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astronomy Astronomy () is a natural science that studies celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and evolution. Objects of interest include planets, moons, stars, nebulae, g ...
, fixed stars ( la, stellae fixae) is a term to name the full set of glowing points,
astronomical object An astronomical object, celestial object, stellar object or heavenly body is a naturally occurring physical entity, association, or structure that exists in the observable universe. In astronomy, the terms ''object'' and ''body'' are often u ...
s actually and mainly
star A star is an astronomical object comprising a luminous spheroid of plasma (physics), plasma held together by its gravity. The List of nearest stars and brown dwarfs, nearest star to Earth is the Sun. Many other stars are visible to the naked ...
s, that appear not to move relative to one another against the darkness of the
night sky The night sky is the nighttime appearance of celestial objects like stars, planets, and the Moon, which are visible in a clear sky between sunset and sunrise, when the Sun is below the horizon. Natural light sources in a night sky in ...
in the background, unlike the few lights visible at
naked eye Naked eye, also called bare eye or unaided eye, is the practice of engaging in visual perception unaided by a magnifying, light-collecting optical instrument, such as a telescope or microscope, or eye protection. Vision corrected to norma ...
, including
comet A comet is an icy, small Solar System body that, when passing close to the Sun, warms and begins to release gases, a process that is called outgassing. This produces a visible atmosphere or coma, and sometimes also a tail. These phenomena ...
s, which appear to move slowly between those "fixed" stars along days, weeks or months on the foreground. Generally speaking, the fixed stars comprise all visible stars other than the Sun, plus the faint strip of the
Milky Way The Milky Way is the galaxy that includes our Solar System, with the name describing the galaxy's appearance from Earth: a hazy band of light seen in the night sky formed from stars that cannot be individually distinguished by the naked eye. ...
. Due to their star-like appareance when sighted at naked eye, individual nebulae and other
deep-sky object A deep-sky object (DSO) is any astronomical object that is not an individual star or Solar System object (such as Sun, Moon, planet, comet, etc.). The classification is used for the most part by amateur astronomers to denote visually observed fa ...
s also are counted among the fixed stars, despite the fact they are not true stars. The term is actually a
misnomer A misnomer is a name that is incorrectly or unsuitably applied. Misnomers often arise because something was named long before its correct nature was known, or because an earlier form of something has been replaced by a later form to which the name ...
due to the fact that those celestial objects are not really fixed with respect to one another; this is only a perceptual illusion, as stars and other extrasolar astronomical objects are so far away from Earth that
human vision Visual perception is the ability to interpret the surrounding environment through photopic vision (daytime vision), color vision, scotopic vision (night vision), and mesopic vision (twilight vision), using light in the visible spectrum refle ...
is unable to perceive the true
three-dimensional Three-dimensional space (also: 3D space, 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called '' parameters'') are required to determine the position of an element (i.e., point). This is the inform ...
depth of the
outer space Outer space, commonly shortened to space, is the expanse that exists beyond Earth and its atmosphere and between celestial bodies. Outer space is not completely empty—it is a near-perfect vacuum containing a low density of particles, pred ...
, and how they move. Given their distance, these objects appear to move so slowly in the sky that the change in their relative positions is nearly imperceptible on typical human timescales, except under careful examination with modern powerful magnifying instruments, namely
telescope A telescope is a device used to observe distant objects by their emission, absorption, or reflection of electromagnetic radiation. Originally meaning only an optical instrument using lenses, curved mirrors, or a combination of both to obse ...
s. So they can be considered to be "fixed" for many purposes, even at professional detail, as
navigation Navigation is a field of study that focuses on the process of monitoring and controlling the movement of a craft or vehicle from one place to another.Bowditch, 2003:799. The field of navigation includes four general categories: land navigation ...
, charting of stars,
astrometry Astrometry is a branch of astronomy that involves precise measurements of the positions and movements of stars and other celestial bodies. It provides the kinematics and physical origin of the Solar System and this galaxy, the Milky Way. Hist ...
, etc. Furthermore, distant stars and galaxies appear to move even more slowly in the sky than comparatively closer ones which, along those closer ones that show low proper motion, reinforce the effect. People in many cultures have imagined that the brightest stars form constellations, which are apparent pictures in the sky seeming to be persistent, being deemed also as ''fixed''. Historically, the fixed stars were believed to exist attached on a giant
celestial sphere In astronomy and navigation, the celestial sphere is an abstract sphere that has an arbitrarily large radius and is concentric to Earth. All objects in the sky can be conceived as being projected upon the inner surface of the celestial sphe ...
, or firmament, which revolves daily around the Earth, and hence it was known as the "sphere of fixed stars", which acted as the supossed limit of the whole
universe The universe is all of space and time and their contents, including planets, stars, galaxies, and all other forms of matter and energy. The Big Bang theory is the prevailing cosmological description of the development of the univers ...
. For many centuries, the term "fixed stars" was a synonym of such sphere.


