Margin of error
The margin of error is a statistic expressing the amount of random sampling error in a surveys results. It asserts a likelihood that the result from a sample is close to the one would get if the whole population had been queried. The likelihood of a result being within the margin of error is itself a probability, commonly 95%, though other values are sometimes used. The larger the margin of error, the confidence one should have that the polls reported results are close to the true figures, that is. Margin of error applies whenever a population is incompletely sampled, Margin of error is often used in non-survey contexts to indicate observational error in reporting measured quantities. The latter notation, with the ±, is commonly seen in most other science. The margin of error is defined as the radius of a confidence interval for a particular statistic from a survey. One example is the percent of people who prefer product A versus product B, when a single, global margin of error is reported for a survey, it refers to the maximum margin of error for all reported percentages using the full sample from the survey.
If the statistic is a percentage, this margin of error can be calculated as the radius of the confidence interval for a reported percentage of 50%. The margin of error has been described as an absolute quantity, for example, if the true value is 50 percentage points, and the statistic has a confidence interval radius of 5 percentage points, we say the margin of error is 5 percentage points. As another example, if the value is 50 people. In some cases, the margin of error is not expressed as an absolute quantity, for example, suppose the true value is 50 people, and the statistic has a confidence interval radius of 5 people. If we use the definition, the margin of error would be 5 people. If we use the definition, we express this absolute margin of error as a percent of the true value. So in this case, the margin of error is 5 people. Often, the distinction is not explicitly made, yet usually is apparent from context, like confidence intervals, the margin of error can be defined for any desired confidence level, but usually a level of 90%, 95% or 99% is chosen.
This level is the percentage of polls, if repeated with the design and procedure. Along with the level, the sample design for a survey
Minute and second of arc
A minute of arc, arc minute, or minute arc is a unit of angular measurement equal to 1/60 of one degree. Since one degree is 1/360 of a turn, one minute of arc is 1/21600 of a turn, a second of arc, arcsecond, or arc second is 1/60 of an arcminute, 1/3600 of a degree, 1/1296000 of a turn, and π/648000 of a radian. To express even smaller angles, standard SI prefixes can be employed, the number of square arcminutes in a complete sphere is 4 π2 =466560000 π ≈148510660 square arcminutes. The standard symbol for marking the arcminute is the prime, though a single quote is used where only ASCII characters are permitted. One arcminute is thus written 1′ and it is abbreviated as arcmin or amin or, less commonly, the prime with a circumflex over it. The standard symbol for the arcsecond is the prime, though a double quote is commonly used where only ASCII characters are permitted. One arcsecond is thus written 1″ and it is abbreviated as arcsec or asec. In celestial navigation, seconds of arc are used in calculations.
This notation has been carried over into marine GPS receivers, which normally display latitude and longitude in the format by default. An arcsecond is approximately the angle subtended by a U. S. dime coin at a distance of 4 kilometres, a milliarcsecond is about the size of a dime atop the Eiffel Tower as seen from New York City. A microarcsecond is about the size of a period at the end of a sentence in the Apollo mission manuals left on the Moon as seen from Earth, since antiquity the arcminute and arcsecond have been used in astronomy. The principal exception is Right ascension in equatorial coordinates, which is measured in units of hours, minutes. These small angles may be written in milliarcseconds, or thousandths of an arcsecond, the unit of distance, the parsec, named from the parallax of one arcsecond, was developed for such parallax measurements. It is the distance at which the radius of the Earths orbit would subtend an angle of one arcsecond. The ESA astrometric space probe Gaia is hoped to measure star positions to 20 microarcseconds when it begins producing catalog positions sometime after 2016, there are about 1.3 trillion µas in a turn.
Currently the best catalog positions of stars actually measured are in terms of milliarcseconds, apart from the Sun, the star with the largest angular diameter from Earth is R Doradus, a red supergiant with a diameter of 0.05 arcsecond. The dwarf planet Pluto has proven difficult to resolve because its angular diameter is about 0.1 arcsecond, space telescopes are not affected by the Earths atmosphere but are diffraction limited. For example, the Hubble space telescope can reach a size of stars down to about 0. 1″
The effective temperature of a body such as a star or planet is the temperature of a black body that would emit the same total amount of electromagnetic radiation. Effective temperature is used as an estimate of a bodys surface temperature when the bodys emissivity curve is not known. When the stars or planets net emissivity in the relevant wavelength band is less than unity, the net emissivity may be low due to surface or atmospheric properties, including greenhouse effect. Notice that the luminosity of a star is L =4 π R2 σ T e f f 4. The definition of the radius is obviously not straightforward. More rigorously the effective temperature corresponds to the temperature at the radius that is defined by a value of the Rosseland optical depth within the stellar atmosphere. The effective temperature and the bolometric luminosity are the two fundamental physical parameters needed to place a star on the Hertzsprung–Russell diagram, both effective temperature and bolometric luminosity depend on the chemical composition of a star.
