1.
System of measurement
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A system of measurement is a collection of units of measurement and rules relating them to each other. Systems of measurement have historically been important, regulated and defined for the purposes of science and commerce, systems of measurement in modern use include the metric system, the imperial system, and United States customary units. The French Revolution gave rise to the system, and this has spread around the world. In most systems, length, mass, and time are base quantities, later science developments showed that either electric charge or electric current could be added to extend the set of base quantities by which many other metrological units could be easily defined. Other quantities, such as power and speed, are derived from the set, for example. Such arrangements were satisfactory in their own contexts, the preference for a more universal and consistent system only gradually spread with the growth of science. Changing a measurement system has substantial financial and cultural costs which must be offset against the advantages to be obtained using a more rational system. However pressure built up, including scientists and engineers for conversion to a more rational. The unifying characteristic is that there was some definition based on some standard, eventually cubits and strides gave way to customary units to met the needs of merchants and scientists. In the metric system and other recent systems, a basic unit is used for each base quantity. Often secondary units are derived from the units by multiplying by powers of ten. Thus the basic unit of length is the metre, a distance of 1.234 m is 1,234 millimetres. Metrication is complete or nearly complete in almost all countries, US customary units are heavily used in the United States and to some degree in Liberia. Traditional Burmese units of measurement are used in Burma, U. S. units are used in limited contexts in Canada due to the large volume of trade, there is also considerable use of Imperial weights and measures, despite de jure Canadian conversion to metric. In the United States, metric units are used almost universally in science, widely in the military, and partially in industry, but customary units predominate in household use. At retail stores, the liter is a used unit for volume, especially on bottles of beverages. Some other standard non-SI units are still in use, such as nautical miles and knots in aviation. Metric systems of units have evolved since the adoption of the first well-defined system in France in 1795, during this evolution the use of these systems has spread throughout the world, first to non-English-speaking countries, and then to English speaking countries
2.
Length
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In geometric measurements, length is the most extended dimension of an object. In the International System of Quantities, length is any quantity with dimension distance, in other contexts length is the measured dimension of an object. For example, it is possible to cut a length of a wire which is shorter than wire thickness. Length may be distinguished from height, which is vertical extent, and width or breadth, length is a measure of one dimension, whereas area is a measure of two dimensions and volume is a measure of three dimensions. In most systems of measurement, the unit of length is a base unit, measurement has been important ever since humans settled from nomadic lifestyles and started using building materials, occupying land and trading with neighbours. As society has become more technologically oriented, much higher accuracies of measurement are required in a diverse set of fields. One of the oldest units of measurement used in the ancient world was the cubit which was the length of the arm from the tip of the finger to the elbow. This could then be subdivided into shorter units like the foot, hand or finger, the cubit could vary considerably due to the different sizes of people. After Albert Einsteins special relativity, length can no longer be thought of being constant in all reference frames. Thus a ruler that is one meter long in one frame of reference will not be one meter long in a frame that is travelling at a velocity relative to the first frame. This means length of an object is variable depending on the observer, in the physical sciences and engineering, when one speaks of units of length, the word length is synonymous with distance. There are several units that are used to measure length, in the International System of Units, the basic unit of length is the metre and is now defined in terms of the speed of light. The centimetre and the kilometre, derived from the metre, are commonly used units. In U. S. customary units, English or Imperial system of units, commonly used units of length are the inch, the foot, the yard, and the mile. Units used to denote distances in the vastness of space, as in astronomy, are longer than those typically used on Earth and include the astronomical unit, the light-year. Dimension Distance Orders of magnitude Reciprocal length Smoot Unit of length
3.
Metric system
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The metric system is an internationally agreed decimal system of measurement. Many sources also cite Liberia and Myanmar as the other countries not to have done so. Although the originators intended to devise a system that was accessible to all. Control of the units of measure was maintained by the French government until 1875, when it was passed to an intergovernmental organisation. From its beginning, the features of the metric system were the standard set of interrelated base units. These base units are used to larger and smaller units that could replace a huge number of other units of measure in existence. Although the system was first developed for use, the development of coherent units of measure made it particularly suitable for science. Although the metric system has changed and developed since its inception, designed for transnational use, it consisted of a basic set of units of measurement, now known as base units. At the outbreak of the French Revolution in 1789, most countries, the metric system was designed to be universal—in the words of the French philosopher Marquis de Condorcet it was to be for all people for all time. However, these overtures failed and the custody of the metric system remained in the hands of the French government until 1875. In languages where the distinction is made, unit names are common nouns, the concept of using consistent classical names for the prefixes was first proposed in a report by the Commission on Weights and Measures in May 1793. The prefix kilo, for example, is used to multiply the unit by 1000, thus the kilogram and kilometre are a thousand grams and metres respectively, and a milligram and millimetre are one thousandth of a gram and metre respectively. These relations can be written symbolically as,1 mg =0, however,1935 extensions to the prefix system did not follow this convention, the prefixes nano- and micro-, for example have Greek roots. During the 19th century the prefix myria-, derived from the Greek word μύριοι, was used as a multiplier for 10000, prefixes are not usually used to indicate multiples of a second greater than 1, the non-SI units of minute, hour and day are used instead. On the other hand, prefixes are used for multiples of the unit of volume. The base units used in the system must be realisable. Each of the units in SI is accompanied by a mise en pratique published by the BIPM that describes in detail at least one way in which the base unit can be measured. In practice, such realisation is done under the auspices of a mutual acceptance arrangement, in the original version of the metric system the base units could be derived from a specified length and the weight of a specified volume of pure water
4.
International System of Units
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The International System of Units is the modern form of the metric system, and is the most widely used system of measurement. It comprises a coherent system of units of measurement built on seven base units, the system also establishes a set of twenty prefixes to the unit names and unit symbols that may be used when specifying multiples and fractions of the units. The system was published in 1960 as the result of an initiative began in 1948. It is based on the system of units rather than any variant of the centimetre-gram-second system. The motivation for the development of the SI was the diversity of units that had sprung up within the CGS systems, the International System of Units has been adopted by most developed countries, however, the adoption has not been universal in all English-speaking countries. The metric system was first implemented during the French Revolution with just the metre and kilogram as standards of length, in the 1830s Carl Friedrich Gauss laid the foundations for a coherent system based on length, mass, and time. In the 1860s a group working under the auspices of the British Association for the Advancement of Science formulated the requirement for a coherent system of units with base units and derived units. Meanwhile, in 1875, the Treaty of the Metre passed responsibility for verification of the kilogram, in 1921, the Treaty was extended to include all physical quantities including electrical units originally defined in 1893. The units associated with these quantities were the metre, kilogram, second, ampere, kelvin, in 1971, a seventh base quantity, amount of substance represented by the mole, was added to the definition of SI. On 11 July 1792, the proposed the names metre, are, litre and grave for the units of length, area, capacity. The committee also proposed that multiples and submultiples of these units were to be denoted by decimal-based prefixes such as centi for a hundredth, on 10 December 1799, the law by which the metric system was to be definitively adopted in France was passed. Prior to this, the strength of the magnetic field had only been described in relative terms. The technique used by Gauss was to equate the torque induced on a magnet of known mass by the earth’s magnetic field with the torque induced on an equivalent system under gravity. The resultant calculations enabled him to assign dimensions based on mass, length, a French-inspired initiative for international cooperation in metrology led to the signing in 1875 of the Metre Convention. Initially the convention only covered standards for the metre and the kilogram, one of each was selected at random to become the International prototype metre and International prototype kilogram that replaced the mètre des Archives and kilogramme des Archives respectively. Each member state was entitled to one of each of the prototypes to serve as the national prototype for that country. Initially its prime purpose was a periodic recalibration of national prototype metres. The official language of the Metre Convention is French and the version of all official documents published by or on behalf of the CGPM is the French-language version
5.
Metre
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The metre or meter, is the base unit of length in the International System of Units. The metre is defined as the length of the path travelled by light in a vacuum in 1/299792458 seconds, the metre was originally defined in 1793 as one ten-millionth of the distance from the equator to the North Pole. In 1799, it was redefined in terms of a metre bar. In 1960, the metre was redefined in terms of a number of wavelengths of a certain emission line of krypton-86. In 1983, the current definition was adopted, the imperial inch is defined as 0.0254 metres. One metre is about 3 3⁄8 inches longer than a yard, Metre is the standard spelling of the metric unit for length in nearly all English-speaking nations except the United States and the Philippines, which use meter. Measuring devices are spelled -meter in all variants of English, the suffix -meter has the same Greek origin as the unit of length. This range of uses is found in Latin, French, English. Thus calls for measurement and moderation. In 1668 the English cleric and philosopher John Wilkins proposed in an essay a decimal-based unit of length, as a result of the French Revolution, the French Academy of Sciences charged a commission with determining a single scale for all measures. In 1668, Wilkins proposed using Christopher Wrens suggestion of defining the metre using a pendulum with a length which produced a half-period of one second, christiaan Huygens had observed that length to be 38 Rijnland inches or 39.26 English inches. This is the equivalent of what is now known to be 997 mm, no official action was taken regarding this suggestion. In the 18th century, there were two approaches to the definition of the unit of length. One favoured Wilkins approach, to define the metre in terms of the length of a pendulum which produced a half-period of one second. The other approach was to define the metre as one ten-millionth of the length of a quadrant along the Earths meridian, that is, the distance from the Equator to the North Pole. This means that the quadrant would have defined as exactly 10000000 metres at that time. To establish a universally accepted foundation for the definition of the metre, more measurements of this meridian were needed. This portion of the meridian, assumed to be the length as the Paris meridian, was to serve as the basis for the length of the half meridian connecting the North Pole with the Equator
6.
