Geocentrism

• 1. Introduction

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  Geocentrism is the old picture of the Universe with Earth at its center, and it has not entirely vanished from modern minds. A report released in 2014 by the National Science Foundation found that 26% of Americans surveyed believe the Sun revolves around the Earth. A 2011 poll by VTSIOM put the figure at 32% for Russians. Astronomers now call the model superseded. Yet it shaped thinking in ancient Greece, in Roman Egypt, and across the Islamic Golden Age. Why did so many careful thinkers hold to it for so long? What mathematics did they build to defend it, and who dared to doubt it? What finally brought it down, and does any part of it still do honest work today?

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• 2. Why Earth Stood Still

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  Stand anywhere on Earth and the Sun appears to circle you once a day. The Moon and the planets seem to follow the same daily loop, and the stars look pinned to a celestial sphere that turns about an axis running through Earth's poles. The ground itself offered the second clue. To anyone standing on it, Earth feels solid, stable, and motionless.

  Ancient astronomers also reasoned about the constellations. If Earth moved, the angular gaps between stars should shift as the viewpoint changed, and the shapes of the constellations should warp over a year. They never did. That left two possibilities: the stars were enormously distant, or Earth was fixed. The Greeks chose what seemed the simpler answer, a stationary Earth.

  Venus supplied a further argument. Its brightness looks steady, which suggests a roughly constant distance from us, and that fits a central Earth better than a Sun-centered layout. The truth is subtler. The light Venus loses through its changing phases is balanced by its changing apparent size as its distance varies.

  Physics of the everyday kind pointed the same way. Critics of a moving Earth observed that earthly objects tend to settle as close as possible to Earth's center. If they could not fall any closer, they stayed put unless something pushed them, or unless heat or moisture changed them into a different element. Greek, Roman, and medieval philosophers usually paired all this with a round Earth, rather than the flat Earth implied in some myths. The next task was to design machinery that could carry the heavens around that fixed globe.

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• 3. Spheres of Aether

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  Anaximander pictured Earth as a cylinder, shaped like a section of a pillar and held aloft at the center of everything. In his cosmos, the Sun, Moon, and planets were holes in invisible wheels surrounding Earth, and people glimpsed concealed fire through those holes. Pythagoras reasoned from eclipses that Earth was a sphere. He did not place it at the center, though, and thought it moved around an unseen fire. The two ideas later merged, and from the 4th century BC onward most educated Greeks imagined a spherical Earth at the center of the universe.

  Plato and his student Aristotle built their works on this arrangement in the 4th century BC. For Plato, a stationary spherical Earth sat in the middle. Outward from it came the Moon, Sun, Venus, Mercury, Mars, Jupiter, Saturn, and then the fixed stars on the celestial sphere. In the Myth of Er, a section of the Republic, Plato described the cosmos as the Spindle of Necessity, attended by the Sirens and turned by the three Fates.

  Eudoxus of Cnidus, who worked with Plato, replaced the myth with mathematics. He started from Plato's dictum that every heavenly phenomenon can be explained by uniform circular motion. Aristotle then elaborated Eudoxus' system.

  In the fully developed Aristotelian cosmos, between 47 and 55 transparent spheres, all sharing Earth as their center, carried the heavenly bodies. The number is so high because each planet needed several spheres. These crystalline spheres turned at different steady speeds and were made of an incorruptible substance called aether. The Moon sat in the innermost sphere, so it touched the realm of Earth. Aristotle blamed that contact for the dark spots on its face and for its phases.

  Below the heavens, Aristotle assigned each earthly element a natural direction. Earth, the heaviest, pulled hardest toward the center, so water gathered in a layer around the earthen sphere. Air and fire rose away from the center, with fire lighter than air. Beyond the fire lay the aether spheres.

  Not every Greek agreed. Hicetas and Ecphantus, two Pythagoreans, and Heraclides Ponticus in the 4th century BC held that Earth spins on its axis while remaining at the center. That still counts as geocentric, and Jean Buridan revived it in the Middle Ages. Aristarchus of Samos went much further. He wrote a work, now lost, placing the Sun at the center of the universe, with Earth and the other planets circling it. The theory was unpopular, and it had one named follower, Seleucus of Seleucia. Martianus Capella definitely put Mercury and Venus in orbit around the Sun.

  Epicurus was the most radical of all. In the 4th century BC he correctly realized that the universe has no single center. Later Epicureans widely accepted the idea, and Lucretius defended it in his poem De rerum natura.

