an opinion false which has been proved to be true. But I do not think there is any such proof since none has been shown to me."—Koestler (1959), p. 447–448
Bellarmine 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. The Vatican files suggest that Galileo was forbidden to teach heliocentrism in any way whatsoever, but whether this ban was known to Galileo is a matter of dispute.
In Astronomia nova (1609), Johannes Kepler had used an elliptical orbit to explain the motion of Mars. In Epitome astronomia 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.
Pope Urban VIII encouraged Galileo to publish the pros and cons of Heliocentrism. In the event, Galileo's Dialogue concerning the two chief world systems clearly advocated heliocentrism and appeared to make fun of the Pope. 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 put under house arrest for the last few years of his life.
Theologian and pastor Thomas Schirrmacher, however, has argued:
"Contrary to legend, Galileo and the Copernican system were well regarded by church officials. Galileo was the victim of his own arrogance, the envy of his colleagues, and the politics of Pope Urban VIII. He was not accused of criticizing the Bible, but disobeying a papal decree."
According to J. L. Heilbron, Catholic scientists have also:
"appreciated that the reference to heresy in connection with Galileo or Copernicus had no general or theological significance."—Heilbron (1999)
The Church's opposition to heliocentrism as a literal description 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. An annotated copy of Philosophiae Naturalis Principia Mathematica 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. 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 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.
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" in his perception of the Sun's motion.
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.
In modern calculations, the origin and orientation of a coordinate system often are selected for practical reasons, and in such systems the origin in the center of mass of the Earth, of the Earth-Moon system, of the Sun, of the Sun and the major planets, or of the entire solar system can be selected. However, such selection of "geocentric" or "heliocentric" coordinates has only practical implications and not philosophical or physical ones.
"Not only did Aryabhata believe that the earth rotates, but there are glimmerings in his system (and other similar systems) of a possible underlying theory in which the earth (and the planets) orbits the sun, rather than the sun orbiting the earth. The evidence is that the basic planetary periods are relative to the sun."
"Such an interpretation, however, shows a complete misunderstanding of Indian planetary theory and is flatly contradicted by every word of Aryabhata's description."
"The reader should note that, in writing this survey, I have disregarded the rather divergent views of B. L. van der Waerden; these have been most recently expounded in his Das heliozentrische System in der griechischen, persischen und indischen Astronomie, Zürich 1970."
"Thus for both outer and inner planets, the mean motion given is the heliocentric mean motion of the planet. There is no textual evidence that the Indians knew anything about this, and there is an overwhelming amount of textual evidence confirming their geocentric point of view. Some commentators, most notably van der Waerden, have however argued in favor of an underlying ancient Greek heliocentric basis, of which the Indians were unaware. See, e.g. B. L. van der Waerden, “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, Annals of the new york academy of sciences, 500 (1987), 525–546. More recently this idea is developed in about as much detail as the scant evidence allows in L. Russo, The Forgotten Revolution (2004)."
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.
"What was needed, and was in fact deployed by Copernicus (1473-1543) himself, was the addition of two new mathematical theorems. Both of those theorems were first produced some three centuries before Copernicus and were used by astronomers working in the Islamic world for the express purpose to reform Greek astronomy. [...] Looking at the evidence from the perspective of transmission of science from one culture to another, and in particular the transmission of the two Arabic mathematical theorems to Copernicus, the small fraction of evidence that has been just examined should make it clear that it also gives rise to at least two new problems as well as to many other important issues that should be reconsidered further."
"In all other respects, particularly in the case of Mercury and Venus, the solutions worked out in Copernicus' De revolutionibus for corresponding planets show a remarkable similarity to those of our source."
"It was also Neugebauer who first noted the "identity" between the models of Ibn al-Shatir and of Copernicus for the moon, an observation that led Victor Roberts to subtitle his 1957 article on the solar and lunar models of Ibn al-Shatir "A Pre-Copernican Copernican Model" (Roberts 1957, p. 428, n. 2). And it was Neugebauer who uncovered evidence that argues for a transmission of the couple (in the form it has in Tusi's Memoir) by means of Greek Byzantine manuscripts that reached Italy in the fifteenth century."