Imperial units
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The system of imperial units or the imperial system is the system of units first defined in the British Weights and Measures Act of 1824, which was later refined and reduced. The Imperial units replaced the Winchester Standards, which were in effect from 1588 to 1825, the system came into official use across the British Empire. The imperial system developed from what were first known as English units, the Weights and Measures Act of 1824 was initially scheduled to go into effect on 1 May 1825. However, the Weights and Measures Act of 1825 pushed back the date to 1 January 1826, the 1824 Act allowed the continued use of pre-imperial units provided that they were customary, widely known, and clearly marked with imperial equivalents. Apothecaries units are mentioned neither in the act of 1824 nor 1825, at the time, apothecaries weights and measures were regulated in England, Wales, and Berwick-upon-Tweed by the London College of Physicians, and in Ireland by the Dublin College of Physicians. In Scotland, apothecaries units were unofficially regulated by the Edinburgh College of Physicians, the three colleges published, at infrequent intervals, pharmacopoeiae, the London and Dublin editions having the force of law. The Medical Act of 1858 transferred to The Crown the right to publish the official pharmacopoeia and to regulate apothecaries weights, Metric equivalents in this article usually assume the latest official definition. Before this date, the most precise measurement of the imperial Standard Yard was 0.914398416 metres, in 1824, the various different gallons in use in the British Empire were replaced by the imperial gallon, a unit close in volume to the ale gallon. It was originally defined as the volume of 10 pounds of distilled water weighed in air with brass weights with the standing at 30 inches of mercury at a temperature of 62 °F. The Weights and Measures Act of 1985 switched to a gallon of exactly 4.54609 l and these measurements were in use from 1826, when the new imperial gallon was defined, but were officially abolished in the United Kingdom on 1 January 1971. In the USA, though no longer recommended, the system is still used occasionally in medicine. The troy pound was made the unit of mass by the 1824 Act, however, its use was abolished in the UK on 1 January 1879, with only the troy ounce. The Weights and Measures Act 1855 made the pound the primary unit of mass. In all the systems, the unit is the pound. For the yard, the length of a pendulum beating seconds at the latitude of Greenwich at Mean Sea Level in vacuo was defined as 39.01393 inches, the imperial system is one of many systems of English units. Although most of the units are defined in more than one system, some units were used to a much greater extent, or for different purposes. The distinctions between these systems are not drawn precisely. One such distinction is that between these systems and older British/English units/systems or newer additions, the US customary system is historically derived from the English units that were in use at the time of settlement
7.
United States customary units
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United States customary units are a system of measurements commonly used in the United States. The United States customary system developed from English units which were in use in the British Empire before the US declared its independence, however, the British system of measures was overhauled in 1824 to create the imperial system, changing the definitions of some units. Therefore, while many U. S. units are similar to their Imperial counterparts. The majority of U. S. customary units were redefined in terms of the meter and these definitions were refined by the international yard and pound agreement of 1959. Americans primarily use customary units in commercial activities, as well as for personal and social use, in science, medicine, many sectors of industry and some of government, metric units are used. The International System of Units, the form of the metric system, is preferred for many uses by the U. S. National Institute of Standards. The United States system of units is similar to the British imperial system, both systems are derived from English units, a system which had evolved over the millennia before American independence, and which had its roots in Roman and Anglo-Saxon units. The customary system was championed by the U. S. -based International Institute for Preserving and Perfecting Weights, advocates of the customary system saw the French Revolutionary, or metric, system as atheistic. An auxiliary of the Institute in Ohio published a poem with wording such as down with every metric scheme and A perfect inch, one adherent of the customary system called it a just weight and a just measure, which alone are acceptable to the Lord. The U. S. government passed the Metric Conversion Act of 1975, the legislation states that the federal government has a responsibility to assist industry as it voluntarily converts to the metric system, i. e. metrification. This is most evident in U. S. labeling requirements on food products, according to the CIA Factbook, the United States is one of three nations that have not adopted the metric system as their official system of weights and measures. U. S. customary units are used on consumer products. Metric units are standard in science, medicine, as well as many sectors of industry and government, the metric system also lacks a parallel to the foot. Frequently, however, these units designate quite different sizes, for example, the mile ranged by country from one-half to five U. S. miles, foot and pound also had varying definitions. Historically, a range of non-SI units were used in the U. S. and in Britain. This article deals only with the commonly used or officially defined in the U. S. For measuring length, the U. S. customary system uses the inch, foot, yard, and mile, since July 1,1959, these have been defined on the basis of 1 yard =0.9144 meters except for some applications in surveying. The U. S. the United Kingdom and other Commonwealth countries agreed on this definition, the NAD27 was replaced in the 1980s by the North American Datum of 1983, which is defined in meters
8.
Mile
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The mile is an English unit of length of linear measure equal to 5,280 feet, or 1,760 yards, and standardised as exactly 1,609.344 metres by international agreement in 1959. The Romans divided their mile into 5,000 feet but the importance of furlongs in pre-modern England meant that the statute mile was made equivalent to 8 furlongs or 5,280 feet in 1593. This form of the mile then spread to the British-colonized nations who continue to employ the mile, the US Geological Survey now employs the metre for official purposes but legacy data from its 1927 geodetic datum has meant that a separate US survey mile continues to see some use. Derived units such as miles per hour and miles per gallon, however, continue to be abbreviated as mph, mpg. The modern English word mile derives from Middle English myl and Old English mīl, the present international mile is usually what is understood by the unqualified term mile. When this distance needs to be distinguished from the nautical mile, in British English, the statute mile may refer to the present international miles or to any other form of English mile since the 1593 Act of Parliament which set it as a distance of 1,760 yards. Under American law, however, the statute mile refers to the US survey mile, the mile has been variously abbreviated—with and without a trailing period—as m, M, ml, and mi. The American National Institute of Standards and Technology now uses and recommends mi in order to avoid confusion with the SI metre and millilitre. Derived units such as miles per hour and miles per gallon, however, continue to be abbreviated in the United States, United Kingdom, the BBC style holds that There is no acceptable abbreviation for ‘miles’ and so it should be spelt out when used in describing areas. The Roman mile consisted of a thousand paces as measured by every other step—as in the distance of the left foot hitting the ground 1,000 times. The ancient Romans, marching their armies through uncharted territory, would push a carved stick in the ground after each 1000 paces. Well-fed and harshly driven Roman legionaries in good weather thus created longer miles, the distance was indirectly standardised by Agrippas establishment of a standard Roman foot in 29 BC, and the definition of a pace as 5 feet. An Imperial Roman mile thus denoted 5,000 Roman feet, surveyors and specialized equipment such as the decempeda and dioptra then spread its use. In modern times, Agrippas Imperial Roman mile was empirically estimated to have been about 1,481 metres in length, in Hellenic areas of the Empire, the Roman mile was used beside the native Greek units as equivalent to 8 stadia of 600 Greek feet. The mílion continued to be used as a Byzantine unit and was used as the name of the zero mile marker for the Byzantine Empire. The Roman mile also spread throughout Europe, with its local variations giving rise to the different units below, also arising from the Roman mile is the milestone. All roads radiated out from the Roman Forum throughout the Empire –50,000 miles of stone-paved roads, at every mile was placed a shaped stone, on which was carved a Roman numeral, indicating the number of miles from the center of Rome – the Forum. Hence, one knew how far one was from Rome
9.
Parsec
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The parsec is a unit of length used to measure large distances to objects outside the Solar System. One parsec is the distance at which one astronomical unit subtends an angle of one arcsecond, a parsec is equal to about 3.26 light-years in length. The nearest star, Proxima Centauri, is about 1.3 parsecs from the Sun, most of the stars visible to the unaided eye in the nighttime sky are within 500 parsecs of the Sun. The parsec unit was likely first suggested in 1913 by the British astronomer Herbert Hall Turner, named from an abbreviation of the parallax of one arcsecond, it was defined so as to make calculations of astronomical distances quick and easy for astronomers from only their raw observational data. Partly for this reason, it is still the unit preferred in astronomy and astrophysics, though the light-year remains prominent in science texts. This corresponds to the definition of the parsec found in many contemporary astronomical references. Derivation, create a triangle with one leg being from the Earth to the Sun. As that point in space away, the angle between the Sun and Earth decreases. A parsec is the length of that leg when the angle between the Sun and Earth is one arc-second. One of the oldest methods used by astronomers to calculate the distance to a star is to record the difference in angle between two measurements of the position of the star in the sky. The first measurement is taken from the Earth on one side of the Sun, and the second is approximately half a year later. The distance between the two positions of the Earth when the two measurements were taken is twice the distance between the Earth and the Sun. The difference in angle between the two measurements is twice the angle, which is formed by lines from the Sun. Then the distance to the star could be calculated using trigonometry. 5-parsec distance of 61 Cygni, the parallax of a star is defined as half of the angular distance that a star appears to move relative to the celestial sphere as Earth orbits the Sun. Equivalently, it is the angle, from that stars perspective. The star, the Sun and the Earth form the corners of a right triangle in space, the right angle is the corner at the Sun. Therefore, given a measurement of the angle, along with the rules of trigonometry. A parsec is defined as the length of the adjacent to the vertex occupied by a star whose parallax angle is one arcsecond
10.
