Ecliptic
The ecliptic is the apparent path of the Sun on the celestial sphere, and is the basis for the ecliptic coordinate system. It refers to the plane of this path, which is coplanar with the orbit of Earth around the Sun, the motions as described above are simplifications. Due to the movement of Earth around the Earth–Moon center of mass, due to further perturbations by the other planets of the Solar System, the Earth–Moon barycenter wobbles slightly around a mean position in a complex fashion. The ecliptic is actually the apparent path of the Sun throughout the course of a year, because Earth takes one year to orbit the Sun, the apparent position of the Sun takes the same length of time to make a complete circuit of the ecliptic. With slightly more than 365 days in one year, the Sun moves a little less than 1° eastward every day, this is a simplification, based on a hypothetical Earth that orbits at uniform speed around the Sun. The actual speed with which Earth orbits the Sun varies slightly during the year, for example, the Sun is north of the celestial equator for about 185 days of each year, and south of it for about 180 days.
The variation of orbital speed accounts for part of the equation of time, if the equator is projected outward to the celestial sphere, forming the celestial equator, it crosses the ecliptic at two points known as the equinoxes. The Sun, in its apparent motion along the ecliptic, crosses the equator at these points, one from south to north. The crossing from south to north is known as the equinox, known as the first point of Aries. The crossing from north to south is the equinox or descending node. Likewise, the ecliptic itself is not fixed, the gravitational perturbations of the other bodies of the Solar System cause a much smaller motion of the plane of Earths orbit, and hence of the ecliptic, known as planetary precession. The combined action of two motions is called general precession, and changes the position of the equinoxes by about 50 arc seconds per year. Once again, this is a simplification, periodic motions of the Moon and apparent periodic motions of the Sun cause short-term small-amplitude periodic oscillations of Earths axis, and hence the celestial equator, known as nutation.
Obliquity of the ecliptic is the used by astronomers for the inclination of Earths equator with respect to the ecliptic. It is about 23. 4° and is currently decreasing 0.013 degrees per hundred years due to planetary perturbations, the angular value of the obliquity is found by observation of the motions of Earth and other planets over many years. From 1984, the Jet Propulsion Laboratorys DE series of computer-generated ephemerides took over as the ephemeris of the Astronomical Almanac. Obliquity based on DE200, which analyzed observations from 1911 to 1979, was calculated, jPLs fundamental ephemerides have been continually updated. J. Laskar computed an expression to order T10 good to 0″. 04/1000 years over 10,000 years, all of these expressions are for the mean obliquity, that is, without the nutation of the equator included
Equilateral triangle
In geometry, an equilateral triangle is a triangle in which all three sides are equal. In the familiar Euclidean geometry, equilateral triangles are equiangular and they are regular polygons, and can therefore be referred to as regular triangles. Thus these are properties that are unique to equilateral triangles, the three medians have equal lengths. The three angle bisectors have equal lengths, every triangle center of an equilateral triangle coincides with its centroid, which implies that the equilateral triangle is the only triangle with no Euler line connecting some of the centers. For some pairs of triangle centers, the fact that they coincide is enough to ensure that the triangle is equilateral, in particular, A triangle is equilateral if any two of the circumcenter, centroid, or orthocenter coincide. It is equilateral if its circumcenter coincides with the Nagel point, for any triangle, the three medians partition the triangle into six smaller triangles. A triangle is equilateral if and only if any three of the triangles have either the same perimeter or the same inradius. A triangle is equilateral if and only if the circumcenters of any three of the triangles have the same distance from the centroid.