The effective temperature of our Sun is around 5780 kelvin, stars have a decreasing temperature gradient, going from their central core up to the atmosphere. The core temperature of the temperature at the centre of the sun where nuclear reactions take place—is estimated to be 15,000,000 K. The effective temperature of a star indicates the amount of heat that the star radiates per unit of surface area, from the warmest surfaces to the coolest is the sequence of star types known as O, B, A, F, G, K, and M. The effective temperature of a planet can be calculated by equating the power received by the planet with the emitted by a blackbody of temperature T. Take the case of a planet at a distance D from the star and we allow the planet to reflect some of the incoming radiation by incorporating a parameter called the albedo. An albedo of 1 means that all the radiation is reflected, the effective temperature for Jupiter from this calculation is 112 K and 51 Pegasi b is 1258 K. A better estimate of effective temperature for some planets, such as Jupiter, the actual temperature depends on albedo and atmosphere effects.
The actual temperature from spectroscopic analysis for HD209458 b is 1130 K, the internal heating within Jupiter raises the effective temperature to about 152 K. The surface temperature of a planet can be estimated by modifying the effective-temperature calculation to account for emissivity and this area intercepts some of the power which is spread over the surface of a sphere of radius D. We allow the planet to some of the incoming radiation by incorporating a parameter a called the albedo. An albedo of 1 means that all the radiation is reflected, there is a factor ε, which is the emissivity and represents atmospheric effects
Stellar evolution is the process by which a star changes over the course of time. The table shows the lifetimes of stars as a function of their masses, all stars are born from collapsing clouds of gas and dust, often called nebulae or molecular clouds. Over the course of millions of years, these protostars settle down into a state of equilibrium, nuclear fusion powers a star for most of its life. Initially the energy is generated by the fusion of hydrogen atoms at the core of the main-sequence star, later, as the preponderance of atoms at the core becomes helium, stars like the Sun begin to fuse hydrogen along a spherical shell surrounding the core. This process causes the star to gradually grow in size, passing through the subgiant stage until it reaches the red giant phase. Once a star like the Sun has exhausted its fuel, its core collapses into a dense white dwarf. Stars with around ten or more times the mass of the Sun can explode in a supernova as their inert iron cores collapse into a dense neutron star or black hole.
Stellar evolution is not studied by observing the life of a star, as most stellar changes occur too slowly to be detected. Instead, astrophysicists come to understand how stars evolve by observing numerous stars at various points in their lifetime, in June 2015, astronomers reported evidence for Population III stars in the Cosmos Redshift 7 galaxy at z =6.60. Stellar evolution starts with the collapse of a giant molecular cloud. Typical giant molecular clouds are roughly 100 light-years across and contain up to 6,000,000 solar masses, as it collapses, a giant molecular cloud breaks into smaller and smaller pieces. In each of these fragments, the collapsing gas releases gravitational potential energy as heat, as its temperature and pressure increase, a fragment condenses into a rotating sphere of superhot gas known as a protostar. A protostar continues to grow by accretion of gas and dust from the molecular cloud, further development is determined by its mass. Protostars are encompassed in dust, and are more readily visible at infrared wavelengths.
Observations from the Wide-field Infrared Survey Explorer have been important for unveiling numerous Galactic protostars. Protostars with masses less than roughly 0.08 M☉ never reach high enough for nuclear fusion of hydrogen to begin. These are known as brown dwarfs, the International Astronomical Union defines brown dwarfs as stars massive enough to fuse deuterium at some point in their lives. Objects smaller than 13 MJ are classified as sub-brown dwarfs, both types, deuterium-burning and not, shine dimly and die away slowly, cooling gradually over hundreds of millions of years
In astronomy and physical cosmology, the metallicity or Z is the fraction of mass of a star or other kind of astronomical object that is not in hydrogen or helium. Most of the matter in the universe is in the form of hydrogen and helium, so astronomers use the word metals as a convenient short term for all elements except hydrogen. This usage is distinct from the physical definition of a solid metal. In cosmological terms, the universe is chemically evolving, according to the Big Bang Theory, the early universe first consisted of hydrogen and helium, with trace amounts of lithium and beryllium, but no heavier elements. It is believed that older generations of stars generally have lower metallicities than those of younger generations and these became commonly known as Population I and Population II stars. A third stellar population was introduced in 1978, known as Population III stars and these extremely metal-poor stars were theorised to have been the first-born stars created in the universe.