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• 4. Ptolemy's Machine

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  Claudius Ptolemaeus, a Hellenistic astronomer, wrote down the system that finally standardized geocentrism in the 2nd century AD. Aristotle's era had settled the basic tenets, but the details of his scheme never became standard. The key work describing the Ptolemaic system survives only through an Arabic translation of a book called Planetary Hypothesis. Because of its reach, people sometimes wrongly treat the Ptolemaic system as identical to geocentrism itself.

  Ptolemy argued for a spherical Earth at the center from a plain observation. At any moment, half the stars are above the horizon and half below. That even split would fail if Earth sat well off center, assuming the stars lie at a modest distance.

  In his machine, each planet rides on two spheres. The first is the deferent, a large circle. The second is the epicycle, a smaller circle embedded in the deferent. The planet travels around the epicycle while the epicycle slides along the deferent. These combined motions bring the planet nearer to Earth and then farther away. They also explain why planets slow, stop, move backward in retrograde motion, and then resume forward motion.

  The deferent's center was not Earth. It sat at a spot called the eccentric, a name from the Greek ek, meaning from, and kentron, meaning center. This older device first served to explain the uneven seasons. In that period northern autumn ran about five days shorter than spring, and placing Earth off the center of rotation captured it.

  Even so, the setup available in Ptolemy's time missed the mark, despite improving on the system of Hipparchus. The size of a planet's retrograde loop, especially for Mars, came out too small or too large. Positional errors reached as much as 30 degrees. Ptolemy's remedy was the equant, a point near the center of a planet's orbit. From the equant, the center of the epicycle appears to move at a uniform speed, though every other vantage point sees uneven motion. Ptolemy claimed this preserved uniform circular motion, but it strayed from Plato's ideal. The maximum error shrank to 10 degrees, a considerable gain.

  Modern astronomers find the result unwieldy, since each planet needed its own epicycle, deferent, and equant. Yet the epicycle model closely mimics an elliptical orbit of low eccentricity. An ellipse's familiar shape is hard to notice when eccentricity is under 5%, but the offset of the center, which is really the focus the Sun occupies, shows plainly even in planetary orbits. Ptolemy's predictions served for charts in astrology and astronomy for over 1,500 years, and they tracked observations well for the next thousand years.

  The order of his spheres, from Earth outward, ran Moon, Mercury, Venus, Sun, Mars, Jupiter, Saturn, the fixed stars, and the Primum Mobile, meaning First Moved. Ptolemy did not invent this sequence. It matches the ancient Seven Heavens cosmology shared by the major religious traditions of Eurasia, and it also follows the orbital periods of the Moon, Sun, planets, and stars.

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• 5. Doubters Abroad

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  Around 1500, Nilakantha Somayaji of the Kerala astronomers produced a single method for computing every planet. Before that, Indian astronomy cared more about predicting solar and planetary motions than about building a model of the cosmos. Earlier astronomers had used two approaches, one for the Sun and the inner planets Mercury and Venus, and another for Mars, Jupiter, and Saturn. The result resembled the Ptolemaic system but calculated a planet's latitude more accurately. Aryabhata argued that Earth rotates, though the rest of his system stayed geocentric.

  In the Islamic world, scholars adopted and refined Ptolemy's model after the translation movement, believing it fit the teachings of Islam. Still, by the 10th century, texts voicing doubts about Ptolemy, called shukuk, appeared regularly. Abu Sa'id al-Sijzi held that Earth rotates on its axis. According to al-Biruni, Sijzi invented an astrolabe called al-zuraqi, built on a belief among some contemporaries that the motion we see comes from the Earth's movement and not the sky's. A 13th-century reference confirms the belief was widespread.

  Early in the 11th century, Alhazen wrote a scathing critique, Doubts on Ptolemy, around 1028. Some read it as an attack on geocentrism. Most agree it targeted the details of Ptolemy's model instead. In the 12th century, Arzachel broke with the Greek ideal of uniform circular motion by proposing that Mercury moves in an elliptic orbit. Alpetragius offered a planetary model without the equant, epicycle, or eccentric. It was mathematically less accurate, yet it spread through most of Europe in the 13th century.

  Fakhr al-Din al-Razi (1149-1209) went furthest in his Matalib. He rejected the Aristotelian notion that Earth is central and argued for "a thousand thousand worlds" beyond this one, each larger than ours. For support, he cited the Qur'anic phrase "Lord of the Worlds", stressing the plural.