Morleys trisector theorem states that, in any triangle, the three points of intersection of the adjacent angle trisectors form an equilateral triangle, a version of the isoperimetric inequality for triangles states that the triangle of greatest area among all those with a given perimeter is equilateral. That is, PA, PB, and PC satisfy the inequality that any two of them sum to at least as great as the third. By Eulers inequality, the triangle has the smallest ratio R/r of the circumradius to the inradius of any triangle, specifically. The triangle of largest area of all those inscribed in a circle is equilateral. The ratio of the area of the incircle to the area of an equilateral triangle, the ratio of the area to the square of the perimeter of an equilateral triangle,1123, is larger than that for any other triangle. If a segment splits an equilateral triangle into two regions with equal perimeters and with areas A1 and A2, 79 ≤ A1 A2 ≤97, in no other triangle is there a point for which this ratio is as small as 2.
For any point P in the plane, with p, q, and t from the vertices A, B. For any point P on the circle of an equilateral triangle, with distances p, q. There are numerous triangle inequalities that hold with equality if and only if the triangle is equilateral, an equilateral triangle is the most symmetrical triangle, having 3 lines of reflection and rotational symmetry of order 3 about its center. Its symmetry group is the group of order 6 D3
Latitude
In geography, latitude is a geographic coordinate that specifies the north–south position of a point on the Earths surface. Latitude is an angle which ranges from 0° at the Equator to 90° at the poles, lines of constant latitude, or parallels, run east–west as circles parallel to the equator. Latitude is used together with longitude to specify the location of features on the surface of the Earth. Without qualification the term latitude should be taken to be the latitude as defined in the following sections. Also defined are six auxiliary latitudes which are used in special applications, there is a separate article on the History of latitude measurements. Two levels of abstraction are employed in the definition of latitude and longitude, in the first step the physical surface is modelled by the geoid, a surface which approximates the mean sea level over the oceans and its continuation under the land masses. The second step is to approximate the geoid by a mathematically simpler reference surface, the simplest choice for the reference surface is a sphere, but the geoid is more accurately modelled by an ellipsoid.
The definitions of latitude and longitude on such surfaces are detailed in the following sections. Lines of constant latitude and longitude together constitute a graticule on the reference surface and longitude together with some specification of height constitute a geographic coordinate system as defined in the specification of the ISO19111 standard. This is of importance in accurate applications, such as a Global Positioning System, but in common usage, where high accuracy is not required. In English texts the latitude angle, defined below, is denoted by the Greek lower-case letter phi. It is measured in degrees and seconds or decimal degrees, the precise measurement of latitude requires an understanding of the gravitational field of the Earth, either to set up theodolites or to determine GPS satellite orbits. The study of the figure of the Earth together with its field is the science of geodesy. These topics are not discussed in this article and this article relates to coordinate systems for the Earth, it may be extended to cover the Moon and other celestial objects by a simple change of nomenclature.
The primary reference points are the poles where the axis of rotation of the Earth intersects the reference surface, the plane through the centre of the Earth and perpendicular to the rotation axis intersects the surface at a great circle called the Equator. Planes parallel to the plane intersect the surface in circles of constant latitude. The Equator has a latitude of 0°, the North Pole has a latitude of 90° North, the latitude of an arbitrary point is the angle between the equatorial plane and the radius to that point. The latitude, as defined in this way for the sphere, is termed the spherical latitude
Calendar
A calendar is a system of organizing days for social, commercial or administrative purposes. This is done by giving names to periods of time, typically days, months, a date is the designation of a single, specific day within such a system. A calendar is a record of such a system. A calendar can mean a list of planned events, such as a calendar or a partly or fully chronological list of documents. Periods in a calendar are usually, though not necessarily, synchronized with the cycle of the sun or the moon. The most common type of calendar was the lunisolar calendar. Latin calendarium meant account book, the Latin term was adopted in Old French as calendier and from there in Middle English as calender by the 13th century. The course of the Sun and the Moon are the most evident forms of timekeeping, the Roman calendar contained very ancient remnants of a pre-Etruscan 10-month solar year. The first recorded calendars date to the Bronze Age, dependent on the development of writing in the Ancient Near East, a larger number of calendar systems of the Ancient Near East becomes accessible in the Iron Age, based on the Babylonian calendar.