Unit of length
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A Unit of length refers to any discrete, pre-established length or distance having a constant magnitude which is used as a reference or convention to express linear dimension. The most common units in use are U. S. customary units in the United States. British Imperial units are used for some purposes in the United Kingdom. The metric system is sub-divided into SI and non-SI units, the base unit in the International System of Units is the metre, defined as the length of the path travelled by light in vacuum during a time interval of 1/299,792,458 of a second. It is approximately equal to 1.0936 yards, other units are derived from the metre by adding prefixes from the table below, For example, a kilometre is 1000 metres. In the Centimetre–gram–second system of units, the unit of length is the centimetre. Other non-SI units are derived from decimal multiples of the metre, the basic unit of length in the Imperial and U. S. customary systems is the yard, defined as exactly 0.9144 m by international treaty in 1959. Common Imperial units and U. S. astronomical unit AU, approximately the distance between the Earth and Sun. Light-year ly ≈9460730472580.8 km The distance that light travels in a vacuum in one Julian year and this is often a characteristic radius or wavelength of a particle. A Measure of All Things, The Story of Man and Measurement
11.
Earth
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Earth, otherwise known as the World, or the Globe, is the third planet from the Sun and the only object in the Universe known to harbor life. It is the densest planet in the Solar System and the largest of the four terrestrial planets, according to radiometric dating and other sources of evidence, Earth formed about 4.54 billion years ago. Earths gravity interacts with objects in space, especially the Sun. During one orbit around the Sun, Earth rotates about its axis over 365 times, thus, Earths axis of rotation is tilted, producing seasonal variations on the planets surface. The gravitational interaction between the Earth and Moon causes ocean tides, stabilizes the Earths orientation on its axis, Earths lithosphere is divided into several rigid tectonic plates that migrate across the surface over periods of many millions of years. About 71% of Earths surface is covered with water, mostly by its oceans, the remaining 29% is land consisting of continents and islands that together have many lakes, rivers and other sources of water that contribute to the hydrosphere. The majority of Earths polar regions are covered in ice, including the Antarctic ice sheet, Earths interior remains active with a solid iron inner core, a liquid outer core that generates the Earths magnetic field, and a convecting mantle that drives plate tectonics. Within the first billion years of Earths history, life appeared in the oceans and began to affect the Earths atmosphere and surface, some geological evidence indicates that life may have arisen as much as 4.1 billion years ago. Since then, the combination of Earths distance from the Sun, physical properties, in the history of the Earth, biodiversity has gone through long periods of expansion, occasionally punctuated by mass extinction events. Over 99% of all species that lived on Earth are extinct. Estimates of the number of species on Earth today vary widely, over 7.4 billion humans live on Earth and depend on its biosphere and minerals for their survival. Humans have developed diverse societies and cultures, politically, the world has about 200 sovereign states, the modern English word Earth developed from a wide variety of Middle English forms, which derived from an Old English noun most often spelled eorðe. It has cognates in every Germanic language, and their proto-Germanic root has been reconstructed as *erþō, originally, earth was written in lowercase, and from early Middle English, its definite sense as the globe was expressed as the earth. By early Modern English, many nouns were capitalized, and the became the Earth. More recently, the name is simply given as Earth. House styles now vary, Oxford spelling recognizes the lowercase form as the most common, another convention capitalizes Earth when appearing as a name but writes it in lowercase when preceded by the. It almost always appears in lowercase in colloquial expressions such as what on earth are you doing, the oldest material found in the Solar System is dated to 4. 5672±0.0006 billion years ago. By 4. 54±0.04 Gya the primordial Earth had formed, the formation and evolution of Solar System bodies occurred along with the Sun
12.
Sun
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The Sun is the star at the center of the Solar System. It is a perfect sphere of hot plasma, with internal convective motion that generates a magnetic field via a dynamo process. It is by far the most important source of energy for life on Earth. Its diameter is about 109 times that of Earth, and its mass is about 330,000 times that of Earth, accounting for about 99. 86% of the total mass of the Solar System. About three quarters of the Suns mass consists of hydrogen, the rest is mostly helium, with smaller quantities of heavier elements, including oxygen, carbon, neon. The Sun is a G-type main-sequence star based on its spectral class and it formed approximately 4.6 billion years ago from the gravitational collapse of matter within a region of a large molecular cloud. Most of this matter gathered in the center, whereas the rest flattened into a disk that became the Solar System. The central mass became so hot and dense that it eventually initiated nuclear fusion in its core and it is thought that almost all stars form by this process. The Sun is roughly middle-aged, it has not changed dramatically for more than four billion years and it is calculated that the Sun will become sufficiently large enough to engulf the current orbits of Mercury, Venus, and probably Earth. The enormous effect of the Sun on Earth has been recognized since prehistoric times, the synodic rotation of Earth and its orbit around the Sun are the basis of the solar calendar, which is the predominant calendar in use today. The English proper name Sun developed from Old English sunne and may be related to south, all Germanic terms for the Sun stem from Proto-Germanic *sunnōn. The English weekday name Sunday stems from Old English and is ultimately a result of a Germanic interpretation of Latin dies solis, the Latin name for the Sun, Sol, is not common in general English language use, the adjectival form is the related word solar. The term sol is used by planetary astronomers to refer to the duration of a solar day on another planet. A mean Earth solar day is approximately 24 hours, whereas a mean Martian sol is 24 hours,39 minutes, and 35.244 seconds. From at least the 4th Dynasty of Ancient Egypt, the Sun was worshipped as the god Ra, portrayed as a falcon-headed divinity surmounted by the solar disk, and surrounded by a serpent. In the New Empire period, the Sun became identified with the dung beetle, in the form of the Sun disc Aten, the Sun had a brief resurgence during the Amarna Period when it again became the preeminent, if not only, divinity for the Pharaoh Akhenaton. The Sun is viewed as a goddess in Germanic paganism, Sól/Sunna, in ancient Roman culture, Sunday was the day of the Sun god. It was adopted as the Sabbath day by Christians who did not have a Jewish background, the symbol of light was a pagan device adopted by Christians, and perhaps the most important one that did not come from Jewish traditions
13.
Aphelion
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The perihelion is the point in the orbit of a celestial body where it is nearest to its orbital focus, generally a star. It is the opposite of aphelion, which is the point in the orbit where the body is farthest from its focus. The word perihelion stems from the Ancient Greek words peri, meaning around or surrounding, aphelion derives from the preposition apo, meaning away, off, apart. According to Keplers first law of motion, all planets, comets. Hence, a body has a closest and a farthest point from its parent object, that is, a perihelion. Each extreme is known as an apsis, orbital eccentricity measures the flatness of the orbit. Because of the distance at aphelion, only 93. 55% of the solar radiation from the Sun falls on a given area of land as does at perihelion. However, this fluctuation does not account for the seasons, as it is summer in the northern hemisphere when it is winter in the southern hemisphere and vice versa. Instead, seasons result from the tilt of Earths axis, which is 23.4 degrees away from perpendicular to the plane of Earths orbit around the sun. Winter falls on the hemisphere where sunlight strikes least directly, and summer falls where sunlight strikes most directly, in the northern hemisphere, summer occurs at the same time as aphelion. Despite this, there are larger land masses in the northern hemisphere, consequently, summers are 2.3 °C warmer in the northern hemisphere than in the southern hemisphere under similar conditions. Apsis Ellipse Solstice Dates and times of Earths perihelion and aphelion, 2000–2025 from the United States Naval Observatory
14.
Perihelion
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The perihelion is the point in the orbit of a celestial body where it is nearest to its orbital focus, generally a star. It is the opposite of aphelion, which is the point in the orbit where the body is farthest from its focus. The word perihelion stems from the Ancient Greek words peri, meaning around or surrounding, aphelion derives from the preposition apo, meaning away, off, apart. According to Keplers first law of motion, all planets, comets. Hence, a body has a closest and a farthest point from its parent object, that is, a perihelion. Each extreme is known as an apsis, orbital eccentricity measures the flatness of the orbit. Because of the distance at aphelion, only 93. 55% of the solar radiation from the Sun falls on a given area of land as does at perihelion. However, this fluctuation does not account for the seasons, as it is summer in the northern hemisphere when it is winter in the southern hemisphere and vice versa. Instead, seasons result from the tilt of Earths axis, which is 23.4 degrees away from perpendicular to the plane of Earths orbit around the sun. Winter falls on the hemisphere where sunlight strikes least directly, and summer falls where sunlight strikes most directly, in the northern hemisphere, summer occurs at the same time as aphelion. Despite this, there are larger land masses in the northern hemisphere, consequently, summers are 2.3 °C warmer in the northern hemisphere than in the southern hemisphere under similar conditions. Apsis Ellipse Solstice Dates and times of Earths perihelion and aphelion, 2000–2025 from the United States Naval Observatory
15.