In Nordic mythology

The attempts to explain the universe stem from observations of the objects found in the sky. Different cultures historically have various stories to provide an answer to the questions of what they are seeing.
Norse mythology Norse, Nordic, or Scandinavian mythology is the body of myths belonging to the North Germanic peoples, stemming from Old Norse religion and continuing after the Christianization of Scandinavia, and into the Nordic folklore of the modern per ...
originates from northern Europe, around the geographical location of modern-day region of
Scandinavia Scandinavia; Sámi languages: /. ( ) is a subregion in Northern Europe, with strong historical, cultural, and linguistic ties between its constituent peoples. In English usage, ''Scandinavia'' most commonly refers to Denmark, Norway, and S ...
and northern
Germany Germany,, officially the Federal Republic of Germany, is a country in Central Europe. It is the second most populous country in Europe after Russia, and the most populous member state of the European Union. Germany is situated betwee ...
. The Norse mythology consists of tales and myths derived from
Old Norse Old Norse, Old Nordic, or Old Scandinavian, is a stage of development of North Germanic dialects before their final divergence into separate Nordic languages. Old Norse was spoken by inhabitants of Scandinavia and their overseas settlement ...
, which was a Northern German language from the
Middle Ages In the history of Europe, the Middle Ages or medieval period lasted approximately from the late 5th to the late 15th centuries, similar to the post-classical period of global history. It began with the fall of the Western Roman Empire ...
. There is a series of manuscript texts written in Old Norse which contain a collection of 5poems written from oral tradition. Among historians there seems to be speculation of the specific dates of the poems written, however, the estimated record of the texts is around the beginning of the thirteenth century. Although the oral tradition of passing down tales existed long before the advent of text manuscripts and print versions. Among surviving texts there is mention of the mythological god,
Odin Odin (; from non, Óðinn, ) is a widely revered god in Germanic paganism. Norse mythology, the source of most surviving information about him, associates him with wisdom, healing, death, royalty, the gallows, knowledge, war, battle, victory, ...
. Scholars have recounted the tale of the Αesir Gods creation myth which includes the idea of fixed stars found within the teleology of the tale. Padaric Colum has written a book, ''The Children of Odin'', which in much detail reiterates the story of how the Aesir gods brought the giant named Ymir to his demise and created the world from his body, affixing sparks from the fiery Muspelheim, or the ''fixed stars,'' to the dome of the sky, which was the skull of Ymir. The Norse creation myth is one of several cases which treated stars as being fixed to a sphere beyond the earth. Later scientific literature shows astronomical thought which kept a version of this idea until the seventeenth century.


Astronomical models which included fixed stars


Pythagoreans

Pythagorean philosophers held a number of different views on the structure of the universe, but each included a sphere of fixed stars as its boundary. Philolaos (c. 5th cent. BCE) proposed a universe which had at its center a central fire, invisible to man. All of the planets, the moon, sun, and stars rotated about this central fire, with the Earth being the nearest object to it. In this system, the stars are contained in the furthest sphere, which also rotates, but too slowly for motion to be observed. The motion of the stars is instead explained by the motion of the Earth about the central fire. Another Pythagorean, Ecphantos of Syracuse (c. 400 BCE) proposed a system quite similar to that of Philolaos, but without a central fire. Instead, this cosmos was centered on the Earth, which remained stationary but rotated on an axis, while the moon, sun, and planets revolved about it. This system's final boundary was a fixed sphere of stars, and the perceived motion of the stars was thought to be caused by the rotation of the Earth.


Plato

Plato Plato ( ; grc-gre, Πλάτων ; 428/427 or 424/423 – 348/347 BC) was a Greek philosopher born in Athens during the Classical period in Ancient Greece. He founded the Platonist school of thought and the Academy, the first institution ...
’s (c. 429-347 BCE) universe was centered on a completely stationary Earth, constructed with a series of concentric spheres. The outer sphere of this system consisted of fire and contained all of the planets (which according to Plato, included the moon and sun). The outermost portion of this sphere was the location of the stars. This sphere of fire rotated about the earth, carrying the stars with it. The belief that the stars were fixed in their place in the sphere of fire was of great importance to all of Plato’s system. The stars’ position was used as a reference for all celestial motions and used to create Plato's ideas of planets possessing multiple motions.


Aristarchus of Samos

Aristarchus (3rd cent. BCE), proposed an early heliocentric universe, which would later inspire the work of
Copernicus Nicolaus Copernicus (; pl, Mikołaj Kopernik; gml, Niklas Koppernigk, german: Nikolaus Kopernikus; 19 February 1473 – 24 May 1543) was a Renaissance polymath, active as a mathematician, astronomer, and Catholic canon, who formulat ...
. In his model, the sun, entirely stationary, laid at the center, and all planets revolved around it. Beyond the planets was the sphere of fixed stars, also motionless. This system presented two more unique ideas in addition to being heliocentric: the Earth rotated daily to create day, night, and the perceived motions of the other heavenly bodies, and the sphere of fixed stars at its boundary were immensely distant from its center. This massive distance had to be assumed due to the fact that stars were observed to have no parallax, which can only be explained by geocentricity or immense distances which create a parallax too small to be measured.


