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 ===== - Enuma Anu Enlil =====
-To begin the story of the *Almagest*, we have to start with another book: the astrology text *Enuma Anu Enlil* (meaning *When Anu and Enlil*) written in Babylon, Iraq, a thousand years before Jesus. This work drew upon nearly two thousand years of the astronomical heritage of Iraq. *Enuma* is a book of omens, meaning portents. Unlike the Greeks, the Babylonians’ focus in astrology was not to discover human fate, but to interpret omens. They identified certain regular events in the sky that could be classified as omens. They believed that if these omens could be understood in advance—that is, predicted—then proper rituals and offerings could avert impending misfortunes.
+To begin the story of the 'Almagest', we have to start with another book: the astrology text 'Enuma Anu Enlil' (meaning 'When Anu and Enlil') written in Babylon, Iraq, a thousand years before Jesus. This work drew upon nearly two thousand years of the astronomical heritage of Iraq. 'Enuma' is a book of omens, meaning portents. Unlike the Greeks, the Babylonians’ focus in astrology was not to discover human fate, but to interpret omens. They identified certain regular events in the sky that could be classified as omens. They believed that if these omens could be understood in advance—that is, predicted—then proper rituals and offerings could avert impending misfortunes.
-It was because the authors of *Enuma* closely observed the motions of the Moon, the Sun, and the five visible planets relative to the fixed stars over at least seven centuries that the first cosmological model could be developed—the *Almagest* being its ultimate culmination. They were concerned with reconciling the twelve lunar months (354 days) with the solar year (365 days). Six hundred years before Jesus, the Babylonians discovered the **Metonic cycle**—realizing that 235 lunar months (29.5 days each, totaling 6,932 days) are nearly equal to 19 solar years (365.2 days each, totaling 6,938 days). And since there are only 228 months in 19 years (which is 7 months fewer than 235), they determined that 7 extra months needed to be added across 19 years, meaning 12 years would have twelve months, and 7 years would have thirteen months.
+It was because the authors of 'Enuma' closely observed the motions of the Moon, the Sun, and the five visible planets relative to the fixed stars over at least seven centuries that the first cosmological model could be developed—the 'Almagest' being its ultimate culmination. They were concerned with reconciling the twelve lunar months (354 days) with the solar year (365 days). Six hundred years before Jesus, the Babylonians discovered the **Metonic cycle**—realizing that 235 lunar months (29.5 days each, totaling 6,932 days) are nearly equal to 19 solar years (365.2 days each, totaling 6,938 days). And since there are only 228 months in 19 years (which is 7 months fewer than 235), they determined that 7 extra months needed to be added across 19 years, meaning 12 years would have twelve months, and 7 years would have thirteen months.
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 The practice of creating ephemerides—tables listing the past and future positions of the Moon, Sun, and planets—began in Babylon. For this, they not only measured angular positions but also began calculating velocities. For example, above is a graph showing the change in the **Sun’s angular velocity** over a year, based on data from a Babylonian tablet dated to 132 BCE. Relative to the background of “fixed” stars, the Sun moves 360 degrees in a year. The graph shows how much distance it covers each month as velocity. We see that in the second month, the Sun's angular velocity decreases to a minimum (around 28 degrees/month), and then increases to a maximum (30 degrees/month) in the eighth month. For six months, the velocity decreases; for six months, it increases.
-They had two methods to explain exactly how the velocity changed. In one method, it was assumed that the Sun's velocity remained constant for half the year, then shifted once, remaining constant again for the other half. In the other method, it was proposed that the Sun’s velocity steadily increased over half the year and steadily decreased over the other half. Humans first applied calculations of displacement, velocity, and acceleration properly to the Sun. Likewise, the displacement, velocity, and acceleration of the Moon and the five visible planets were also calculated by the authors of *Enuma*. However, building a cosmology—a complete model of the universe—based on these calculations happened later, in Greece.
+They had two methods to explain exactly how the velocity changed. In one method, it was assumed that the Sun's velocity remained constant for half the year, then shifted once, remaining constant again for the other half. In the other method, it was proposed that the Sun’s velocity steadily increased over half the year and steadily decreased over the other half. Humans first applied calculations of displacement, velocity, and acceleration properly to the Sun. Likewise, the displacement, velocity, and acceleration of the Moon and the five visible planets were also calculated by the authors of 'Enuma'. However, building a cosmology—a complete model of the universe—based on these calculations happened later, in Greece.