Solar System
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The Solar System is the gravitationally bound system comprising the Sun and the objects that orbit it, either directly or indirectly. Of those objects that orbit the Sun directly, the largest eight are the planets, with the remainder being significantly smaller objects, such as dwarf planets, of the objects that orbit the Sun indirectly, the moons, two are larger than the smallest planet, Mercury. The Solar System formed 4.6 billion years ago from the collapse of a giant interstellar molecular cloud. The vast majority of the mass is in the Sun. The four smaller inner planets, Mercury, Venus, Earth and Mars, are terrestrial planets, being composed of rock. The four outer planets are giant planets, being more massive than the terrestrials. All planets have almost circular orbits that lie within a flat disc called the ecliptic. The Solar System also contains smaller objects, the asteroid belt, which lies between the orbits of Mars and Jupiter, mostly contains objects composed, like the terrestrial planets, of rock and metal. Beyond Neptunes orbit lie the Kuiper belt and scattered disc, which are populations of trans-Neptunian objects composed mostly of ices, within these populations are several dozen to possibly tens of thousands of objects large enough that they have been rounded by their own gravity. Such objects are categorized as dwarf planets, identified dwarf planets include the asteroid Ceres and the trans-Neptunian objects Pluto and Eris. In addition to two regions, various other small-body populations, including comets, centaurs and interplanetary dust clouds. Six of the planets, at least four of the dwarf planets, each of the outer planets is encircled by planetary rings of dust and other small objects. The solar wind, a stream of charged particles flowing outwards from the Sun, the heliopause is the point at which pressure from the solar wind is equal to the opposing pressure of the interstellar medium, it extends out to the edge of the scattered disc. The Oort cloud, which is thought to be the source for long-period comets, the Solar System is located in the Orion Arm,26,000 light-years from the center of the Milky Way. For most of history, humanity did not recognize or understand the concept of the Solar System, the invention of the telescope led to the discovery of further planets and moons. The principal component of the Solar System is the Sun, a G2 main-sequence star that contains 99. 86% of the known mass. The Suns four largest orbiting bodies, the giant planets, account for 99% of the mass, with Jupiter. The remaining objects of the Solar System together comprise less than 0. 002% of the Solar Systems total mass, most large objects in orbit around the Sun lie near the plane of Earths orbit, known as the ecliptic
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International Astronomical Union
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The International Astronomical Union is an international association of professional astronomers, at the PhD level and beyond, active in professional research and education in astronomy. Among other activities, it acts as the recognized authority for assigning designations to celestial bodies. The IAU is a member of the International Council for Science and its main objective is to promote and safeguard the science of astronomy in all its aspects through international cooperation. The IAU maintains friendly relations with organizations that include amateur astronomers in their membership, the IAU has its head office on the second floor of the Institut dAstrophysique de Paris in the 14th arrondissement of Paris. The IAU is also responsible for the system of astronomical telegrams which are produced and distributed on its behalf by the Central Bureau for Astronomical Telegrams, the Minor Planet Center also operates under the IAU, and is a clearinghouse for all non-planetary or non-moon bodies in the Solar System. The Working Group for Meteor Shower Nomenclature and the Meteor Data Center coordinate the nomenclature of meteor showers, the IAU was founded on July 28,1919, at the Constitutive Assembly of the International Research Council held in Brussels, Belgium. The 7 initial member states were Belgium, Canada, France, Great Britain, Greece, Japan, the first executive committee consisted of Benjamin Baillaud, Alfred Fowler, and four vice presidents, William Campbell, Frank Dyson, Georges Lecointe, and Annibale Riccò. Thirty-two Commissions were appointed at the Brussels meeting and focused on topics ranging from relativity to minor planets, the reports of these 32 Commissions formed the main substance of the first General Assembly, which took place in Rome, Italy, May 2–10,1922. By the end of the first General Assembly, ten nations had joined the Union. Although the Union was officially formed eight months after the end of World War I, the first 50 years of the Unions history are well documented. Subsequent history is recorded in the form of reminiscences of past IAU Presidents, twelve of the fourteen past General Secretaries in the period 1964-2006 contributed their recollections of the Unions history in IAU Information Bulletin No.100. Six past IAU Presidents in the period 1976–2003 also contributed their recollections in IAU Information Bulletin No.104, the IAU includes a total of 12,664 individual members who are professional astronomers from 96 countries worldwide. 83% of all members are male, while 17% are female, among them the unions current president. Membership also includes 79 national members, professional astronomical communities representing their countrys affiliation with the IAU, the sovereign body of the IAU is its General Assembly, which comprises all members. The Assembly determines IAU policy, approves the Statutes and By-Laws of the Union, the right to vote on matters brought before the Assembly varies according to the type of business under discussion. On budget matters, votes are weighted according to the subscription levels of the national members. A second category vote requires a turnout of at least two-thirds of national members in order to be valid, an absolute majority is sufficient for approval in any vote, except for Statute revision which requires a two-thirds majority. An equality of votes is resolved by the vote of the President of the Union, since 1922, the IAU General Assembly meets every three years, with the exception of the period between 1938 and 1948, due to World War II
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International Bureau of Weights and Measures
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The organisation is usually referred to by its French initialism, BIPM. The BIPM reports to the International Committee for Weights and Measures and these organizations are also commonly referred to by their French initialisms. The BIPM was created on 20 May 1875, following the signing of the Metre Convention, under the authority of the Metric Convention, the BIPM helps to ensure uniformity of SI weights and measures around the world. It does so through a series of committees, whose members are the national metrology laboratories of the Conventions member states. The BIPM carries out measurement-related research and it takes part in and organises international comparisons of national measurement standards and performs calibrations for member states. The BIPM has an important role in maintaining accurate worldwide time of day and it combines, analyses, and averages the official atomic time standards of member nations around the world to create a single, official Coordinated Universal Time. The BIPM is also the keeper of the prototype of the kilogram. Metrologia Institute for Reference Materials and Measurements International Organization for Standardization National Institute of Standards and Technology Official website
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Earth's orbit
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Earths orbit is the path through which the Earth travels around the Sun. The average distance between the Earth and the Sun is 149.60 million kilometers, and a complete orbit occurs every 365.256 days, Earths orbit has an eccentricity of 0.0167. Earths orbital motion gives an apparent movement of the Sun with respect to other stars at a rate of about 1° per day eastward as seen from Earth. Earths orbital speed averages about 30 km/s, which is fast enough to cover the planets diameter in seven minutes, viewed from a vantage point above the north poles of both the Sun and the Earth, the Earth would appear to revolve in a counterclockwise direction about the Sun. From the same point, both the Earth and the Sun would appear to rotate in a counterclockwise direction about their respective axes. Heliocentrism is the model that first placed the Sun at the center of the Solar System and put the planets, including Earth. Historically, heliocentrism is opposed to geocentrism, which placed the Earth at the center, aristarchus of Samos already proposed a heliocentric model in the 3rd century BC. This Copernican revolution resolved the issue of planetary motion by arguing that such motion was only perceived. Although Copernicuss groundbreaking book. had been over a century earlier, because of Earths axial tilt, the inclination of the Suns trajectory in the sky varies over the course of the year. For an observer at a northern latitude, when the pole is tilted toward the Sun the day lasts longer. This results in average temperatures, as additional solar radiation reaches the surface. When the north pole is tilted away from the Sun, the reverse is true, above the Arctic Circle and below the Antarctic Circle, an extreme case is reached in which there is no daylight at all for part of the year. This is called a polar night and this variation in the weather results in the seasons. The solstices and equinoxes divide the year up into four equal parts. In the northern winter solstice occurs on or about December 21, summer solstice is near June 21, spring equinox is around March 20. In modern times, Earths perihelion occurs around January 3, the changing Earth–Sun distance results in an increase of about 6. 9% in total solar energy reaching the Earth at perihelion relative to aphelion. The Hill sphere of the Earth is about 1,500,000 kilometers in radius and this is the maximal distance at which the Earths gravitational influence is stronger than the more distant Sun and planets. Objects orbiting the Earth must be within this radius, otherwise they can become unbound by the perturbation of the Sun
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Ellipse