Eudoxus

Eudoxus, a student of Plato, was born around 400 BC. A mathematician and an astronomer, he generated one of the earliest sphere-centric models of the planet systems, based on his background as a mathematician. Eudoxus's model was geocentric, with the Earth being a stationary sphere at the center of the system, surrounded by 27 rotating spheres. The farthest sphere carried stars, which he declared to be fixed within the sphere. Thus, though the stars were moved around the earth by the sphere which they occupied, they themselves did not move and were therefore considered fixed.


Aristotle

Aristotle Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher and polymath during the Classical period in Ancient Greece. Taught by Plato, he was the founder of the Peripatetic school of ...
, who lived from 384 to 322 BC studied and published similar ideas to Plato, but he improved on them through his books ''
Metaphysics Metaphysics is the branch of philosophy that studies the fundamental nature of reality, the first principles of being, identity and change, space and time, causality, necessity, and possibility. It includes questions about the nature of conscio ...
'' and ''
On the Heavens ''On the Heavens'' (Greek: ''Περὶ οὐρανοῦ''; Latin: ''De Caelo'' or ''De Caelo et Mundo'') is Aristotle's chief cosmological treatise: written in 350 BC, it contains his astronomical theory and his ideas on the concrete workings ...
'' written around 350 BC. He claimed that all things have some way of moving, (including "heavenly bodies," or planets,) but he denies that the movement could be caused by a vacuum, because then the objects would move much too fast and without sensible directions. He stated that everything was moved by something and started exploring a concept similar to gravity. He was one of the first to argue (and prove) that the Earth was round, drawing on observations of eclipses and the movements of the other planets relative to the Earth. He proceeded to conclude that most planets navigated in a circular motion. His cosmos was geocentric, with the Earth at the center, surrounded by a layer of water and air, which was in turn surrounded by a layer of fire which filled the space until reaching the Moon. Aristotle also proposed a fifth element called "aether," which is purported to make up the sun, the planets, and the stars. However, Aristotle believed that while the planets rotate, the stars still remain fixed. His argument was that if such a massive body was moving, there must surely be evidence that is noticeable from the Earth. However, one cannot hear the stars moving, nor can they really see their progress, so Aristotle concludes that while they may be shifted by the planets, they do not move themselves. He writes in ''On the Heavens'', "If the bodies of the stars moved in a quantity either of air or of fire...the noise which they created would inevitably be tremendous, and this being so, it would reach and shatter things here on earth". His theory that the stars may be carried but were fixed and do not autonomously move or rotate was widely accepted for a time.


Ptolemy

Ptolemy Claudius Ptolemy (; grc-gre, Πτολεμαῖος, ; la, Claudius Ptolemaeus; AD) was a mathematician, astronomer, astrologer, geographer, and music theorist, who wrote about a dozen scientific treatises, three of which were of importanc ...
, 100-175 AD, summarized ideas about the cosmos through his mathematical models and his book ''Mathematical Syntaxis'', much more commonly known as the ''Almagest.'' It was written around 150 AD, and Ptolemy declared that the stars' placement in relation to each other and distances apart remained unchanged by the rotation of the heavens. He utilized a method using eclipses to find the star distances and calculated the distance of the moon based on parallax observations. Shortly after, he wrote a follow-up called ''Planetary Hypotheses.'' Ptolemy used and wrote about the geocentric system, drawing greatly on traditional Aristotelian physics. He declared that the stars are fixed within their celestial spheres, but the spheres themselves are not fixed. The rotations of these spheres thus explain the subtle movements of the constellations throughout the year.


Nicolaus Copernicus

Nicolaus Copernicus Nicolaus Copernicus (; pl, Mikołaj Kopernik; gml, Niklas Koppernigk, german: Nikolaus Kopernikus; 19 February 1473 – 24 May 1543) was a Renaissance polymath, active as a mathematician, astronomer, and Catholic canon, who formulat ...
(1473-1543) (see illustration in Developing Western Astronomy) created a heliocentric system composed of orbs carrying each of the heavenly bodies. The final orb in his model was that of the fixed stars. This final orb was the largest of his cosmos, in both diameter and thickness. This orb of stars is entirely fixed, as the stars are embedded in the sphere, and the sphere itself is immobile. The perceived motion of the stars, therefore, is created by the daily rotation of the Earth about its axis.


Tycho Brahe

Tycho Brahe’s (1546-1601) system of the universe has been called “geo-heliocentric” due to its twofold structure. At its center lies the stationary Earth, which is orbited by the moon and sun. The planets then revolve about the sun while it revolves about the Earth. Beyond all of these heavenly bodies lies a sphere of fixed stars. This sphere rotates about the stationary Earth, creating the perceived motion of the stars in the sky. This system has an interesting feature in that the sun and planets cannot be contained in solid orbs (their orbs would collide), but yet the stars are represented as being contained in a fixed sphere at the boundary of the cosmos.