This includes the calendar of the Persian Empire, which in turn gave rise to the Zoroastrian calendar as well as the Hebrew calendar, calendars in antiquity were lunisolar, depending on the introduction of intercalary months to align the solar and the lunar years. This was mostly based on observation, but there may have been attempts to model the pattern of intercalation algorithmically. The Roman calendar was reformed by Julius Caesar in 45 BC, the Julian calendar was no longer dependent on the observation of the new moon but simply followed an algorithm of introducing a leap day every four years. This created a dissociation of the month from the lunation. The Islamic calendar is based on the prohibition of intercalation by Muhammad and this resulted in an observationally based lunar calendar that shifts relative to the seasons of the solar year. The first calendar reform of the modern era was the Gregorian calendar. Such ideas are mooted from time to time but have failed to gain traction because of the loss of continuity, massive upheaval in implementation, a full calendar system has a different calendar date for every day.
Thus the week cycle is by not a full calendar system. The simplest calendar system just counts time periods from a reference date and this applies for the Julian day or Unix Time
Astronomy
Astronomy is a natural science that studies celestial objects and phenomena. It applies mathematics and chemistry, in an effort to explain the origin of those objects and phenomena and their evolution. Objects of interest include planets, stars and comets, while the phenomena include supernovae explosions, gamma ray bursts, more generally, all astronomical phenomena that originate outside Earths atmosphere are within the purview of astronomy. A related but distinct subject, physical cosmology, is concerned with the study of the Universe as a whole, Astronomy is the oldest of the natural sciences. The early civilizations in recorded history, such as the Babylonians, Indians, Nubians, Chinese, during the 20th century, the field of professional astronomy split into observational and theoretical branches. Observational astronomy is focused on acquiring data from observations of astronomical objects, theoretical astronomy is oriented toward the development of computer or analytical models to describe astronomical objects and phenomena.
The two fields complement each other, with theoretical astronomy seeking to explain the results and observations being used to confirm theoretical results. Astronomy is one of the few sciences where amateurs can play an active role, especially in the discovery. Amateur astronomers have made and contributed to many important astronomical discoveries, Astronomy means law of the stars. Astronomy should not be confused with astrology, the system which claims that human affairs are correlated with the positions of celestial objects. Although the two share a common origin, they are now entirely distinct. Generally, either the term astronomy or astrophysics may be used to refer to this subject, since most modern astronomical research deals with subjects related to physics, modern astronomy could actually be called astrophysics. Few fields, such as astrometry, are purely astronomy rather than astrophysics, some titles of the leading scientific journals in this field includeThe Astronomical Journal, The Astrophysical Journal and Astronomy and Astrophysics.
In early times, astronomy only comprised the observation and predictions of the motions of objects visible to the naked eye, in some locations, early cultures assembled massive artifacts that possibly had some astronomical purpose. Before tools such as the telescope were invented, early study of the stars was conducted using the naked eye, most of early astronomy actually consisted of mapping the positions of the stars and planets, a science now referred to as astrometry. From these observations, early ideas about the motions of the planets were formed, and the nature of the Sun, the Earth was believed to be the center of the Universe with the Sun, the Moon and the stars rotating around it. This is known as the model of the Universe, or the Ptolemaic system. The Babylonians discovered that lunar eclipses recurred in a cycle known as a saros
Chord (geometry)
A chord of a circle is a straight line segment whose endpoints both lie on the circle. A secant line, or just secant, is the line extension of a chord. More generally, a chord is a line segment joining two points on any curve, for instance an ellipse, a chord that passes through a circles center point is the circles diameter. Every diameter is a chord, but not every chord is a diameter, the word chord is from the Latin chorda meaning bowstring. Among properties of chords of a circle are the following, Chords are equidistant from the center if, a chord that passes through the center of a circle is called a diameter, and is the longest chord. If the line extensions of chords AB and CD intersect at a point P, the area that a circular chord cuts off is called a circular segment. The midpoints of a set of chords of an ellipse are collinear. Chords were used extensively in the development of trigonometry. The first known trigonometric table, compiled by Hipparchus, tabulated the value of the function for every 7.5 degrees.