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In mathematics, an ellipse is a curve in a plane surrounding two focal points such that the sum of the distances to the two focal points is constant for every point on the curve. As such, it is a generalization of a circle, which is a type of an ellipse having both focal points at the same location. The shape of an ellipse is represented by its eccentricity, which for an ellipse can be any number from 0 to arbitrarily close to, ellipses are the closed type of conic section, a plane curve resulting from the intersection of a cone by a plane. Ellipses have many similarities with the two forms of conic sections, parabolas and hyperbolas, both of which are open and unbounded. The cross section of a cylinder is an ellipse, unless the section is parallel to the axis of the cylinder and this ratio is called the eccentricity of the ellipse. Ellipses are common in physics, astronomy and engineering, for example, the orbit of each planet in our solar system is approximately an ellipse with the barycenter of the planet–Sun pair at one of the focal points. The same is true for moons orbiting planets and all other systems having two astronomical bodies, the shapes of planets and stars are often well described by ellipsoids. It is also the simplest Lissajous figure formed when the horizontal and vertical motions are sinusoids with the same frequency, a similar effect leads to elliptical polarization of light in optics. The name, ἔλλειψις, was given by Apollonius of Perga in his Conics, in order to omit the special case of a line segment, one presumes 2 a > | F1 F2 |, E =. The midpoint C of the segment joining the foci is called the center of the ellipse. The line through the foci is called the major axis and it contains the vertices V1, V2, which have distance a to the center. The distance c of the foci to the center is called the distance or linear eccentricity. The quotient c a is the eccentricity e, the case F1 = F2 yields a circle and is included. C2 is called the circle of the ellipse. This property should not be confused with the definition of an ellipse with help of a directrix below, for an arbitrary point the distance to the focus is 2 + y 2 and to the second focus 2 + y 2. Hence the point is on the ellipse if the condition is fulfilled 2 + y 2 +2 + y 2 =2 a. The shape parameters a, b are called the major axis. The points V3 =, V4 = are the co-vertices and it follows from the equation that the ellipse is symmetric with respect to both of the coordinate axes and hence symmetric with respect to the origin
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Semi-major axis
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In geometry, the major axis of an ellipse is its longest diameter, a line segment that runs through the center and both foci, with ends at the widest points of the perimeter. The semi-major axis is one half of the axis, and thus runs from the centre, through a focus. Essentially, it is the radius of an orbit at the two most distant points. For the special case of a circle, the axis is the radius. One can think of the axis as an ellipses long radius. The semi-major axis of a hyperbola is, depending on the convention, thus it is the distance from the center to either vertex of the hyperbola. A parabola can be obtained as the limit of a sequence of ellipses where one focus is fixed as the other is allowed to move arbitrarily far away in one direction. Thus a and b tend to infinity, a faster than b, the semi-minor axis is a line segment associated with most conic sections that is at right angles with the semi-major axis and has one end at the center of the conic section. It is one of the axes of symmetry for the curve, in an ellipse, the one, in a hyperbola. The semi-major axis is the value of the maximum and minimum distances r max and r min of the ellipse from a focus — that is. In astronomy these extreme points are called apsis, the semi-minor axis of an ellipse is the geometric mean of these distances, b = r max r min. The eccentricity of an ellipse is defined as e =1 − b 2 a 2 so r min = a, r max = a. Now consider the equation in polar coordinates, with one focus at the origin, the mean value of r = ℓ / and r = ℓ /, for θ = π and θ =0 is a = ℓ1 − e 2. In an ellipse, the axis is the geometric mean of the distance from the center to either focus. The semi-minor axis of an ellipse runs from the center of the ellipse to the edge of the ellipse, the semi-minor axis is half of the minor axis. The minor axis is the longest line segment perpendicular to the axis that connects two points on the ellipses edge. The semi-minor axis b is related to the axis a through the eccentricity e. A parabola can be obtained as the limit of a sequence of ellipses where one focus is fixed as the other is allowed to move arbitrarily far away in one direction
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Elliptic orbit
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In astrodynamics or celestial mechanics an elliptic orbit is a Kepler orbit with the eccentricity less than 1, this includes the special case of a circular orbit, with eccentricity equal to zero. In a stricter sense, it is a Kepler orbit with the eccentricity greater than 0, in a wider sense it is a Kepler orbit with negative energy. This includes the radial elliptic orbit, with eccentricity equal to 1, in a gravitational two-body problem with negative energy both bodies follow similar elliptic orbits with the same orbital period around their common barycenter. Also the relative position of one body with respect to the other follows an elliptic orbit, examples of elliptic orbits include, Hohmann transfer orbit, Molniya orbit and tundra orbit. A is the length of the semi-major axis, the velocity equation for a hyperbolic trajectory has either +1 a, or it is the same with the convention that in that case a is negative. Conclusions, For a given semi-major axis the orbital energy is independent of the eccentricity. ν is the true anomaly. The angular momentum is related to the cross product of position and velocity. Here ϕ is defined as the angle which differs by 90 degrees from this and this set of six variables, together with time, are called the orbital state vectors. Given the masses of the two bodies they determine the full orbit, the two most general cases with these 6 degrees of freedom are the elliptic and the hyperbolic orbit. Special cases with fewer degrees of freedom are the circular and parabolic orbit, another set of six parameters that are commonly used are the orbital elements. In the Solar System, planets, asteroids, most comets, the following chart of the perihelion and aphelion of the planets, dwarf planets and Halleys Comet demonstrates the variation of the eccentricity of their elliptical orbits. For similar distances from the sun, wider bars denote greater eccentricity, note the almost-zero eccentricity of Earth and Venus compared to the enormous eccentricity of Halleys Comet and Eris. A radial trajectory can be a line segment, which is a degenerate ellipse with semi-minor axis =0. Although the eccentricity is 1, this is not a parabolic orbit, most properties and formulas of elliptic orbits apply. However, the orbit cannot be closed and it is an open orbit corresponding to the part of the degenerate ellipse from the moment the bodies touch each other and move away from each other until they touch each other again. In the case of point masses one full orbit is possible, the velocities at the start and end are infinite in opposite directions and the potential energy is equal to minus infinity. The radial elliptic trajectory is the solution of a problem with at some instant zero speed
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Line segment
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In geometry, a line segment is a part of a line that is bounded by two distinct end points, and contains every point on the line between its endpoints. A closed line segment includes both endpoints, while a line segment excludes both endpoints, a half-open line segment includes exactly one of the endpoints. Examples of line include the sides of a triangle or square. More generally, when both of the end points are vertices of a polygon or polyhedron, the line segment is either an edge if they are adjacent vertices. When the end points both lie on a such as a circle, a line segment is called a chord. Sometimes one needs to distinguish between open and closed line segments, thus, the line segment can be expressed as a convex combination of the segments two end points. In geometry, it is defined that a point B is between two other points A and C, if the distance AB added to the distance BC is equal to the distance AC. Thus in R2 the line segment with endpoints A = and C = is the collection of points. A line segment is a connected, non-empty set, if V is a topological vector space, then a closed line segment is a closed set in V. However, an open line segment is an open set in V if and only if V is one-dimensional. More generally than above, the concept of a segment can be defined in an ordered geometry. A pair of segments can be any one of the following, intersecting, parallel, skew. The last possibility is a way that line segments differ from lines, in an axiomatic treatment of geometry, the notion of betweenness is either assumed to satisfy a certain number of axioms, or else be defined in terms of an isometry of a line. Segments play an important role in other theories, for example, a set is convex if the segment that joins any two points of the set is contained in the set. This is important because it transforms some of the analysis of sets to the analysis of a line segment. The Segment Addition Postulate can be used to add congruent segment or segments with equal lengths and consequently substitute other segments into another statement to make segments congruent. A line segment can be viewed as a case of an ellipse in which the semiminor axis goes to zero, the foci go to the endpoints. A complete orbit of this ellipse traverses the line segment twice, as a degenerate orbit this is a radial elliptic trajectory. In addition to appearing as the edges and diagonals of polygons and polyhedra, some very frequently considered segments in a triangle include the three altitudes, the three medians, the perpendicular bisectors of the sides, and the internal angle bisectors
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Perihelion and aphelion
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The perihelion is the point in the orbit of a celestial body where it is nearest to its orbital focus, generally a star. It is the opposite of aphelion, which is the point in the orbit where the body is farthest from its focus. The word perihelion stems from the Ancient Greek words peri, meaning around or surrounding, aphelion derives from the preposition apo, meaning away, off, apart. According to Keplers first law of motion, all planets, comets. Hence, a body has a closest and a farthest point from its parent object, that is, a perihelion. Each extreme is known as an apsis, orbital eccentricity measures the flatness of the orbit. Because of the distance at aphelion, only 93. 55% of the solar radiation from the Sun falls on a given area of land as does at perihelion. However, this fluctuation does not account for the seasons, as it is summer in the northern hemisphere when it is winter in the southern hemisphere and vice versa. Instead, seasons result from the tilt of Earths axis, which is 23.4 degrees away from perpendicular to the plane of Earths orbit around the sun. Winter falls on the hemisphere where sunlight strikes least directly, and summer falls where sunlight strikes most directly, in the northern hemisphere, summer occurs at the same time as aphelion. Despite this, there are larger land masses in the northern hemisphere, consequently, summers are 2.3 °C warmer in the northern hemisphere than in the southern hemisphere under similar conditions. Apsis Ellipse Solstice Dates and times of Earths perihelion and aphelion, 2000–2025 from the United States Naval Observatory
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Parallax