Johannes Kepler

Johannes Kepler Johannes Kepler (; ; 27 December 1571 – 15 November 1630) was a German astronomer, mathematician, astrologer, natural philosopher and writer on music. He is a key figure in the 17th-century Scientific Revolution, best known for his laws ...
, 1571–1630, was a devoted Copernican, following Copernicus's models and ideas yet developing them. He was also a student of Tycho Brahe from 1600 to 1601 and has many writings to his name. Some of his more referenced works are the ''Mysterium cosmographicum'' (1596), ''Astronomiae pars optica'' (1604), ''Dioptrice'' (1611) which discussed the optics of lenses, ''Harmonice mundi'' (1618), and ''Epitome astronomiae Copernicanae'' (1618) which was a beginner's textbook for general Copernican astronomy along with the newer Keplerian astronomy. He also established Kepler's Laws and the Rudolphine Tables, which are working tables from which planetary positions could be shown. Kepler's laws were the tipping point in finally disproving the old geocentric (or Ptolemaic) cosmic theories and models.


Estimated radius

First Greeks, as many other ancient cultures, thought of sky as it was a giant dome-like structure only a few meters above the highest mountains. The myth of Atlas tells this
Titan Titan most often refers to: * Titan (moon), the largest moon of Saturn * Titans, a race of deities in Greek mythology Titan or Titans may also refer to: Arts and entertainment Fictional entities Fictional locations * Titan in fiction, fictiona ...
held the whole heavens on his shoulders. Around 560 BCE, Anaximander was the first philosopher to consider the Sun as a huge object, and consequently, to realize how far from Earth it might be, and the first to present a system where the celestial bodies turned at different distances. But erroneously, he thought the stars were closer to Earth than the Moon and the Sun. Nonetheless, later Pythagorians as Philolaus around 400 BCE, also conceived an universe with orbiting bodies, thus assuming the fixed stars were, at least, a bit farther than the Moon, the Sun and the rest of the planets. Meanwhile, circa 450 BCE Anaxagoras had suggested that the Moon is
rocky ''Rocky'' is a 1976 American sports drama film directed by John G. Avildsen and written by and starring Sylvester Stallone. It is the first installment in the ''Rocky'' franchise and stars Talia Shire, Burt Young, Carl Weathers, and Burges ...
, thus
opaque Opacity or opaque may refer to: * Impediments to (especially, visible) light: ** Opacities, absorption coefficients ** Opacity (optics), property or degree of blocking the transmission of light * Metaphors derived from literal optics: ** In lingui ...
, and closer to the Earth than the Sun, giving a correct explanation of
eclipse An eclipse is an astronomical event that occurs when an astronomical object or spacecraft is temporarily obscured, by passing into the shadow of another body or by having another body pass between it and the viewer. This alignment of three c ...
s. As far as the Sun and the Moon were since conceived as spherical bodies, and as they do not collide at
solar eclipse A solar eclipse occurs when the Moon passes between Earth and the Sun, thereby obscuring the view of the Sun from a small part of the Earth, totally or partially. Such an alignment occurs during an eclipse season, approximately every six mon ...
s, this implies than the
outer space Outer space, commonly shortened to space, is the expanse that exists beyond Earth and its atmosphere and between celestial bodies. Outer space is not completely empty—it is a near-perfect vacuum containing a low density of particles, pred ...
should have some certain, indeterminate depth.
Eudoxus of Cnidus Eudoxus of Cnidus (; grc, Εὔδοξος ὁ Κνίδιος, ''Eúdoxos ho Knídios''; ) was an ancient Greek astronomer, mathematician, scholar, and student of Archytas and Plato. All of his original works are lost, though some fragments are ...
, in around 380 BCE, devised a geometric-mathematical model for the movements of the planets based on (conceptual)
concentric spheres The cosmological model of concentric (or homocentric) spheres, developed by Eudoxus, Callippus, and Aristotle, employed celestial spheres all centered on the Earth. In this respect, it differed from the epicyclic and eccentric models with multip ...
centered on Earth, and by 360 BCE Plato claimed in his '' Timaeus'' that circles and spheres were the preferred shape of the universe, and that the Earth was at the centre and the stars forming the outermost shell, followed by planets, the Sun, and the Moon. Around 350 BCE
Aristotle Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher and polymath during the Classical period in Ancient Greece. Taught by Plato, he was the founder of the Peripatetic school of ...
modified Eudoxus' model by supposing the spheres were material and crystalline. He was able to articulate the spheres for most planets, however, the spheres for Jupiter and Saturn crossed each other. Aristotle solved this complication by introducing an unrolled sphere. By all these devices, and even assuming the planets were mere star-like, single points, implicitely the sphere of the fixed stars should be farther yet than previuosly thought. Around 280 BCE, Aristarchus of Samos offered the first definite discussion of the possibility of a heliocentric cosmos, and by geometrical means he estimated the Moon's orbital radius at 60 Earth radii, and its physical radius as one-third that of the Earth. He made an inaccurate attempt to measure the distance to the Sun, but sufficient to assert that the Sun is much bigger than Earth and it is much further away than the Moon. So the minor body, the Earth, must orbit the major one, the Sun, and not the opposite. This reasoning led him to assert that, as stars do not show evident parallax viewed from Earth along a single year, they must be very, very far away from the terrestrial surface, and he gave a relative estimation, yet assuming they were all at the same distance from us. Following the heliocentric ideas of Aristarcus (but not explicitly supporting them), around 250 BCE