The circle was of diameter 120, and the lengths are accurate to two base-60 digits after the integer part. The chord function is defined geometrically as shown in the picture, the chord of an angle is the length of the chord between two points on a unit circle separated by that angle. The last step uses the half-angle formula, much as modern trigonometry is built on the sine function, ancient trigonometry was built on the chord function. Hipparchus is purported to have written a twelve volume work on chords, all now lost, so presumably a great deal was known about them
Degree (angle)
A degree, usually denoted by °, is a measurement of a plane angle, defined so that a full rotation is 360 degrees. It is not an SI unit, as the SI unit of measure is the radian. Because a full rotation equals 2π radians, one degree is equivalent to π/180 radians, the original motivation for choosing the degree as a unit of rotations and angles is unknown. One theory states that it is related to the fact that 360 is approximately the number of days in a year. Ancient astronomers noticed that the sun, which follows through the path over the course of the year. Some ancient calendars, such as the Persian calendar, used 360 days for a year, the use of a calendar with 360 days may be related to the use of sexagesimal numbers. The earliest trigonometry, used by the Babylonian astronomers and their Greek successors, was based on chords of a circle, a chord of length equal to the radius made a natural base quantity. One sixtieth of this, using their standard sexagesimal divisions, was a degree, Aristarchus of Samos and Hipparchus seem to have been among the first Greek scientists to exploit Babylonian astronomical knowledge and techniques systematically.
Timocharis, Aristillus and Hipparchus were the first Greeks known to divide the circle in 360 degrees of 60 arc minutes, eratosthenes used a simpler sexagesimal system dividing a circle into 60 parts. Furthermore, it is divisible by every number from 1 to 10 except 7 and this property has many useful applications, such as dividing the world into 24 time zones, each of which is nominally 15° of longitude, to correlate with the established 24-hour day convention. Finally, it may be the case more than one of these factors has come into play. For many practical purposes, a degree is a small enough angle that whole degrees provide sufficient precision. When this is not the case, as in astronomy or for geographic coordinates, degree measurements may be written using decimal degrees, with the symbol behind the decimals. Alternatively, the sexagesimal unit subdivisions can be used. One degree is divided into 60 minutes, and one minute into 60 seconds, use of degrees-minutes-seconds is called DMS notation.
These subdivisions, called the arcminute and arcsecond, are represented by a single and double prime. For example,40. 1875° = 40° 11′ 15″, or, using quotation mark characters, additional precision can be provided using decimals for the arcseconds component. The older system of thirds, etc. which continues the sexagesimal unit subdivision, was used by al-Kashi and other ancient astronomers, but is rarely used today
Hour
An hour is a unit of time conventionally reckoned as 1⁄24 of a day and scientifically reckoned as 3, 599–3,601 seconds, depending on conditions. The seasonal, temporal, or unequal hour was established in the ancient Near East as 1⁄12 of the night or daytime, such hours varied by season and weather. It was subsequently divided into 60 minutes, each of 60 seconds, the modern English word hour is a development of the Anglo-Norman houre and Middle English ure, first attested in the 13th century. It displaced the Old English tide and stound, the Anglo-Norman term was a borrowing of Old French ure, a variant of ore, which derived from Latin hōra and Greek hṓrā. Like Old English tīd and stund, hṓrā was originally a word for any span of time, including seasons. Its Proto-Indo-European root has been reconstructed as *yeh₁-, making hour distantly cognate with year, the time of day is typically expressed in English in terms of hours. Whole hours on a 12-hour clock are expressed using the contracted phrase oclock, Hours on a 24-hour clock are expressed as hundred or hundred hours.
