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fixed stars and the sun remain unmoved that the earth revolves about the sun on the circumference of a circle the sun lying in the middle of the orbit and that the sphere of fixed stars situated about the same center as the sun is so great that the circle in which he supposes the earth to revolve bears such a proportion to the distance of the fixed stars as the center of the sphere bears to its surface 30 around 210 bc apollonius of perga shows the equivalence of two descriptions of the apparent retrograde motions of planets assuming the geocentric model one using eccentrics and another deferent and epicycles 11 in the following century measures of the sizes and distances of the earth and the moon improved around 200 bc eratosthenes determined that the radius of the earth is roughly 6 400 km 4 000 mi 31 circa 150 bc hipparchus used parallax to determine that the distance to the moon is roughly 380 000 km 236 100 mi 32 nearly matching aristarchus this imposed a minimum radius for the sphere of fixed stars at center to center earth to moon distance plus the moon s radius approx 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 386 400 km 240 100 mi this was around 24 500 000 times lower than archimedes computation the complexity to be described by the geocentric model around 130 ad ptolemy adopted apollonius epicycles in his geocentric model 33 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 each 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 34 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 4 million kilometres 2 5 million miles and to the edge of the universe about 73 million kilometres 45 million miles 35 still around 130 000 times less than archimedes ptolemy s methods written in his almagest were accurate enough to keep them largely undisputed for more than 1 500 years 36 but by the european renaissance the possibility that such a huge sphere could complete a single revolution of 360 around the earth in only 24 hours was deemed improbable 37 and this point was one of the arguments of nicholas copernicus for leaving behind the centuries old geocentric model the highest upper bound ever given was by jewish astronomer levi ben gershon gersonides who circa 1300 estimated the distance to the fixed stars to be no less than 159 651 513 380 944 earth radii or about 100 000 light years in modern units 38 this was an overestimate although in the actual universe there are stars farther than that distance both in the milky way 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 in other cultures edit the examples and perspective in this article may not represent a worldwide view of the subject you may improve this article discuss the issue on the talk page or create a new article as appropriate september 2024 learn how and when to remove this message in nordic mythology edit 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 originates from northern europe around the geographical location of modern day region of scandinavia and northern germany the norse mythology consists of tales and myths derived from old norse which was a northern german language from the middle ages there is a series of manuscript texts written in old norse which contain a collection of 35 poems written from oral tradition 39 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 40 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 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 41 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 developing western astronomy edit copernicus nicolaus on the revolutions of the heavenly spheres nüremberg 1543 print copy of copernicus s work showing the model of the universe with the sun in the center and a sphere of immobile stars on the outside according to his theory of the cosmos 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 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 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 42 all other later models of the planetary system show a celestial sphere containing fixed stars on the outermost part of the universe its edge within it lie all the rest of the moving luminaires plato aristotle and other like greek thinkers of antiquity and later the ptolemaic model of the cosmos showed an earth centered universe 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 this geocentric view was held through the middle ages and was later countered by subsequent astronomers and mathematicians alike such as nicolaus copernicus and johannes kepler who challenged the long standing view of geocentrism and constructed a sun centered universe this being known as the heliocentric system the tradition of thought which appears in all of these systems of the universe even with their divergent mechanisms is the presence of the sphere of fixed stars the heliocentric universe appearing in de mundo nostro sublunari philosophia nova new philosophy about our sublunary world attributed to william gilbert 1631 posthumous the text reads the stars outside the orb of the sun s power or in the form of an effusion are not moved by the sun but appear fixed to us in the sixteenth century a number of writers inspired by copernicus such as thomas digges 43 giordano bruno 44 and william gilbert 37 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 this was a revival of beliefs held by democritus epicurus 45 and fakhr al din al razi 46 the studies of the heavens were revolutionized with the invention of the telescope first developed in 1608 galileo galilei heard about it and made a telescope for himself 10 he immediately noticed that the planets were not in fact perfectly smooth a theory formerly put forth by aristotle 10 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 10 when in 1610 he aimed his telescope to the faint strip of the milky way he found it resolves into countless white star like spots presumably farther stars themselves 47 the development of isaac newton s laws published in his work philosophiæ naturalis principia mathematica in 1687 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 5 the term solar system entered the english language by 1704 when john locke used it to refer to the sun planets and comets as a whole 48 by then it had been established beyond doubt thanks to increased telescopic observations plus keplerian and newtonian celestial mechanics that planets are other worlds and stars are other distant suns so the whole solar system is actually only a small part of an immensely large universe and definitively something distinct fixed stars not fixed edit principle of the stellar parallax effect and the definition of one parsec as a unit of distance not to scale relation between proper motion and velocity components of a distant moving celestial object as seen from the solar system not to scale doppler redshift and blueshift 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 and show no evident stellar parallax which is a change in apparent position caused by the orbital motion of the earth the other group contained the naked eye planets which they called wandering stars the sun and moon were sometimes called stars and planets as well the planets seem to move forward and back changing their position over short periods of time weeks or months they always seem to move within the band of stars called the zodiac 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 show parallax 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 jean picard robert hooke john flamsteed and others began detecting motion from the stars and attempting measurements these movements amounted to significant if almost imperceptibly small fractions 10 the first successful stellar parallax measurements were done by thomas henderson in cape town south africa from 1832 to 1833 where he measured the parallax of and distance to one of the closest stars alpha centauri 49 henderson did not publish these observations until 1839 after friedrich wilhelm bessel published his parallax observations and distance estimate to 61 cygni in 1838 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 systems or star clusters the individual components even move with respect to each other in a non linear manner relative to the solar system 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 50 in 1718 edmund halley announced his discovery that the fixed stars actually have proper motion 51 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 52 another approach is to compare photographs of a star at different times against a large background of more distant objects 53 the star with the largest known proper motion is barnard s star 51 radial velocity of stars and other deep space objects can be revealed spectroscopically thru the doppler fizeau effect by which the frequency of the received light decreases for objects that were receding redshift and increases for objects that were approaching blueshift when compared to the light emitted by a stationary object william huggins ventured in 1868 to estimate the radial velocity of sirius with respect to the sun based on observed redshift of the star s light 54 the phrase fixed star is technically incorrect but nonetheless it is used in an historical context and in classical mechanics when used as a visual reference for observations they usually are called background stars or simply distant stars still retaining the intuitive meaning of they being fixed in some practical sense in classical mechanics edit main article inertial frame of reference 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 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 for example the coriolis force and the centrifugal force 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 law...
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