Hipparchus in the context of First-magnitude star

Science in classical antiquity encompasses inquiries into the workings of the world or universe aimed at both practical goals (e.g., establishing a reliable calendar or determining how to cure a variety of illnesses) as well as more abstract investigations belonging to natural philosophy. Classical antiquity is traditionally defined as the period between the 8th century BC (beginning of Archaic Greece) and the 6th century AD (after which there was medieval science). It is typically limited geographically to the Greco-Roman West, Mediterranean basin, and Ancient Near East, thus excluding traditions of science in the ancient world in regions such as China and the Indian subcontinent.

Ideas regarding nature that were theorized during classical antiquity were not limited to science but included myths as well as religion. Those who are now considered as the first scientists may have thought of themselves as natural philosophers, as practitioners of a skilled profession (e.g., physicians), or as followers of a religious tradition (e.g., temple healers). Some of the more widely known figures active in this period include Hippocrates, Aristotle, Euclid, Archimedes, Hipparchus, Galen, and Ptolemy. Their contributions and commentaries spread throughout the Eastern, Islamic, and Latin worlds and contributed to the birth of modern science. Their works covered many different categories including mathematics, cosmology, medicine, and physics.

Ancient Greek mathematics refers to the history of mathematical ideas and texts in Ancient Greece during classical and late antiquity, mostly from the 5th century BC to the 6th century AD. Greek mathematicians lived in cities spread around the shores of the ancient Mediterranean, from Anatolia to Italy and North Africa, but were united by Greek culture and the Greek language. The development of mathematics as a theoretical discipline and the use of deductive reasoning in proofs is an important difference between Greek mathematics and those of preceding civilizations.

The early history of Greek mathematics is obscure, and traditional narratives of mathematical theorems found before the fifth century BC are regarded as later inventions. It is now generally accepted that treatises of deductive mathematics written in Greek began circulating around the mid-fifth century BC, but the earliest complete work on the subject is Euclid's Elements, written during the Hellenistic period. The works of renown mathematicians Archimedes and Apollonius, as well as of the astronomer Hipparchus, also belong to this period. In the Imperial Roman era, Ptolemy used trigonometry to determine the positions of stars in the sky, while Nicomachus and other ancient philosophers revived ancient number theory and harmonics. During late antiquity, Pappus of Alexandria wrote his Collection, summarizing the work of his predecessors, while Diophantus' Arithmetica dealt with the solution of arithmetic problems by way of pre-modern algebra. Later authors such as Theon of Alexandria, his daughter Hypatia, and Eutocius of Ascalon wrote commentaries on the authors making up the ancient Greek mathematical corpus.

Eudoxus of Cnidus (/ˈjuːdəksəs/; Ancient Greek: Εὔδοξος ὁ Κνίδιος, Eúdoxos ho Knídios; c. 390 – c. 340 BC) was an ancient Greek astronomer, mathematician, doctor, and lawmaker. He was a student of Archytas and Plato. All of his original works are lost, though some fragments are preserved in Hipparchus's Commentaries on the Phenomena of Aratus and Eudoxus. Spherics by Theodosius of Bithynia may be based on a work by Eudoxus.

In astronomy, axial precession is a gravity-induced, slow, and continuous change in the orientation of an astronomical body's rotational axis. In the absence of precession, the astronomical body's orbit would show axial parallelism. In particular, axial precession can refer to the gradual shift in the orientation of Earth's axis of rotation in a cycle of approximately 26,000 years. This is similar to the precession of a spinning top, with the axis tracing out a pair of cones joined at their apices. The term "precession" typically refers only to this largest part of the motion; other changes in the alignment of Earth's axis—nutation and polar motion—are much smaller in magnitude.

Earth's precession was historically called the precession of the equinoxes, because the equinoxes moved westward along the ecliptic relative to the fixed stars, opposite to the yearly motion of the Sun along the ecliptic. Historically, the discovery of the precession of the equinoxes is usually attributed in the West to the 2nd-century-BC astronomer Hipparchus. With improvements in the ability to calculate the gravitational force between planets during the first half of the nineteenth century, it was recognized that the ecliptic itself moved slightly, which was named planetary precession, as early as 1863, while the dominant component was named lunisolar precession. Their combination was named general precession, instead of precession of the equinoxes.

In the Hipparchian, Ptolemaic, and Copernican systems of astronomy, the epicycle (from Ancient Greek ἐπίκυκλος (epíkuklos) 'upon the circle', meaning "circle moving on another circle") was a geometric model used to explain the variations in speed and direction of the apparent motion of the Moon, Sun, and planets. In particular it explained the apparent retrograde motion of the five planets known at the time. Secondarily, it also explained changes in the apparent distances of the planets from the Earth.