  The Maragha school, named for its observatory, later continued at the Damascus mosque and the Samarkand observatory. Its astronomers included Mo'ayyeduddin Urdi, Nasir al-Din al-Tusi (1201-1274), Qutb al-Din al-Shirazi (1236-1311), and Ibn al-Shatir (1304-1375). They set out to fix the equant problem without giving up geocentrism, and they succeeded better than their Andalusian predecessors. Their configurations removed the equant and eccentrics and predicted planetary positions more accurately than Ptolemy. Even so, they never made the leap to heliocentrism.

  Did their work reach Copernicus? No documentary evidence says so, and the question stays speculative. Whether Copernicus independently developed the Tusi couple also remains open, because no researcher has shown that he knew of Tusi's work or the Maragha school.

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• 6. The Slow Dethroning

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  In 1543, Copernicus published De revolutionibus orbium coelestium, On the Revolutions of the Heavenly Spheres, placing the Sun at the center with Earth and the other planets circling it. Geocentrism stayed in force for many years afterward. Copernicus still used circular orbits, so his predictions were no better than Ptolemy's, and his system troubled both natural philosophy and scripture. Yet it could drop Ptolemy's epicycles, since retrograde motion now arose from the combined movements and speeds of Earth and the planets. Copernicus felt that equants violated Aristotelian purity, and he showed that a pair of new epicycles did the same job. Many astronomers kept the equant anyway, because it was easier to calculate.

  Tycho Brahe (1545-1601) measured the positions of planets and stars with greater accuracy than anyone before. He hunted for stellar parallax, which would have been direct proof of Earth's motion around the Sun. He found none and rejected the idea that Earth moves. His Tychonic system kept Earth at the center with the Sun revolving around it, while the other planets circled the Sun on epicycles. The Copernican, Ptolemaic, and Tychonic models proved computationally equivalent, producing identical results from identical inputs.

  The telescope changed the mood. In 1609, Galileo Galilei began observing the heavens with one. He saw dark spots and craters on the Moon, so it was no perfect celestial body. Aristotle had blamed the Moon's flaws on contamination from Earth and its heavier elements. Galileo also saw moons orbiting Jupiter, which he dedicated to Cosimo II de' Medici. They circled Jupiter, not Earth. That showed that not everything revolves around Earth. It also showed that a moving body can keep a satellite, which strengthened the case that a moving Earth could retain the Moon. Christoph Scheiner, Johannes Kepler, and Giovan Paulo Lembo verified his observations.

  In December 1610, Galileo watched Venus show every phase, as the Moon does. Under the Ptolemaic scheme, Venus between Earth and Sun must always look crescent or dark. Beyond the Sun, it must always look gibbous or full. Galileo saw it first small and full, then large and crescent. So Venus's epicycle could be neither wholly inside nor wholly outside the Sun's orbit. Ptolemaic defenders dropped the idea that it lay entirely inside, and the 17th-century contest narrowed to variations of the Tychonic and Copernican systems.

  Johannes Kepler broke the old assumption of circles. Western culture had not challenged circular planetary motion until the 17th century. Kepler studied Brahe's famously accurate observations and built his three laws of planetary motion, published in 1609 and 1619, around a Sun-centered model with elliptical paths. He was the first astronomer to predict a transit of Venus successfully, for the year 1631. Kepler's laws were the first demonstration that the physical Sun is directly involved in setting an orbit, and geocentrists could not easily answer them.

  In 1687, Isaac Newton stated the law of universal gravitation, which Robert Hooke and others had earlier described as a hypothesis. Newton's achievement was to derive Kepler's laws mathematically from gravitation. In his Principia he used the newly developed differential calculus to describe centripetal force, replacing the mysterious occult force of earlier thought. Even so, acceptance was gradual. Between 1673 and 1738, tests of his theory accumulated, including the longer pendulum period at the equator and the differing size of a degree of latitude. Hooke observed stellar aberration in 1674, Jean Picard tested it over ten years ending in 1680, and James Bradley explained it in 1729 through the Earth's revolution about the Sun.

  The last piece arrived in 1838. Friedrich Wilhelm Bessel measured the parallax of the star 61 Cygni, disproving Ptolemy's claim that parallax motion does not exist. It confirmed the assumptions of Copernicus and revealed how far away the stars truly are.