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The term is derived from the Greek word παράλλαξις, meaning alternation. Due to foreshortening, nearby objects have a larger parallax than more distant objects when observed from different positions, astronomers use the principle of parallax to measure distances to the closer stars. Here, the parallax is the semi-angle of inclination between two sight-lines to the star, as observed when the Earth is on opposite sides of the Sun in its orbit. Parallax also affects optical instruments such as rifle scopes, binoculars, microscopes, many animals, including humans, have two eyes with overlapping visual fields that use parallax to gain depth perception, this process is known as stereopsis. In computer vision the effect is used for stereo vision, and there is a device called a parallax rangefinder that uses it to find range. A simple everyday example of parallax can be seen in the dashboard of motor vehicles that use a needle-style speedometer gauge. When viewed from directly in front, the speed may show exactly 60, as the eyes of humans and other animals are in different positions on the head, they present different views simultaneously. This is the basis of stereopsis, the process by which the brain exploits the parallax due to the different views from the eye to gain depth perception, animals also use motion parallax, in which the animals move to gain different viewpoints. For example, pigeons bob their heads up and down to see depth, the motion parallax is exploited also in wiggle stereoscopy, computer graphics which provide depth cues through viewpoint-shifting animation rather than through binocular vision. Parallax arises due to change in viewpoint occurring due to motion of the observer, of the observed, what is essential is relative motion. By observing parallax, measuring angles, and using geometry, one can determine distance, astronomers also use the word parallax as a synonym for distance measurent by other methods, see parallax #Astronomy. In a geostatic model, the movement of the star would have to be taken as real with the star oscillating across the sky with respect to the background stars, the parsec is defined as the distance for which the annual parallax is 1 arcsecond. Annual parallax is measured by observing the position of a star at different times of the year as the 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. Stellar parallax remains the standard for calibrating other measurement methods, accurate calculations of distance based on stellar parallax require a measurement of the distance from the Earth to the Sun, now based on radar reflection off the surfaces of planets. 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, the fact that stellar parallax was so small that it was unobservable at the time was used as the main scientific argument against heliocentrism during the early modern age. In 1989, the satellite Hipparcos was launched primarily for obtaining improved parallaxes and proper motions for over 100,000 nearby stars, increasing the reach of the method tenfold
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Albert Einstein
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Albert Einstein was a German-born theoretical physicist. He developed the theory of relativity, one of the two pillars of modern physics, Einsteins work is also known for its influence on the philosophy of science. Einstein is best known in popular culture for his mass–energy equivalence formula E = mc2, near the beginning of his career, Einstein thought that Newtonian mechanics was no longer enough to reconcile the laws of classical mechanics with the laws of the electromagnetic field. This led him to develop his theory of relativity during his time at the Swiss Patent Office in Bern. Briefly before, he aquired the Swiss citizenship in 1901, which he kept for his whole life and he continued to deal with problems of statistical mechanics and quantum theory, which led to his explanations of particle theory and the motion of molecules. He also investigated the properties of light which laid the foundation of the photon theory of light. In 1917, Einstein applied the theory of relativity to model the large-scale structure of the universe. He was visiting the United States when Adolf Hitler came to power in 1933 and, being Jewish, did not go back to Germany and he settled in the United States, becoming an American citizen in 1940. This eventually led to what would become the Manhattan Project, Einstein supported defending the Allied forces, but generally denounced the idea of using the newly discovered nuclear fission as a weapon. Later, with the British philosopher Bertrand Russell, Einstein signed the Russell–Einstein Manifesto, Einstein was affiliated with the Institute for Advanced Study in Princeton, New Jersey, until his death in 1955. Einstein published more than 300 scientific papers along with over 150 non-scientific works, on 5 December 2014, universities and archives announced the release of Einsteins papers, comprising more than 30,000 unique documents. Einsteins intellectual achievements and originality have made the word Einstein synonymous with genius, Albert Einstein was born in Ulm, in the Kingdom of Württemberg in the German Empire, on 14 March 1879. His parents were Hermann Einstein, a salesman and engineer, the Einsteins were non-observant Ashkenazi Jews, and Albert attended a Catholic elementary school in Munich from the age of 5 for three years. At the age of 8, he was transferred to the Luitpold Gymnasium, the loss forced the sale of the Munich factory. In search of business, the Einstein family moved to Italy, first to Milan, when the family moved to Pavia, Einstein stayed in Munich to finish his studies at the Luitpold Gymnasium. His father intended for him to electrical engineering, but Einstein clashed with authorities and resented the schools regimen. He later wrote that the spirit of learning and creative thought was lost in strict rote learning, at the end of December 1894, he travelled to Italy to join his family in Pavia, convincing the school to let him go by using a doctors note. During his time in Italy he wrote an essay with the title On the Investigation of the State of the Ether in a Magnetic Field
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Theory of relativity
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The theory of relativity usually encompasses two interrelated theories by Albert Einstein, special relativity and general relativity. Special relativity applies to particles and their interactions, describing all their physical phenomena except gravity. General relativity explains the law of gravitation and its relation to other forces of nature and it applies to the cosmological and astrophysical realm, including astronomy. The theory transformed theoretical physics and astronomy during the 20th century and it introduced concepts including spacetime as a unified entity of space and time, relativity of simultaneity, kinematic and gravitational time dilation, and length contraction. In the field of physics, relativity improved the science of elementary particles and their fundamental interactions, with relativity, cosmology and astrophysics predicted extraordinary astronomical phenomena such as neutron stars, black holes, and gravitational waves. Max Planck, Hermann Minkowski and others did subsequent work, Einstein developed general relativity between 1907 and 1915, with contributions by many others after 1915. The final form of general relativity was published in 1916, the term theory of relativity was based on the expression relative theory used in 1906 by Planck, who emphasized how the theory uses the principle of relativity. In the discussion section of the paper, Alfred Bucherer used for the first time the expression theory of relativity. By the 1920s, the community understood and accepted special relativity. It rapidly became a significant and necessary tool for theorists and experimentalists in the new fields of physics, nuclear physics. By comparison, general relativity did not appear to be as useful and it seemed to offer little potential for experimental test, as most of its assertions were on an astronomical scale. Its mathematics of general relativity seemed difficult and fully understandable only by a number of people. Around 1960, general relativity became central to physics and astronomy, new mathematical techniques to apply to general relativity streamlined calculations and made its concepts more easily visualized. Special relativity is a theory of the structure of spacetime and it was introduced in Einsteins 1905 paper On the Electrodynamics of Moving Bodies. Special relativity is based on two postulates which are contradictory in classical mechanics, The laws of physics are the same for all observers in motion relative to one another. The speed of light in a vacuum is the same for all observers, the resultant theory copes with experiment better than classical mechanics. For instance, postulate 2 explains the results of the Michelson–Morley experiment, moreover, the theory has many surprising and counterintuitive consequences. Some of these are, Relativity of simultaneity, Two events, simultaneous for one observer, time dilation, Moving clocks are measured to tick more slowly than an observers stationary clock
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Ephemeris
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In astronomy and celestial navigation, an ephemeris gives the positions of naturally occurring astronomical objects as well as artificial satellites in the sky at a given time or times. Historically, positions were given as printed tables of values, given at intervals of date. Modern ephemerides are often computed electronically from mathematical models of the motion of astronomical objects, the astronomical position calculated from an ephemeris is given in the spherical polar coordinate system of right ascension and declination. Ephemerides are used in navigation and astronomy. They are also used by some astrologers, 1st millennium BC — Ephemerides in Babylonian astronomy. 13th century — the Zīj-i Īlkhānī were compiled at the Maragheh observatory in Persia, 13th century — the Alfonsine Tables were compiled in Spain to correct anomalies in the Tables of Toledo, remaining the standard European ephemeris until the Prutenic Tables almost 300 years later. 1531 — Work of Johannes Stöffler is published posthumously at Tübingen,1551 — the Prutenic Tables of Erasmus Reinhold were published, based on Copernicuss theories. 1554 — Johannes Stadius published Ephemerides novae et auctae, the first major ephemeris computed according to Copernicus heliocentric model, one of the users of Stadiuss tables is Tycho Brahe. 1627 — the Rudolphine Tables of Johannes Kepler based on elliptical planetary motion became the new standard. 1679 — La Connaissance des Temps ou calendrier et éphémérides du lever & coucher du Soleil, de la Lune & des autres planètes, first published yearly by Jean Picard and still extent. According to Gingerich, the patterns are as distinctive as fingerprints. Typically, such ephemerides cover several centuries, past and future, nevertheless, there are secular phenomena which cannot adequately be considered by ephemerides. The greatest uncertainties in the positions of planets are caused by the perturbations of asteroids, most of whose masses and orbits are poorly known. Reflecting the continuing influx of new data and observations, NASAs Jet Propulsion Laboratory has revised its published ephemerides nearly every year for the past 20 years. Solar system ephemerides are essential for the navigation of spacecraft and for all kinds of observations of the planets, their natural satellites, stars. The equinox of the system must be given. It is, in all cases, either the actual equinox, or that of one of the standard equinoxes, typically J2000.0, B1950.0. Star maps almost always use one of the standard equinoxes, Ephemerides of the planet Saturn also sometimes contain the apparent inclination of its ring