Archimedes Archimedes of Syracuse (;; ) was a Greek mathematician, physicist, engineer, astronomer, and inventor from the ancient city of Syracuse in Sicily. Although few details of his life are known, he is regarded as one of the leading scientis ...
in his work '' The Sand Reckoner'' computes the diameter of the universe centered around the Sun to be about 1014 stadia (in modern units, about 2 light years, , ).Archimedes, The Sand Reckoner 511 R U, by Ilan Vardi
accessed 28-II-2007.
In Archimedes' own words: Around 210 BCE,
Apollonius of Perga Apollonius of Perga ( grc-gre, Ἀπολλώνιος ὁ Περγαῖος, Apollṓnios ho Pergaîos; la, Apollonius Pergaeus; ) was an Ancient Greek geometer and astronomer known for his work on conic sections. Beginning from the contributio ...
shows the equivalence of two descriptions of the apparent retrograde planet motions (assuming the geocentric model), one using excentrics and another deferent and epicycles. Later astronomers made use of this latter device. In the following century, measures of sizes and distances of the Earth and the Moon are improved. Around 200 BCE
Eratosthenes Eratosthenes of Cyrene (; grc-gre, Ἐρατοσθένης ;  – ) was a Greek polymath: a mathematician, geographer, poet, astronomer, and music theorist. He was a man of learning, becoming the chief librarian at the Library of Alexandr ...
determines that the radius of the Earth is roughly . Circa 150 BCE
Hipparchus Hipparchus (; el, Ἵππαρχος, ''Hipparkhos'';  BC) was a Greek astronomer, geographer, and mathematician. He is considered the founder of trigonometry, but is most famous for his incidental discovery of the precession of the e ...
uses parallax to determine that the distance to the Moon is roughly , nearly matching Aristarchus. This imposed a minimun radius for the sphere of fixed stars at center-to-center Earth to Moon distance plus the Moon's radius (aprox. 1/3 Earth radius), plus the width of the Sun (it being, at least, the same that the Moon), plus the indeterminate thickness of the planets' spheres (believed to be thin, anyway), for a total about . This was around 24,500,000 times lower than Archimedes' computes. Around 130 AD,
Ptolemy Claudius Ptolemy (; grc-gre, Πτολεμαῖος, ; la, Claudius Ptolemaeus; AD) was a mathematician, astronomer, astrologer, geographer, and music theorist, who wrote about a dozen scientific treatises, three of which were of importanc ...
adopted the Apollonius' epicycles in his
geocentric model In astronomy, the geocentric model (also known as geocentrism, often exemplified specifically by the Ptolemaic system) is a superseded description of the Universe with Earth at the center. Under most geocentric models, the Sun, Moon, stars, an ...
. Epicycles are described as an orbit within an orbit. For example, looking at Venus, Ptolemy claimed that it orbits the Earth, and as it orbits the Earth, it also orbits the original orbit riding a second, minor local sphere. (Ptolemy emphasised that the epicycle motion does not apply to the Sun.) This device necessarily enlarges every of the celestial spheres, thus making the outer sphere of the fixed stars yet larger. When scholars applied Ptolemy's epicycles, they presumed that each planetary sphere was exactly thick enough to accommodate them. By combining this nested sphere model with astronomical observations, scholars calculated what became generally accepted values at the time for the distances to the Sun: about , and to the edge of the universe: about , still around 130,000 times less than Archimedes. Ptolomy's methods, written in his '' Almagest'', were accurate enough to keep them largely undisputed for more than 1,500 years. But by the European
Renaissance The Renaissance ( , ) , from , with the same meanings. is a period in European history marking the transition from the Middle Ages to modernity and covering the 15th and 16th centuries, characterized by an effort to revive and surpass ide ...
, the possibility of such huge sphere could complete a single revolution of 360° around the Earth in only 24 hours was deemed as improbable, and this point was one of the reasonings of Nicholas Copernicus for left behind the centuries-old geocentric model. The highest upper bound ever given was by
Jewish Jews ( he, יְהוּדִים, , ) or Jewish people are an ethnoreligious group and nation originating from the Israelites Israelite origins and kingdom: "The first act in the long drama of Jewish history is the age of the Israelites""The ...
astronomer
Levi ben Gershon Levi ben Gershon (1288 – 20 April 1344), better known by his Graecized name as Gersonides, or by his Latinized name Magister Leo Hebraeus, or in Hebrew by the abbreviation of first letters as ''RaLBaG'', was a medieval French Jewish philosoph ...
(Gersonides) circa 1300, who estimated the distance to the fixed stars to be no less than 159,651,513,380,944 Earth radii, or about 100,000
light-year A light-year, alternatively spelled light year, is a large unit of length used to express astronomical distance, astronomical distances and is equivalent to about 9.46 Orders of magnitude (numbers)#1012, trillion kilometers (), or 5.88  ...
s in modern units. This was an overestimate; although in the actual universe there are stars farther than that distance, both in the
Milky Way The Milky Way is the galaxy that includes our Solar System, with the name describing the galaxy's appearance from Earth: a hazy band of light seen in the night sky formed from stars that cannot be individually distinguished by the naked eye. ...
(about three times wider) and all the external galaxies, the closest star from Earth (other than the Sun) is Proxima Centauri at about 4.25 light-years only.