Measurements have demonstrated the connection between a stars metallicity and gas giant planets, like Jupiter and Saturn, the more metals in a star and thus its planetary system and proplyd, the more likely the system may have gas giant planets and rocky planets. Current models show that the metallicity along with the planetary system temperature and distance from the star are key to planet. Metallicity affects a stars color temperature, metal poor stars are bluer and metal rich stars are redder. The Sun, with 8 planets and 5 planetesimals, is used as the reference, other stars are noted with a positive or negative value. A star with a =0.0 has the iron abundance as the Sun. A star with =−1.0 has one tenth heavy elements of found in the Sun. At =+1, the element abundance is 10 times the Suns value. The survey of population of stars shows that older stars have less metallicity. Stellar composition, as determined by spectroscopy, is simply defined by the parameters X, Y and Z. Here X is the percentage of hydrogen, Y is the fractional percentage of helium.
It is simply defined as, X + Y + Z =1.00 In most stars and other sources, hydrogen. The hydrogen mass fraction is generally expressed as X ≡ m H M where M is the mass of the system
The solar luminosity, L☉, is a unit of radiant flux conventionally used by astronomers to measure the luminosity of stars. It is defined in terms of the Suns output, one solar luminosity is 3. 828×1026 W. This does not include the solar luminosity, which would add 0.023 L☉. The Sun is a variable star, and its luminosity therefore fluctuates. The major fluctuation is the solar cycle that causes a periodic variation of about ±0. 1%. Other variations over the last 200–300 years are thought to be smaller than this. Solar luminosity is related to solar irradiance, Solar irradiance is responsible for the orbital forcing that causes the Milankovitch cycles, which determine Earthly glacial cycles. The mean irradiance at the top of the Earths atmosphere is known as the solar constant. Solar mass Solar radius Nuclear fusion Triple-alpha process Sackmann, I. -J, a Bright Young Sun Consistent with Helioseismology and Warm Temperatures on Ancient Earth and Mars, Astrophys. J.583, 1024–39, arXiv, astro-ph/0210128, Bibcode, 2003ApJ.583. 1024S, doi,10.
1086/345408 Foukal, P. Fröhlich, spruit, H. Wigley, T. M. L. Variations in solar luminosity and their effect on the Earths climate, Nature,443, 161–66, Bibcode, 2006Natur.443. 161F, doi,10. 1038/nature05072, PMID16971941 Pelletier, variations in Solar Luminosity from Timescales of Minutes to Months, Astrophys. J.463, L41–L45, arXiv, astro-ph/9510026, Bibcode, 1996ApJ. 463L. 41P, doi,10. 1086/310049 Stoykova, D. A. Shopov, ford, D. Georgiev, L. N. et al
The celestial equator is a great circle on the imaginary celestial sphere, in the same plane as the Earths equator. In other words, it is a projection of the terrestrial equator out into space, as a result of the Earths axial tilt, the celestial equator is inclined by 23. 4° with respect to the ecliptic plane. An observer standing on the Earths equator visualizes the celestial equator as a semicircle passing directly overhead through the zenith, as the observer moves north, the celestial equator tilts towards the opposite horizon. Celestial objects near the equator are visible worldwide, but they culminate the highest in the sky in the tropics. The celestial equator currently passes through these constellations, Celestial bodies other than Earth have similarly defined celestial equators, Celestial pole Celestial sphere Declination Equatorial coordinate system
Stellar parallax is parallax on an interstellar scale, the apparent shift of position of any nearby star against the background of distant objects. Stellar parallax is so difficult to detect that its existence was the subject of debate in astronomy for thousands of years. It was first observed by Giuseppe Calandrelli who reported parallax in α-Lyrae in his work Osservazione e riflessione sulla parallasse annua dall’alfa della Lira, in 1838 Friedrich Bessel made the first successful parallax measurement ever, for the star 61 Cygni, using a Fraunhofer heliometer at Königsberg Observatory. Once a stars parallax is known, its distance from Earth can be computed trigonometrically, but the more distant an object is, the smaller its parallax. Even with 21st-century techniques in astrometry, the limits of accurate measurement make distances farther away than about 100 parsecs too approximate to be useful when obtained by this technique. Relatively close on a scale, the applicability of stellar parallax leaves most astronomical distance measurements to be calculated by spectral red-shift or other methods.