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NASA
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President Dwight D. Eisenhower established NASA in 1958 with a distinctly civilian orientation encouraging peaceful applications in space science. The National Aeronautics and Space Act was passed on July 29,1958, disestablishing NASAs predecessor, the new agency became operational on October 1,1958. Since that time, most US space exploration efforts have led by NASA, including the Apollo Moon landing missions, the Skylab space station. Currently, NASA is supporting the International Space Station and is overseeing the development of the Orion Multi-Purpose Crew Vehicle, the agency is also responsible for the Launch Services Program which provides oversight of launch operations and countdown management for unmanned NASA launches. NASA shares data with various national and international such as from the Greenhouse Gases Observing Satellite. Since 2011, NASA has been criticized for low cost efficiency, from 1946, the National Advisory Committee for Aeronautics had been experimenting with rocket planes such as the supersonic Bell X-1. In the early 1950s, there was challenge to launch a satellite for the International Geophysical Year. An effort for this was the American Project Vanguard, after the Soviet launch of the worlds first artificial satellite on October 4,1957, the attention of the United States turned toward its own fledgling space efforts. This led to an agreement that a new federal agency based on NACA was needed to conduct all non-military activity in space. The Advanced Research Projects Agency was created in February 1958 to develop technology for military application. On July 29,1958, Eisenhower signed the National Aeronautics and Space Act, a NASA seal was approved by President Eisenhower in 1959. Elements of the Army Ballistic Missile Agency and the United States Naval Research Laboratory were incorporated into NASA, earlier research efforts within the US Air Force and many of ARPAs early space programs were also transferred to NASA. In December 1958, NASA gained control of the Jet Propulsion Laboratory, NASA has conducted many manned and unmanned spaceflight programs throughout its history. Some missions include both manned and unmanned aspects, such as the Galileo probe, which was deployed by astronauts in Earth orbit before being sent unmanned to Jupiter, the experimental rocket-powered aircraft programs started by NACA were extended by NASA as support for manned spaceflight. This was followed by a space capsule program, and in turn by a two-man capsule program. This goal was met in 1969 by the Apollo program, however, reduction of the perceived threat and changing political priorities almost immediately caused the termination of most of these plans. NASA turned its attention to an Apollo-derived temporary space laboratory, to date, NASA has launched a total of 166 manned space missions on rockets, and thirteen X-15 rocket flights above the USAF definition of spaceflight altitude,260,000 feet. The X-15 was an NACA experimental rocket-powered hypersonic research aircraft, developed in conjunction with the US Air Force, the design featured a slender fuselage with fairings along the side containing fuel and early computerized control systems
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Jet Propulsion Laboratory
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The Jet Propulsion Laboratory is a federally funded research and development center and NASA field center in La Cañada Flintridge, California and Pasadena, California, United States. The JPL is managed by the nearby California Institute of Technology for NASA, the laboratorys primary function is the construction and operation of planetary robotic spacecraft, though it also conducts Earth-orbit and astronomy missions. It is also responsible for operating NASAs Deep Space Network and they are also responsible for managing the JPL Small-Body Database, and provides physical data and lists of publications for all known small Solar System bodies. The JPLs Space Flight Operations Facility and Twenty-Five-Foot Space Simulator are designated National Historic Landmarks, JPL traces its beginnings to 1936 in the Guggenheim Aeronautical Laboratory at the California Institute of Technology when the first set of rocket experiments were carried out in the Arroyo Seco. Malinas thesis advisor was engineer/aerodynamicist Theodore von Kármán, who arranged for U. S. Army financial support for this GALCIT Rocket Project in 1939. In 1941, Malina, Parsons, Forman, Martin Summerfield, in 1943, von Kármán, Malina, Parsons, and Forman established the Aerojet Corporation to manufacture JATO motors. The project took on the name Jet Propulsion Laboratory in November 1943, during JPLs Army years, the laboratory developed two deployed weapon systems, the MGM-5 Corporal and MGM-29 Sergeant intermediate range ballistic missiles. These missiles were the first US ballistic missiles developed at JPL and it also developed a number of other weapons system prototypes, such as the Loki anti-aircraft missile system, and the forerunner of the Aerobee sounding rocket. At various times, it carried out testing at the White Sands Proving Ground, Edwards Air Force Base. A lunar lander was developed in 1938-39 which influenced design of the Apollo Lunar Module in the 1960s. The team lost that proposal to Project Vanguard, and instead embarked on a project to demonstrate ablative re-entry technology using a Jupiter-C rocket. They carried out three successful flights in 1956 and 1957. Using a spare Juno I, the two organizations then launched the United States first satellite, Explorer 1, on February 1,1958, JPL was transferred to NASA in December 1958, becoming the agencys primary planetary spacecraft center. JPL engineers designed and operated Ranger and Surveyor missions to the Moon that prepared the way for Apollo, JPL also led the way in interplanetary exploration with the Mariner missions to Venus, Mars, and Mercury. In 1998, JPL opened the Near-Earth Object Program Office for NASA, as of 2013, it has found 95% of asteroids that are a kilometer or more in diameter that cross Earths orbit. JPL was early to employ women mathematicians, in the 1940s and 1950s, using mechanical calculators, women in an all-female computations group performed trajectory calculations. In 1961, JPL hired Dana Ulery as their first woman engineer to work alongside male engineers as part of the Ranger and Mariner mission tracking teams, when founded, JPLs site was a rocky flood-plain just outside the city limits of Pasadena. Almost all of the 177 acres of the U. S, the city of La Cañada Flintridge, California was incorporated in 1976, well after JPL attained international recognition with a Pasadena address
30.
Standard gravitational parameter
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In celestial mechanics, the standard gravitational parameter μ of a celestial body is the product of the gravitational constant G and the mass M of the body. μ = G M For several objects in the Solar System, the SI units of the standard gravitational parameter are m3 s−2. However, units of km3 s−2 are frequently used in the scientific literature, the central body in an orbital system can be defined as the one whose mass is much larger than the mass of the orbiting body, or M ≫ m. This approximation is standard for planets orbiting the Sun or most moons, conversely, measurements of the smaller bodys orbit only provide information on the product, μ, not G and M separately. This can be generalized for elliptic orbits, μ =4 π2 a 3 / T2 where a is the semi-major axis, for parabolic trajectories rv2 is constant and equal to 2μ. For elliptic and hyperbolic orbits μ = 2a| ε |, where ε is the orbital energy. The value for the Earth is called the gravitational constant. However, the M can be out only by dividing the MG by G. The uncertainty of those measures is 1 to 7000, so M will have the same uncertainty, the value for the Sun is called the heliocentric gravitational constant or geopotential of the Sun and equals 1. 32712440018×1020 m3 s−2. Note that the mass is also denoted by μ. Astronomical system of units Planetary mass
31.
Space probe
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A space probe is a robotic spacecraft that does not orbit the Earth, but, instead, explores further into outer space. A space probe may approach the Moon, travel through space, flyby, orbit, or land on other planetary bodies. Approximately fifteen missions are currently operational, once a probe has left the vicinity of Earth, its trajectory will likely take it along an orbit around the Sun similar to the Earths orbit. To reach another planet, the simplest practical method is a Hohmann transfer orbit, more complex techniques, such as gravitational slingshots, can be more fuel-efficient, though they may require the probe to spend more time in transit. Some high Delta-V missions can only be performed, within the limits of modern propulsion, a technique using very little propulsion, but requiring a considerable amount of time, is to follow a trajectory on the Interplanetary Transport Network. First man-made object to land on the Moon, or any other extra terrestrial surface. First mission to photograph the far side of the Moon, launched in 1959, first robotic sample return probe from the Moon. It was sent to the Moon on November 10,1970, first successful in-place analysis of another planet. It may have also been the first space probe to impact the surface of another planet, the Venera 7 probe was the first spacecraft to successfully soft land on another planet and to transmit data from there back to Earth. Upon its arrival at Mars on November 13,1971, Mariner 9 became the first space probe to orbit around another planet. Although, the spacecraft failed shortly after landing, the Mars Exploration Rovers, Spirit and Opportunity surface and geology, and searched for clues to past water activity on Mars. They were each launched in 2003 and landed in 2004, communication with Spirit stopped on sol 2210. JPL continued to attempt to regain contact until May 24,2011, Opportunity arrived at Endeavour crater on 9 August 2011, at a landmark called Spirit Point named after its rover twin, after traversing 13 miles from Victoria crater, over a three-year period. As of January 26,2016, Opportunity has lasted for more than twelve years on Mars — although the rovers were intended to last only three months. The first dedicated missions to a comet, in this case and they dropped landers and balloons at Venus before their rendezvous with Halleys Comet. This Japanese probe was the first non-US, non-Soviet interplanetary probe, a second Japanese probe, it made ultraviolet wavelength observations of the comet. The first space probe to penetrate a comets coma and take images of its nucleus. First solar wind sample return probe from sun-earth L1, first sample return probe from a comet tail
32.