Developing western astronomy

Western astronomical knowledge was based on the traditional thoughts from philosophical and observational inquiries of Greek Antiquity. Other cultures contributed to thought about the fixed stars including the Babylonians, who from the eighteenth to the sixth century BC constructed
constellation A constellation is an area on the celestial sphere in which a group of visible stars forms a perceived pattern or outline, typically representing an animal, mythological subject, or inanimate object. The origins of the earliest constellation ...
maps. Maps of the stars and the idea of mythological stories to explain them were largely being acquired all over the world and in several cultures. One similarity between them all was the preliminary understanding that the stars were fixed and immobile in the universe. This understanding was incorporated into theorized models and mathematical representations of the cosmos by philosophers like Anaximander and
Aristotle Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher and polymath during the Classical period in Ancient Greece. Taught by Plato, he was the founder of the Peripatetic school of ...
from the Ancient Greeks. Anaximander proposed this original (and erroneous) order of the celestial objects above the Earth: first a nearest layer with the fixed stars plus planets, then another layer with the Moon, and finally an outer one with the Sun. To him, the ''stars'', as well as the Sun and Moon, were apertures of "wheel-like condensations filled with fire". All other later models of the planetary system show a
celestial sphere In astronomy and navigation, the celestial sphere is an abstract sphere that has an arbitrarily large radius and is concentric to Earth. All objects in the sky can be conceived as being projected upon the inner surface of the celestial sphe ...
containing fixed stars on the outer most part of the universe, its edge, within it lie all the rest of the moving luminaires. Aristotle and other like Greek thinkers of antiquity, and later the Ptolemaic model of the cosmos showed an Earth-centered universe. This geocentric view was held through the Middle Ages and was later countered by subsequent astronomers and mathematicians alike, such as
Nicolaus Copernicus Nicolaus Copernicus (; pl, Mikołaj Kopernik; gml, Niklas Koppernigk, german: Nikolaus Kopernikus; 19 February 1473 – 24 May 1543) was a Renaissance polymath, active as a mathematician, astronomer, and Catholic canon, who formulat ...
and
Johannes Kepler Johannes Kepler (; ; 27 December 1571 – 15 November 1630) was a German astronomer, mathematician, astrologer, natural philosopher and writer on music. He is a key figure in the 17th-century Scientific Revolution, best known for his laws ...
. The tradition of thought which appears in all of these systems of the universe, even with their divergent mechanisms, is the presence of a celestial sphere which contains the fixed stars. Ptolemy was influential with his heavily mathematical work, the '' Almagest'', which attempts to explain the peculiarity of stars that moved. These "wandering stars", planets, moved across the background of fixed stars which were spread along a sphere surrounding encompassing the universe. Later on, contemporary astronomers and mathematicians, like Copernicus challenged the long-standing view of geocentrism and constructed a Sun-centered universe, this being known as the heliocentric system. His system still upheld the tradition of a celestial sphere holding the fixed stars. Kepler also provided a model of the cosmos in his 1596 book ''Mysterium Cosmopgraphicum'' which pictures an image, labelling one celestial sphere, in Latin, "sphaera stellar fixar," or a sphere of fixed stars. In the sixteenth century, a number of writers inspired by Copernicus, such as Thomas Digges,
Giordano Bruno Giordano Bruno (; ; la, Iordanus Brunus Nolanus; born Filippo Bruno, January or February 1548 – 17 February 1600) was an Italian philosopher, mathematician, poet, cosmological theorist, and Hermetic occultist. He is known for his cosmolog ...
and William Gilbert argued for an indefinitely extended or even infinite universe, with other stars as distant suns, paving the way to deprecate the Aristotelian sphere of the fixed stars. The studies of the heavens were revolutionized with the invention of the
telescope A telescope is a device used to observe distant objects by their emission, absorption, or reflection of electromagnetic radiation. Originally meaning only an optical instrument using lenses, curved mirrors, or a combination of both to obse ...
. First developed in 1608,
Galileo Galilei Galileo di Vincenzo Bonaiuti de' Galilei (15 February 1564 – 8 January 1642) was an Italian astronomer, physicist and engineer, sometimes described as a polymath. Commonly referred to as Galileo, his name was pronounced (, ). He ...
heard about it and made a telescope for himself. He immediately noticed that the planets were not, in fact, perfectly smooth, a theory formerly put forth by Aristotle. He continued to examine the skies and constellations and soon knew that the "fixed stars" which had been studied and mapped were only a tiny portion of the massive universe that lay beyond the reach of the naked eye. When in 1610 he aimed his telescope to the faint strip of the
Milky Way The Milky Way is the galaxy that includes our Solar System, with the name describing the galaxy's appearance from Earth: a hazy band of light seen in the night sky formed from stars that cannot be individually distinguished by the naked eye. ...
, he found it resolves into countless white star-like spots, presumably farther stars themselves.Galileo Galilei, ''Sidereus Nuncius'' (Venice, (Italy): Thomas Baglioni, 1610)
pages 15 and 16.