 ===== - From Arithmetic to Geometry =====
-Babylonian astronomers emphasized arithmetic, while the Greeks emphasized geometry. Since the moon, sun, and planets actually follow geometric paths, Greek predictions were easier and more accurate. Analyzing all the data, the Greeks created a geocentric model of the universe. The first major contribution to this model was made by the Greek philosopher Anaximander from the city of Miletus in Turkey. According to him, the Earth is a cylinder fixed at the center of the universe, with humans living on one flat surface; everything in the sky revolves around it; the sun is the farthest, followed by the moon, then all the stars, and the five planets closest to the Earth.
+Babylonian astronomers emphasized arithmetic, while the Greeks emphasized geometry. Since the moon, sun, and planets actually follow geometric paths, Greek predictions were easier. Analyzing all the data, the Greeks created a geocentric model of the universe. The first major contribution to this model was made by the Greek philosopher Anaximander from the city of Miletus in Turkey. According to him, the Earth is a cylinder fixed at the center of the universe, with humans living on one flat surface; everything in the sky revolves around it; the sun is the farthest, followed by the moon, then all the stars, and the five planets closest to the Earth.
 Pythagoras' followers were the first to firmly establish that the Earth is a sphere, not a cylinder or any other shape. Aristotle beautifully described this proof through lunar eclipses. During these eclipses, the Earth's shadow passes over the moon, and the moving edge of the shadow remains round, which is only possible if the Earth is spherical.
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 In the work of transforming astronomy from mathematics to physics through cosmology, Galileo's name must be mentioned. Following the Dutch, Galileo made a telescope and first pointed it at the sky in 1610, seeing many unseen stars, mountains and valleys on the moon, the phases of Venus, and four satellites of Jupiter. By observing the phases of Venus, he understood that Venus indeed revolves around the sun, and Jupiter's satellites (observations from January 1610 are shown above) made him realize that it was possible for something other than the Earth to be orbited in the universe. Although not definitive proof, these two pieces of information made Galileo the greatest propagandist for Copernicus, for which he was sentenced to lifelong house arrest.
-By the time Newton published 'Mathematical Principles of Natural Philosophy' in 1687, there was little doubt among scientists and philosophers about the heliocentric model of 'Revolutions,' although it was not yet proven beyond all reasonable doubt. However, it is ironic that when Einstein published his modified gravity through the theory of general relativity, we somewhat returned to Ptolemy and Copernicus, to the Almagest and Revolutions. Because Einstein's relativity ultimately showed that there is no absolute motion; all motion ultimately depends on the coordinate system. To calculate the motion of the solar system, we can take any point as a reference, whether it is the Earth, the sun, or the center of mass of the entire system.
+By the time Newton published [[wp>Philosophiæ Naturalis Principia Mathematica|Principia]] in 1687, there was little doubt among scientists and philosophers about the heliocentric model of 'Revolutions,' although it was not yet proven beyond all reasonable doubt. However, it is ironic that when Einstein published his modified gravity through the theory of general relativity, we somewhat returned to Ptolemy and Copernicus, to the Almagest and Revolutions. Because Einstein's relativity ultimately showed that there is no absolute motion; all motion ultimately depends on the coordinate system. To calculate the motion of the solar system, we can take any point as a reference, whether it is the Earth, the sun, or the center of mass of the entire system.
 ===== - Proof of Revolutions =====
+==== - Aberration: 1720s ====
 To understand the first observational proof of the 'Revolutions' model, we need to go back to the eighteenth and nineteenth centuries from Einstein in the twentieth century. In the eighteenth century, the direct proof of Earth's motion around the sun came from measuring the aberration of light. The significant proof of the nineteenth century came from stellar parallax. The amount of aberration is about 20 arcseconds, while parallax is only 1 arcsecond. It took almost a hundred years for telescope precision to improve from 20 to 1 arcsecond, which is why the discovery of aberration (1720s) and parallax (1830s) are about a hundred years apart.
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 One of the greatest astronomers of the eighteenth century, England's James Bradley, published this change in the position of stars due to Earth's velocity in 1727. The observations of the aberration of Gamma Draconis (blue curve) and 35 Camelopardalis (red curve) are shown above. It is seen that the aberration of Gamma Draconis is at its maximum of 20 arcseconds in March and September. After Bradley's discovery, astronomers began to calculate the proper motion of stars by subtracting the effect of aberration caused by Earth's orbit from the star's position. This greatly increased the precision of observations.
+==== - Parallax: 1830s ====
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