Stellar parallax measures are given in the units of arcseconds. The distance unit parsec is defined as the length of the leg of a right triangle adjacent to the angle of one arcsecond at one vertex, because stellar parallaxes and distances all involve such skinny right triangles, a convenient trigonometric approximation can be used to convert parallaxes to distance. The distance is simply the reciprocal of the parallax, d =1 / p, for example, Proxima Centauri, whose parallax is 0.7687, is 1 /0.7687 =1.3009 parsecs distant. Stellar parallax is so small that its apparent absence was used as an argument against heliocentrism during the early modern age. James Bradley first tried to measure stellar parallaxes in 1729, the stellar movement proved too insignificant for his telescope, but he instead discovered the aberration of light, the nutation of Earth’s axis, and catalogued 3222 stars. The parsec is defined as the distance for which the annual parallax is 1 arcsecond, annual parallax is normally measured by observing the position of a star at different times of the year as Earth moves through its orbit.
Measurement of annual parallax was the first reliable way to determine the distances to the closest stars, the first successful measurements of stellar parallax were made by Friedrich Bessel in 1838 for the star 61 Cygni using a heliometer. Being very difficult to measure, only about 60 stellar parallaxes had been obtained by the end of the 19th century, astrographs using astronomical photographic plates sped the process in the early 20th century. Automated plate-measuring machines and more sophisticated technology of the 1960s allowed more efficient compilation of star catalogues. In the 1980s, charge-coupled devices replaced photographic plates and reduced optical uncertainties to one milliarcsecond, stellar parallax remains the standard for calibrating other measurement methods. The angles involved in these calculations are very small and thus difficult to measure, the nearest star to the Sun, Proxima Centauri, has a parallax of 0.7687 ±0.0003 arcsec. This angle is approximately that subtended by an object 2 centimeters in diameter located 5.3 kilometers away
Right ascension is the angular distance measured eastward along the celestial equator from the vernal equinox to the hour circle of the point in question. When combined with declination, these astronomical coordinates specify the direction of a point on the sphere in the equatorial coordinate system. Right ascension is the equivalent of terrestrial longitude. Both right ascension and longitude measure an angle from a direction on an equator. Right ascension is measured continuously in a circle from that equinox towards the east. Any units of measure could have been chosen for right ascension, but it is customarily measured in hours, minutes. Astronomers have chosen this unit to measure right ascension because they measure a stars location by timing its passage through the highest point in the sky as the Earth rotates. The highest point in the sky, called meridian, is the projection of a line onto the celestial sphere. A full circle, measured in units, contains 24 × 60 × 60 = 86 400s, or 24 × 60 = 1 440m.
Because right ascensions are measured in hours, they can be used to time the positions of objects in the sky. For example, if a star with RA = 01h 30m 00s is on the meridian, sidereal hour angle, used in celestial navigation, is similar to right ascension, but increases westward rather than eastward. Usually measured in degrees, it is the complement of right ascension with respect to 24h and it is important not to confuse sidereal hour angle with the astronomical concept of hour angle, which measures angular distance of an object westward from the local meridian. The Earths axis rotates slowly westward about the poles of the ecliptic and this effect, known as precession, causes the coordinates of stationary celestial objects to change continuously, if rather slowly. Therefore, equatorial coordinates are inherently relative to the year of their observation, coordinates from different epochs must be mathematically rotated to match each other, or to match a standard epoch. The right ascension of Polaris is increasing quickly, the North Ecliptic Pole in Draco and the South Ecliptic Pole in Dorado are always at right ascension 18h and 6h respectively.
The currently used standard epoch is J2000.0, which is January 1,2000 at 12,00 TT, the prefix J indicates that it is a Julian epoch. Prior to J2000.0, astronomers used the successive Besselian Epochs B1875.0, B1900.0, the concept of right ascension has been known at least as far back as Hipparchus who measured stars in equatorial coordinates in the 2nd century BC. But Hipparchus and his successors made their star catalogs in ecliptic coordinates, the easiest way to do that is to use an equatorial mount, which allows the telescope to be aligned with one of its two pivots parallel to the Earths axis
A star catalogue or star catalog, is an astronomical catalogue that lists stars. In astronomy, many stars are referred to simply by catalogue numbers, there are a great many different star catalogues which have been produced for different purposes over the years, and this article covers only some of the more frequently quoted ones. Star catalogues were compiled by many different ancient peoples, including the Babylonians, Chinese, most modern catalogues are available in electronic format and can be freely downloaded from space agencies data center. Completeness and accuracy is described by the weakest apparent magnitude V, from their existing records, it is known that the ancient Egyptians recorded the names of only a few identifiable constellations and a list of thirty-six decans that were used as a star clock. They are better known by their Assyrian-era name Three Stars Each and these star catalogues, written on clay tablets, listed thirty-six stars, twelve for Anu along the celestial equator, twelve for Ea south of that, and twelve for Enlil to the north.