English translation: Galileo Galilei with Edward Stafford Carlos, trans., ''The Sidereal Messenger'' (London: Rivingtons, 1880)
pages 42 and 43.


"Fixed stars" not fixed

Astronomers and natural philosophers before divided the lights in the sky into two groups. One group contained the ''fixed stars'', which appear to rise and set but keep the same relative arrangement over time. The other group contained the naked eye planets, which they called ''wandering stars''. (The Sun and
Moon The Moon is Earth's only natural satellite. It is the fifth largest satellite in the Solar System and the largest and most massive relative to its parent planet, with a diameter about one-quarter that of Earth (comparable to the width of ...
were sometimes called stars and planets as well.) The planets seem to move and change their position over short periods of time (weeks or months). They always seem to move within the band of stars called the
zodiac The zodiac is a belt-shaped region of the sky that extends approximately 8° north or south (as measured in celestial latitude) of the ecliptic, the apparent path of the Sun across the celestial sphere over the course of the year. The pa ...
by Westerners. The planets can also be distinguished from fixed stars because stars tend to twinkle, while planets appear to shine with a steady light. However, fixed stars do have parallax, which is a change in apparent position caused by the orbital motion of the Earth. It can be used to find the distance to nearby stars. This motion is only apparent; it is the Earth that moves. This effect was small enough not to be accurately measured until the 19th century, but from about 1670 and onward, astronomers such as Pickard, Hooke, Flamsteed, and others began detecting motion from the stars and attempting measurements. These movements amounted to significant, if almost imperceptibly small, fractions. The fixed stars exhibit real motion as well, however. This motion may be viewed as having components that consist in part of motion of the galaxy to which the star belongs, in part of rotation of that galaxy, and in part of motion peculiar to the star itself within its galaxy. In the case of
star system A star system or stellar system is a small number of stars that orbit each other, bound by gravitational attraction. A large group of stars bound by gravitation is generally called a '' star cluster'' or ''galaxy'', although, broadly speaking ...
s or
star cluster Star clusters are large groups of stars. Two main types of star clusters can be distinguished: globular clusters are tight groups of ten thousand to millions of old stars which are gravitationally bound, while open clusters are more loosely cl ...
s, the individual components move with respect to each other in a non-linear manner. The development of Newton's laws raised further questions among theorists about the mechanisms of the heavens: the universal force of gravity suggested that stars could not simply be fixed or at rest, as their gravitational pulls cause "mutual attraction" and therefore cause them to move in relation to each other. This real motion of a star is divided into ''radial'' motion and '' proper motion'', with "proper motion" being the component across the line of sight. In 1718 Edmund Halley announced his discovery that the fixed stars actually have proper motion. Proper motion was not noticed by ancient cultures because it requires precise measurements over long periods of time to notice. In fact, the night sky today looks very much as it did thousands of years ago, so much so that some modern constellations were first named by the Babylonians. A typical method to determine proper motion is to measure the position of a star relative to a limited, selected set of very distant objects that exhibit no mutual movement, and that, because of their distance, are assumed to have very small proper motion. Another approach is to compare photographs of a star at different times against a large background of more distant objects. The star with the largest known proper motion is
Barnard's Star Barnard's Star is a red dwarf about six light-years from Earth in the constellation of Ophiuchus. It is the fourth-nearest-known individual star to the Sun after the three components of the Alpha Centauri system, and the closest star in t ...
. The phrase "fixed star" is technically incorrect, but nonetheless it is used in an historical context, and in classical mechanics.


