Fixed stars
The fixed stars () compose the background of astronomical objects that appear not to move relative to one another in the night sky, unlike the foreground of Solar System objects, which appear to move. Generally, the fixed stars are taken to include all stars other than the Sun. Nebulae and other deep-sky objects may also be counted among the fixed stars. Exact delimitation of the term is complicated by the fact that celestial objects are in fact not fixed with respect to one another. Nonetheless, extrasolar objects move so slowly in the sky that the change in their  relative positions is nearly imperceptible on typical human timescales, except to careful examination, and so can be considered to be "fixed" for many purposes. Furthermore, distant stars and galaxies move even more slowly in the sky than comparatively closer ones. People in many cultures have imagined that the stars form constellations, which are apparent pictures in the sky. In Ancient Greek astronomy, the fixed stars were believed to exist on a giant celestial sphere, or firmament, which revolves daily around the Earth. Origin of name. 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  poems 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. 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’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. 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, lived from 435 to 408 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, who lived from 384 to 322 BC studied and published similar ideas to Plato, but he improved on them through his books "Metaphysics" and "On the Heavens" 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, 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. Copernicus. Nicolaus Copernicus (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. Kepler. Johannes Kepler, 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. 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 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 wrote a treatise, of which only few excerpts remain. In this work he states his proposed order of the celestial objects, the sun moon and the fixed stars. The stars he mentions are apertures of "wheel-like condensations filled with fire", situated nearest to the earth in this system. The records of Anaximander's work left in fragments only gives a slight insight into reconstructing his intended meaning in understanding his views of the cosmos. Anaximander proposed a differing perspective from other later astronomers in proposing the fixed stars were nearest of the  heavenly bodies to the earth. Other models of the planetary system show a celestial sphere containing fixed stars on the outer most part of the universe. Aristotle and other like Greek thinkers of antiquity, and later the Ptolemaic model of the cosmos demonstrated 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 and Johannes Kepler. 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. The studies of the heavens were revolutionized with the invention of the telescope. First developed in 1608, the development of telescopes was widely publicized, and Galileo heard 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. Section::::"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 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 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 systems or star clusters, 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. 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 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 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. Fixed stars can be observed outside the view of classical mechanics and the view of relational mechanics. Relational quantum mechanics 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 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, 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.