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• 7. The Church Reconsiders

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  Two popes, Leo XIII and Pius XII, took up the question of whether everyday descriptive language forces an admission of error in Scripture. The Galileo affair had pitted geocentrism against Galileo's claims, and both popes answered no. Leo XIII wrote that the sacred writers used figurative language and common speech of their day. Citing Augustine, he held that they did not intend to teach the essential nature of the visible universe. Maurice Finocchiaro, an author on the Galileo affair, notes that this view matches the one Galileo advanced in his Letter to the Grand Duchess Christina. Pius XII later repeated the teaching.

  In 1664, Pope Alexander VII republished the Index Librorum Prohibitorum, the List of Prohibited Books, with the decrees attached, including those on heliocentrism. His papal bull said the aim was that "the succession of things done from the beginning might be made known". After that, the curia's position evolved slowly toward permitting the heliocentric view.

  In 1757, under Benedict XIV, the Congregation of the Index withdrew its decree against all books teaching the Earth's motion. The Dialogue and a few other books stayed explicitly listed. In 1820, the Holy Office, with the pope's approval, ruled that Giuseppe Settele, professor of optics and astronomy at La Sapienza University, could treat Earth's motion as established fact. In 1822, the Holy Office lifted the ban on books treating Earth's motion, and Pius VII ratified the decision. The 1835 edition of the List of Prohibited Books finally omitted the Dialogue.

  Later statements went further. In his 1921 encyclical In praeclara summorum, Benedict XV said that Earth may not be the center of the universe, though it remained the scene of humankind's first happiness and fall. In 1965, the Second Vatican Council deplored habits of mind that lead many to think faith and science are opposed. Its footnote pointed to Msgr. Pio Paschini's two-volume Vita e opere di Galileo Galilei, published in 1964.

  In 1992, Pope John Paul II addressed the Pontifical Academy of Sciences and regretted Galileo's treatment. He called the episode a "tragic mutual miscomprehension". Citing Cardinal Poupard, he observed that the sentence of 1633 was not irreformable, and that the debate closed in 1820 with the imprimatur for Settele's work. The error of the theologians, he said, was to assume that the literal sense of Scripture dictated our understanding of the physical world's structure.

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• 8. Frames and Afterlives

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  In The Evolution of Physics, published in 1938, Albert Einstein and Leopold Infeld asked whether physical laws could hold in every coordinate system, however it moves. If so, they wrote, the old struggle between Ptolemy and Copernicus would become meaningless. Saying the Sun is at rest and saying the Earth is at rest would be two conventions for two coordinate systems.

  Relativity gives geocentrism more respectability than Newtonian physics does, yet it is not geocentric. It says the Sun, Earth, Moon, Jupiter, or any other point could serve as the center of the Solar System with equal validity. Measured against the average frame of the fixed stars, planets do circle the Sun, which moves far less than its own diameter because of its great mass. Earth and Moon behave almost like a binary planet. Their shared center of mass lies about 4624 km, or 72.6% of Earth's radius, from Earth's center, still inside the planet.

  Choosing a frame is therefore a matter of convenience. A heliocentric frame suits Solar System mechanics and space travel. A geocentric one is handier for artificial satellites, for the Moon, and for working out how the sky looks from Earth. For galactic astronomy, it is easier to treat the Sun as circling the center of the Milky Way, which itself is not at rest in the cosmic background.

  Geocentrism as a religious belief never fully died out. Between 1870 and 1920, members of the Lutheran Church-Missouri Synod published articles disparaging Copernican astronomy. In 1902, A. L. Graebner wrote in the Theological Quarterly that the synod held no doctrinal position on any scientific model unless it contradicted Scripture. Some early creation science newsletters argued that geocentrism was the biblical view, and Robert Sungenis later wrote the 2006 book Galileo Was Wrong and appeared in the 2014 pseudo-documentary film The Principle. Most contemporary creationist organizations reject such views.

  A few Orthodox Jewish leaders maintain a geocentric universe, based on an interpretation of Maimonides, and the Lubavitcher Rebbe explained that geocentrism is defensible through relativity. The great majority of Jewish scholars do not believe that the Bible or Maimonides commands the belief. Among Islamic scholars, Ahmed Raza Khan Barelvi, a Sunni scholar of the Indian subcontinent, wrote a book explaining the motion of the Sun, Moon, and planets around the Earth. Gallup polls in the 1990s found the Sun-around-Earth view held by 16% of Germans, 18% of Americans, and 19% of Britons.

  Many planetariums can switch between heliocentric and geocentric models, and the geocentric one still projects the celestial sphere and lunar phases in teaching. Ephemerides, the tables of positions needed for astronomy and navigation, assume Earth at the center for the Sun's position, simply because it makes the arithmetic easier.

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