In classical mechanics

In Newton's time the fixed stars were invoked as a reference frame supposedly at rest relative to absolute space. In other reference frames either at rest with respect to the fixed stars or in uniform translation relative to these stars,
Newton's laws of motion Newton's laws of motion are three basic laws of classical mechanics that describe the relationship between the motion of an object and the forces acting on it. These laws can be paraphrased as follows: # A body remains at rest, or in mo ...
were supposed to hold. In contrast, in frames accelerating with respect to the fixed stars, in particular frames rotating relative to the fixed stars, the laws of motion did not hold in their simplest form, but had to be supplemented by the addition of
fictitious forces A fictitious force is a force that appears to act on a mass whose motion is described using a non-inertial frame of reference, such as a linearly accelerating or rotating reference frame. It is related to Newton's second law of motion, which tre ...
, for example, the
Coriolis force In physics, the Coriolis force is an inertial or fictitious force that acts on objects in motion within a frame of reference that rotates with respect to an inertial frame. In a reference frame with clockwise rotation, the force acts to the ...
and the
centrifugal force In Newtonian mechanics, the centrifugal force is an inertial force (also called a "fictitious" or "pseudo" force) that appears to act on all objects when viewed in a rotating frame of reference. It is directed away from an axis which is paralle ...
. As we now know, the fixed stars are not ''fixed''. The concept of inertial frames of reference is no longer tied to either the fixed stars or to absolute space. Rather, the identification of an inertial frame is based upon the simplicity of the laws of physics in the frame, in particular, the absence of fictitious forces. Law of inertia holds for Galilean coordinate system which is a hypothetical system relative to which fixed stars remain fixed.


In relational mechanics

:''References for this section: '' Fixed stars can be observed outside the view of classical mechanics and the view of relational mechanics.
Relational quantum mechanics :''This article is intended for those already familiar with quantum mechanics and its attendant interpretational difficulties. Readers who are new to the subject may first want to read the introduction to quantum mechanics.'' Relational quantum m ...
is a field theory that is a part of classical mechanics that dictates only the evolution of distances between particles and not their motion. The formation of this field theory gives solutions to the criticisms made by
Leibniz Gottfried Wilhelm (von) Leibniz . ( – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat. He is one of the most prominent figures in both the history of philosophy and the history of ma ...
and Mach of Newton's mechanics. As Newton relied on absolute space, relational mechanics does not. Describing fixed stars in terms of relational mechanics agrees with Newtonian mechanics. The use of privileged frames (Newtonian Frame) allows for the observation of Keplerian orbits for the motion of the planets; however, the observation of individual evolutions does not hold value in relational mechanics. An individual evolution can be distorted by changing the frame to which the position and velocity of an individual evolution are considered not observable. The observables in relational mechanics are the distance between the particles and the angles of the straight lines that joins the particles. Relational equations deal with the evolution of observation variables because they are independent of frames and can calculate a given evolution of distances that individual evolutions can describe from different frames. This can only mean that gauge symmetry employs mechanics with the essential relational feature that Leibniz claimed. Leibniz and Mach criticized the use of absolute space to validate Newtonian frames. Leibniz believed in the relation of the bodies as opposed to individual evolutions relative to metaphysically defined frames. Mach would criticize Newton's concept of absolute acceleration, stating that the shape of the water only proves the rotation with respect to the rest of the universe. Mach's criticism was later taken up by
Einstein Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born Theoretical physics, theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time. Einstein is best known for d ...
, stating "Mach's principle," the idea that inertia is determined by the interaction with the rest of the universe. Relational mechanics can be referred to as a Machian theory. The reformation of mechanics in the 20th century was ripe with relational principles. The laws of mechanics combine potential and kinetic variables, which in this case, the potential is already relational because it contains distances between the particles. The Newtonian kinetic energy contained individual velocities that were attempted to be reformulated into relative velocities and the possibility of distances. However, these attempts led to many opposing concepts to inertia that were not supported, to which many agreed that the basic premise of Newtonian kinetic energy should be preserved. The evolution of distances between particles does not require inertial frames to show themselves but instead uses them as coordinates for particles. The two different laws of mechanics are conceptually different. An example would be the isolation of a subsystem where Newton's law would describe its evolution in terms of absolute, initial, and final conditions. Relational mechanics would describe its evolution in terms of internal and external distances, so even if the system is "isolated," its evolution will always be described by the relation of the subsystem to the rest of the universe.


See also

*
Celestial sphere In astronomy and navigation, the celestial sphere is an abstract sphere that has an arbitrarily large radius and is concentric to Earth. All objects in the sky can be conceived as being projected upon the inner surface of the celestial sphe ...
* Pole star *
Apparent magnitude Apparent magnitude () is a measure of the brightness of a star or other astronomical object observed from Earth. An object's apparent magnitude depends on its intrinsic luminosity, its distance from Earth, and any extinction of the object's ...
(Related to ''apparent brightness'') * Historical models of the Solar System *
Behenian fixed star The Behenian fixed stars are a selection of fifteen stars considered especially useful for magical applications in the medieval astrology of Europe and the Arab world. Their name derives from Arabic ''bahman'', "root," as each was considered a s ...
* Firmament * Galaxy rotation curve *
Milky Way The Milky Way is the galaxy that includes our Solar System, with the name describing the galaxy's appearance from Earth: a hazy band of light seen in the night sky formed from stars that cannot be individually distinguished by the naked eye. ...


References

{{Authority control Astrometry Stellar astronomy