Fifteen and thirty minutes past the hour is expressed as a quarter past or after and half past, fifteen minutes before the hour may be expressed as a quarter to, of, till, or before the hour. Sumerian and Babylonian hours divided the day and night into 24 equal hours, the ancient Egyptians began dividing the night into wnwt at some time before the compilation of the Dynasty V Pyramid Texts in the 24th century BC. By 2150 BC, diagrams of stars inside Egyptian coffin lids—variously known as diagonal calendars or star clocks—attest that there were exactly 12 of these. The coffin diagrams show that the Egyptians took note of the risings of 36 stars or constellations. Each night, the rising of eleven of these decans were noted, the original decans used by the Egyptians would have fallen noticeably out of their proper places over a span of several centuries. By the time of Amenhotep III, the priests at Karnak were using water clocks to determine the hours and these were filled to the brim at sunset and the hour determined by comparing the water level against one of its twelve gauges, one for each month of the year.
During the New Kingdom, another system of decans was used, the division of the day into 12 hours was accomplished by sundials marked with ten equal divisions. The morning and evening periods when the failed to note time were observed as the first and last hours. The Egyptian hours were closely connected both with the priesthood of the gods and with their divine services, by the New Kingdom, each hour was conceived as a specific region of the sky or underworld through which Ras solar bark travelled. Protective deities were assigned to each and were used as the names of the hours, as the protectors and resurrectors of the sun, the goddesses of the night hours were considered to hold power over all lifespans and thus became part of Egyptian funerary rituals. The Egyptian for astronomer, used as a synonym for priest, was wnwty, the earliest forms of wnwt include one or three stars, with the solar hours including the determinative hieroglyph for sun
History of trigonometry
Early study of triangles can be traced to the 2nd millennium BC, in Egyptian mathematics and Babylonian mathematics. Systematic study of trigonometric functions began in Hellenistic mathematics, reaching India as part of Hellenistic astronomy, in Indian astronomy, the study of trigonometric functions flourished in the Gupta period, especially due to Aryabhata. During the Middle Ages, the study of continued in Islamic mathematics. The development of modern trigonometry shifted during the western Age of Enlightenment, beginning with 17th-century mathematics, the term trigonometry was derived from Greek τρίγωνον trigōnon, triangle and μέτρον metron, measure. Our modern word sine is derived from the Latin word sinus, the Arabic term is in origin a corruption of Sanskrit jīvā, or chord. Sanskrit jīvā in learned usage was a synonym of jyā chord, Sanskrit jīvā was loaned into Arabic as jiba. Particularly Fibonaccis sinus rectus arcus proved influential in establishing the term sinus, the words minute and second are derived from the Latin phrases partes minutae primae and partes minutae secundae.
These roughly translate to first small parts and second small parts, the ancient Egyptians and Babylonians had known of theorems on the ratios of the sides of similar triangles for many centuries. However, as pre-Hellenic societies lacked the concept of an angle measure, based on one interpretation of the Plimpton 322 cuneiform tablet, some have even asserted that the ancient Babylonians had a table of secants. There is, much debate as to whether it is a table of Pythagorean triples, the Egyptians, on the other hand, used a primitive form of trigonometry for building pyramids in the 2nd millennium BC. Ahmes solution to the problem is the ratio of half the side of the base of the pyramid to its height, in other words, the quantity he found for the seked is the cotangent of the angle to the base of the pyramid and its face. Ancient Greek and Hellenistic mathematicians made use of the chord, given a circle and an arc on the circle, the chord is the line that subtends the arc. A chords perpendicular bisector passes through the center of the circle and bisects the angle.