In Ancient Greece, the astronomer and mathematician Eudoxus laid down a set of the classical constellations around 370 BC. His catalogue Phaenomena, rewritten by Aratus of Soli between 275 and 250 BC as a poem, became one of the most consulted astronomical texts in antiquity. It contains descriptions of the positions of the stars, the shapes of the constellations, approximately in the 3rd century BC, the Greek astronomers Timocharis of Alexandria and Aristillus created another star catalogue. Hipparchus completed his star catalogue in 129 BC, which he compared to Timocharis and this led him to determine the first value of the precession of the equinoxes. In the 2nd century, Ptolemy of Roman Egypt published a star catalogue as part of his Almagest, ptolemys catalogue was based almost entirely on an earlier one by Hipparchus. It remained the star catalogue in the Western and Arab worlds for over eight centuries. The earliest known inscriptions for Chinese star names were written on oracle bones, sources dating from the Zhou Dynasty which provide star names include the Zuo Zhuan, the Shi Jing, and the Canon of Yao in the Book of Documents.
The Lüshi Chunqiu written by the Qin statesman Lü Buwei provides most of the names for the twenty-eight mansions, an earlier lacquerware chest found in the Tomb of Marquis Yi of Zeng contains a complete list of the names of the twenty-eight mansions. Star catalogues are traditionally attributed to Shi Shen and Gan De, the Shi Shen astronomy is attributed to Shi Shen, and the Astronomic star observation to Gan De. It was not until the Han Dynasty that astronomers started to observe and record names for all the stars that were apparent in the night sky, not just those around the ecliptic. A star catalogue is featured in one of the chapters of the late 2nd-century-BC history work Records of the Grand Historian by Sima Qian and contains the schools of Shi Shen and Gan Des work. For his Spiritual Constitution of the Universe of 120 AD, the astronomer Zhang Heng compiled a star catalogue comprising 124 constellations, Chinese constellation names were adopted by the Koreans and Japanese. A large number of star catalogues were published by Muslim astronomers in the medieval Islamic world and these were mainly Zij treatises, including Arzachels Tables of Toledo, the Maragheh observatorys Zij-i Ilkhani and Ulugh Begs Zij-i-Sultani
In nuclear physics, nuclear fusion is a reaction in which two or more atomic nuclei come close enough to form one or more different atomic nuclei and subatomic particles. The difference in mass between the products and reactants is manifested as the release of large amounts of energy and this difference in mass arises due to the difference in atomic binding energy between the atomic nuclei before and after the reaction. Fusion is the process that powers active or main sequence stars, the fusion process that produces a nucleus lighter than iron-56 or nickel-62 will generally yield a net energy release. These elements have the smallest mass per nucleon and the largest binding energy per nucleon, the opposite is true for the reverse process, nuclear fission. This means that the elements, such as hydrogen and helium, are in general more fusable, while the heavier elements. The extreme astrophysical event of a supernova can produce energy to fuse nuclei into elements heavier than iron. During the remainder of that decade the steps of the cycle of nuclear fusion in stars were worked out by Hans Bethe.
Research into fusion for military purposes began in the early 1940s as part of the Manhattan Project, fusion was accomplished in 1951 with the Greenhouse Item nuclear test. Nuclear fusion on a scale in an explosion was first carried out on November 1,1952. Research into developing controlled thermonuclear fusion for civil purposes began in earnest in the 1950s, the protons are positively charged and repel each other but they nonetheless stick together, demonstrating the existence of another force referred to as nuclear attraction. This force, called the nuclear force, overcomes electric repulsion at very close range. The effect of force is not observed outside the nucleus. The same force pulls the nucleons together allowing ordinary matter to exist, light nuclei, are sufficiently small and proton-poor allowing the nuclear force to overcome the repulsive Coulomb force. This is because the nucleus is small that all nucleons feel the short-range attractive force at least as strongly as they feel the infinite-range Coulomb repulsion.
Building up these nuclei from lighter nuclei by fusion thus releases the energy from the net attraction of these particles. For larger nuclei, however, no energy is released, since the force is short-range. Thus, energy is no longer released when such nuclei are made by fusion, fusion reactions create the light elements that power the stars and produce virtually all elements in a process called nucleosynthesis. The fusion of elements in stars releases energy and the mass that always accompanies it