It was first proposed by Apollonius of Perga at the end of the 3rd century BC. It was developed by Apollonius of Perga and Hipparchus of Rhodes, who used it extensively, during the 2nd century BC, then formalized and extensively used by Ptolemy in his 2nd century AD astronomical treatise the Almagest.

In astronomy, magnitude is a measure of the brightness of an object, usually in a defined passband. An imprecise but systematic determination of the magnitude of objects was introduced in ancient times by Hipparchus.

Magnitude values do not have a unit. The scale is logarithmic and defined such that a magnitude 1 star is exactly 100 times brighter than a magnitude 6 star. Thus each step of one magnitude is ${\displaystyle {\sqrt[{5}]{100}}\approx 2.512}$ times brighter than the magnitude 1 higher. The brighter an object appears, the lower the value of its magnitude, with the brightest objects reaching negative values.

In astronomy, stars have a variety of different stellar designations and names, including catalogue designations, current and historical proper names, and foreign language names.

Only a tiny minority of known stars have proper names; all others have only designations from various catalogues or lists, or no identifier at all. Hipparchus in the 2nd century BC enumerated about 850 naked-eye stars. Johann Bayer in 1603 listed about twice this number. Only in the 19th century did star catalogues list the naked-eye stars exhaustively. The Bright Star Catalogue, which is a star catalogue listing all stars of apparent magnitude 6.5 or brighter, or roughly every star visible to the naked eye from Earth, contains 9,096 stars. The most voluminous modern catalogues list on the order of a billion stars, out of an estimated total of 200 to 400 billion in the Milky Way.

Gan De (Chinese: 甘德; fl. 4th century BC), also known as the Lord Gan (Gan Gong), was an ancient Chinese astronomer and astrologer born in the State of Qi. Along with Shi Shen, he is believed to be the first in history known by name to compile a star catalogue, preceded by the anonymous authors of the early Babylonian star catalogues and followed by the Greek Hipparchus who is the first known in the Western tradition of Hellenistic astronomy to have compiled a star catalogue. He also made observations of the planets, particularly Jupiter. His writings are lost, but some of his works' titles and fragments quoted from them are known from later texts.

Gan De may have been the first to describe one of the Galilean moons of Jupiter, usually invisible without the aid of telescopes. In the 20th century, a fragment of Gan's work, in a later compilation of astronomical texts, was identified by Xi Zezong as describing a naked-eye observation of either of the two largest and brightest moons, Ganymede or Callisto in summer 365 BC.

The table of chords, created by the Greek astronomer, geometer, and geographer Ptolemy in Egypt during the 2nd century AD, is a trigonometric table in Book I, chapter 11 of Ptolemy's Almagest, a treatise on mathematical astronomy. It is essentially equivalent to a table of values of the sine function. It was the earliest trigonometric table extensive enough for many practical purposes, including those of astronomy (an earlier table of chords by Hipparchus gave chords only for arcs that were multiples of ⁠7+1/2⁠° = ⁠π/24⁠ radians). Since the 8th and 9th centuries, the sine and other trigonometric functions have been used in Islamic mathematics and astronomy, reforming the production of sine tables. Khwarizmi and Habash al-Hasib later produced a set of trigonometric tables.

Hipparcos was a scientific satellite of the European Space Agency (ESA), launched in 1989 and operated until 1993. It was the first space experiment devoted to precision astrometry, the accurate measurement of the positions and distances of celestial objects on the sky. This was the first practical attempt at all-sky absolute parallax measurement, something not possible with groundside observatories, and thus represented a fundamental breakthrough in astronomy. The resulting high-precision measurements of the absolute positions, proper motions, and parallaxes of stars enabled better calculations of their distance and tangential velocity; when combined with radial velocity measurements from spectroscopy, astrophysicists were able to finally measure all six quantities needed to determine the motion of stars. The resulting Hipparcos Catalogue, a high-precision catalogue of more than 118,200 stars, was published in 1997. The lower-precision Tycho Catalogue of more than a million stars was published at the same time, while the enhanced Tycho-2 Catalogue of 2.5 million stars was published in 2000. Hipparcos's follow-up mission, Gaia, was launched in 2013.

The word "Hipparcos" is an acronym for High Precision Parallax Collecting Satellite and also a reference to the ancient Greek astronomer Hipparchus of Nicaea, who is noted for applications of trigonometry to astronomy and his discovery of the precession of the equinoxes.