One half of the chord is the sine of one half the bisected angle, that is, c h o r d θ =2 sin θ2. Due to this relationship, a number of identities and theorems that are known today were known to Hellenistic mathematicians. For instance, propositions twelve and thirteen of book two of the Elements are the laws of cosines for obtuse and acute angles, theorems on the lengths of chords are applications of the law of sines. And Archimedes theorem on broken chords is equivalent to formulas for sines of sums, the first trigonometric table was apparently compiled by Hipparchus of Nicaea, who is now consequently known as the father of trigonometry. Hipparchus was the first to tabulate the corresponding values of arc and it seems that the systematic use of the 360° circle is largely due to Hipparchus and his table of chords
Aristarchus of Samos
Aristarchus of Samos was an ancient Greek astronomer and mathematician who presented the first known model that placed the Sun at the center of the known universe with the Earth revolving around it. He was influenced by Philolaus of Croton, but he identified the central fire with the Sun, like Anaxagoras before him, he suspected that the stars were just other bodies like the Sun, albeit further away from Earth. His astronomical ideas were rejected in favor of the geocentric theories of Aristotle and Ptolemy. Nicolaus Copernicus had attributed the theory to Aristarchus. This is the account as you have heard from astronomers. Since stellar parallax is only detectable with telescopes, his accurate speculation was unprovable at the time and it is a common misconception that the heliocentric view was held as sacrilegious by the contemporaries of Aristarchus. This is due to Gilles Ménages translation of a passage from Plutarchs On the Apparent Face in the Orb of the Moon. Plutarch reported that Cleanthes as a worshipper of the Sun and opponent to the model, was jokingly told by Aristarchus that he should be charged with impiety.
Gilles Ménage, shortly after the trials of Galileo and Giordano Bruno, amended an accusative with a nominative, the resulting misconception of an isolated and persecuted Aristarchus is still transmitted today. In his Naturalis Historia, Pliny the Elder wondered whether errors in the predictions about the heavens could be attributed to a displacement of the Earth from its central position. Pliny and Seneca referred to planets retrograde motion as an apparent phenomenon, still, no stellar parallax was observed, and Plato and Ptolemy preferred the geocentric model, which was held as true throughout the Middle Ages. The heliocentric theory was revived by Copernicus, after which Johannes Kepler described planetary motions with greater accuracy with his three laws, isaac Newton gave a theoretical explanation based on laws of gravitational attraction and dynamics. The only surviving work attributed to Aristarchus, On the Sizes and Distances of the Sun. The discrepancy may come from a misinterpretation of what unit of measure was meant by a certain Greek term in Aristarchus text, Aristarchus claimed that at half moon, the angle between the Sun and Moon was 87°.
He might have proposed 87° as a bound, since gauging the lunar terminators deviation from linearity to 1° accuracy is beyond the unaided human ocular limit. Aristarchus is known to have studied light and vision, using correct geometry, but the insufficiently accurate 87° datum, Aristarchus concluded that the Sun was between 18 and 20 times farther away than the Moon. The implicit false solar parallax of slightly under 3° was used by astronomers up to and including Tycho Brahe, Aristarchus inequality Belief Perseverance Heath, Sir Thomas. Gomez, A. G. Aristarchos of Samos, the Polymath, online Galleries, History of Science Collections, University of Oklahoma Libraries High resolution images of works by Aristarchus of Samos in. jpg and. tiff format
Radian
The radian is the standard unit of angular measure, used in many areas of mathematics. The length of an arc of a circle is numerically equal to the measurement in radians of the angle that it subtends. The unit was formerly an SI supplementary unit, but this category was abolished in 1995, the SI unit of solid angle measurement is the steradian. The radian is represented by the symbol rad, so for example, a value of 1.2 radians could be written as 1.2 rad,1.2 r,1. 2rad, or 1. 2c. Radian describes the angle subtended by a circular arc as the length of the arc divided by the radius of the arc. One radian is the angle subtended at the center of a circle by an arc that is equal in length to the radius of the circle. Conversely, the length of the arc is equal to the radius multiplied by the magnitude of the angle in radians. As the ratio of two lengths, the radian is a number that needs no unit symbol, and in mathematical writing the symbol rad is almost always omitted. When quantifying an angle in the absence of any symbol, radians are assumed, and it follows that the magnitude in radians of one complete revolution is the length of the entire circumference divided by the radius, or 2πr / r, or 2π.
Thus 2π radians is equal to 360 degrees, meaning that one radian is equal to 180/π degrees, the concept of radian measure, as opposed to the degree of an angle, is normally credited to Roger Cotes in 1714. He described the radian in everything but name, and he recognized its naturalness as a unit of angular measure, the idea of measuring angles by the length of the arc was already in use by other mathematicians. For example, al-Kashi used so-called diameter parts as units where one part was 1/60 radian. The term radian first appeared in print on 5 June 1873, in examination questions set by James Thomson at Queens College, Belfast. He had used the term as early as 1871, while in 1869, Thomas Muir, of the University of St Andrews, in 1874, after a consultation with James Thomson, Muir adopted radian. As stated, one radian is equal to 180/π degrees, thus, to convert from radians to degrees, multiply by 180/π. The length of circumference of a circle is given by 2 π r, so, to convert from radians to gradians multiply by 200 / π, and to convert from gradians to radians multiply by π /200.
This is because radians have a mathematical naturalness that leads to a more elegant formulation of a number of important results, most notably, results in analysis involving trigonometric functions are simple and elegant when the functions arguments are expressed in radians. Because of these and other properties, the trigonometric functions appear in solutions to problems that are not obviously related to the functions geometrical meanings
Babylonian astronomy
Modern knowledge of Sumerian astronomy is indirect, via the earliest Babylonian star catalogues dating from about 1200 BC. The fact that many names appear in Sumerian suggests a continuity reaching into the Early Bronze Age. The history of astronomy in Mesopotamia, and the world, begins with the Sumerians who developed the earliest writing system—known as cuneiform—around 3500–3200 BC, the Sumerians developed a form of astronomy that had an important influence on the sophisticated astronomy of the Babylonians. Astrolatry, which gave planetary gods an important role in Mesopotamian mythology and religion and they used a sexagesimal place-value number system, which simplified the task of recording very great and very small numbers. The modern practice of dividing a circle into 360 degrees, of 60 minutes each hour, during the 8th and 7th centuries BC, Babylonian astronomers developed a new empirical approach to astronomy. They began studying philosophy dealing with the nature of the universe. This was an important contribution to astronomy and the philosophy of science and this new approach to astronomy was adopted and further developed in Greek and Hellenistic astronomy.
Classical Greek and Latin sources frequently use the term Chaldeans for the astronomers of Mesopotamia, the surviving fragments show that, according to the historian A. Old Babylonian astronomy refers to the astronomy that was practiced during and after the First Babylonian Dynasty, the Babylonians were the first to recognize that astronomical phenomena are periodic and apply mathematics to their predictions. Tablets dating back to the Old Babylonian period document the application of mathematics to the variation in the length of daylight over a solar year and it is the earliest evidence that planetary phenomena were recognized as periodic. There are dozens of cuneiform Mesopotamian texts with real observations of eclipses, the Babylonians were the first civilization known to possess a functional theory of the planets. The Babylonian astrologers laid the foundations of what would eventually become Western astrology and this is largely due to the current fragmentary state of Babylonian planetary theory, and due to Babylonian astronomy being independent from cosmology at the time.
Nevertheless, traces of cosmology can be found in Babylonian literature and their worldview was not exactly geocentric either. In contrast, Babylonian cosmology suggested that the cosmos revolved around circularly with the heavens, the Babylonians and their predecessors, the Sumerians, believed in a plurality of heavens and earths. Neo-Babylonian astronomy refers to the astronomy developed by Chaldean astronomers during the Neo-Babylonian, Seleucid, a significant increase in the quality and frequency of Babylonian observations appeared during the reign of Nabonassar. The systematic records of phenomena in Babylonian astronomical diaries that began at this time allowed for the discovery of a repeating 18-year Saros cycle of lunar eclipses. The Greco-Egyptian astronomer Ptolemy used Nabonassars reign to fix the beginning of an era, the last stages in the development of Babylonian astronomy took place during the time of the Seleucid Empire. In the 3rd century BC, astronomers began to use texts to predict the motions of the planets