Radar
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Radar is an object-detection system that uses radio waves to determine the range, angle, or velocity of objects. It can be used to detect aircraft, ships, spacecraft, guided missiles, motor vehicles, weather formations, Radio waves from the transmitter reflect off the object and return to the receiver, giving information about the objects location and speed. Radar was developed secretly for military use by several nations in the period before, the term RADAR was coined in 1940 by the United States Navy as an acronym for RAdio Detection And Ranging or RAdio Direction And Ranging. The term radar has since entered English and other languages as a common noun, high tech radar systems are associated with digital signal processing, machine learning and are capable of extracting useful information from very high noise levels. Other systems similar to make use of other parts of the electromagnetic spectrum. One example is lidar, which uses ultraviolet, visible, or near infrared light from lasers rather than radio waves, as early as 1886, German physicist Heinrich Hertz showed that radio waves could be reflected from solid objects. In 1895, Alexander Popov, an instructor at the Imperial Russian Navy school in Kronstadt. The next year, he added a spark-gap transmitter, in 1897, while testing this equipment for communicating between two ships in the Baltic Sea, he took note of an interference beat caused by the passage of a third vessel. In his report, Popov wrote that this phenomenon might be used for detecting objects, the German inventor Christian Hülsmeyer was the first to use radio waves to detect the presence of distant metallic objects. In 1904, he demonstrated the feasibility of detecting a ship in dense fog and he obtained a patent for his detection device in April 1904 and later a patent for a related amendment for estimating the distance to the ship. He also got a British patent on September 23,1904 for a radar system. It operated on a 50 cm wavelength and the radar signal was created via a spark-gap. In 1915, Robert Watson-Watt used radio technology to advance warning to airmen. Watson-Watt became an expert on the use of direction finding as part of his lightning experiments. As part of ongoing experiments, he asked the new boy, Arnold Frederic Wilkins, Wilkins made an extensive study of available units before selecting a receiver model from the General Post Office. Its instruction manual noted that there was fading when aircraft flew by, in 1922, A. Hoyt Taylor and Leo C. Taylor submitted a report, suggesting that this might be used to detect the presence of ships in low visibility, eight years later, Lawrence A. Australia, Canada, New Zealand, and South Africa followed prewar Great Britain, and Hungary had similar developments during the war. Hugon, began developing a radio apparatus, a part of which was installed on the liner Normandie in 1935
33.
Telemetry
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Telemetry is an automated communications process by which measurements and other data are collected at remote or inaccessible points and transmitted to receiving equipment for monitoring. The word is derived from Greek roots, tele = remote, systems that need external instructions and data to operate require the counterpart of telemetry, telecommand. Many modern telemetry systems take advantage of the low cost and ubiquity of GSM networks by using SMS to receive, a telemeter is a device used to remotely measure any quantity. It consists of a sensor, a path, and a display, recording. Telemeters are the devices used in telemetry. Electronic devices are used in telemetry and can be wireless or hard-wired. Other technologies are possible, such as mechanical, hydraulic. Telemetry may be commutated to allow the transmission of data streams in a fixed frame. Telemetering information over wire had its origins in the 19th century, One of the first data-transmission circuits was developed in 1845 between the Russian Tsars Winter Palace and army headquarters. In 1874, French engineers built a system of weather and snow-depth sensors on Mont Blanc that transmitted real-time information to Paris, in 1901 the American inventor C. Michalke patented the selsyn, a circuit for sending synchronized rotation information over a distance, in 1906 a set of seismic stations were built with telemetering to the Pulkovo Observatory in Russia. In 1912, Commonwealth Edison developed a system of telemetry to monitor electrical loads on its power grid, the Panama Canal used extensive telemetry systems to monitor locks and water levels. Wireless telemetry made early appearances in the radiosonde, developed concurrently in 1930 by Robert Bureau in France, mochanovs system modulated temperature and pressure measurements by converting them to wireless Morse code. In the US and the USSR, the Messina system was replaced with better systems. Early Soviet missile and space telemetry systems which were developed in the late 1940s used either pulse-position modulation or pulse-duration modulation, in the United States, early work employed similar systems, but were later replaced by pulse-code modulation. Later Soviet interplanetary probes used redundant radio systems, transmitting telemetry by PCM on a decimeter band, telemetry has been used by weather balloons for transmitting meteorological data since 1920. Telemetry is used to transmit drilling mechanics and formation evaluation information uphole, in real time and these services are known as Measurement while drilling and Logging while drilling. Information acquired thousands of feet below ground, while drilling, is sent through the hole to the surface sensors
34.
Photons
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A photon is an elementary particle, the quantum of the electromagnetic field including electromagnetic radiation such as light, and the force carrier for the electromagnetic force. The photon has zero rest mass and is moving at the speed of light. Like all elementary particles, photons are currently best explained by quantum mechanics and exhibit wave–particle duality, exhibiting properties of both waves and particles. For example, a photon may be refracted by a lens and exhibit wave interference with itself. The quanta in a light wave cannot be spatially localized, some defined physical parameters of a photon are listed. The modern concept of the photon was developed gradually by Albert Einstein in the early 20th century to explain experimental observations that did not fit the classical model of light. The benefit of the model was that it accounted for the frequency dependence of lights energy. The photon model accounted for observations, including the properties of black-body radiation. In that model, light was described by Maxwells equations, in 1926 the optical physicist Frithiof Wolfers and the chemist Gilbert N. Lewis coined the name photon for these particles. After Arthur H. Compton won the Nobel Prize in 1927 for his studies, most scientists accepted that light quanta have an independent existence. In the Standard Model of particle physics, photons and other particles are described as a necessary consequence of physical laws having a certain symmetry at every point in spacetime. The intrinsic properties of particles, such as charge, mass and it has been applied to photochemistry, high-resolution microscopy, and measurements of molecular distances. Recently, photons have been studied as elements of quantum computers, in 1900, the German physicist Max Planck was studying black-body radiation and suggested that the energy carried by electromagnetic waves could only be released in packets of energy. In his 1901 article in Annalen der Physik he called these packets energy elements, the word quanta was used before 1900 to mean particles or amounts of different quantities, including electricity. In 1905, Albert Einstein suggested that waves could only exist as discrete wave-packets. He called such a wave-packet the light quantum, the name photon derives from the Greek word for light, φῶς. Arthur Compton used photon in 1928, referring to Gilbert N. Lewis, the name was suggested initially as a unit related to the illumination of the eye and the resulting sensation of light and was used later in a physiological context. Although Wolferss and Lewiss theories were contradicted by many experiments and never accepted, in physics, a photon is usually denoted by the symbol γ
35.
Speed of light
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The speed of light in vacuum, commonly denoted c, is a universal physical constant important in many areas of physics. Its exact value is 299792458 metres per second, it is exact because the unit of length, the metre, is defined from this constant, according to special relativity, c is the maximum speed at which all matter and hence information in the universe can travel. It is the speed at which all particles and changes of the associated fields travel in vacuum. Such particles and waves travel at c regardless of the motion of the source or the reference frame of the observer. In the theory of relativity, c interrelates space and time, the speed at which light propagates through transparent materials, such as glass or air, is less than c, similarly, the speed of radio waves in wire cables is slower than c. The ratio between c and the speed v at which light travels in a material is called the index n of the material. In communicating with distant space probes, it can take minutes to hours for a message to get from Earth to the spacecraft, the light seen from stars left them many years ago, allowing the study of the history of the universe by looking at distant objects. The finite speed of light limits the theoretical maximum speed of computers. The speed of light can be used time of flight measurements to measure large distances to high precision. Ole Rømer first demonstrated in 1676 that light travels at a speed by studying the apparent motion of Jupiters moon Io. In 1865, James Clerk Maxwell proposed that light was an electromagnetic wave, in 1905, Albert Einstein postulated that the speed of light c with respect to any inertial frame is a constant and is independent of the motion of the light source. He explored the consequences of that postulate by deriving the theory of relativity and in doing so showed that the parameter c had relevance outside of the context of light and electromagnetism. After centuries of increasingly precise measurements, in 1975 the speed of light was known to be 299792458 m/s with a measurement uncertainty of 4 parts per billion. In 1983, the metre was redefined in the International System of Units as the distance travelled by light in vacuum in 1/299792458 of a second, as a result, the numerical value of c in metres per second is now fixed exactly by the definition of the metre. The speed of light in vacuum is usually denoted by a lowercase c, historically, the symbol V was used as an alternative symbol for the speed of light, introduced by James Clerk Maxwell in 1865. In 1856, Wilhelm Eduard Weber and Rudolf Kohlrausch had used c for a different constant later shown to equal √2 times the speed of light in vacuum, in 1894, Paul Drude redefined c with its modern meaning. Einstein used V in his original German-language papers on special relativity in 1905, but in 1907 he switched to c, sometimes c is used for the speed of waves in any material medium, and c0 for the speed of light in vacuum. This article uses c exclusively for the speed of light in vacuum, since 1983, the metre has been defined in the International System of Units as the distance light travels in vacuum in 1⁄299792458 of a second
36.
Russian Academy of Sciences
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Headquartered in Moscow, the Academy is considered a civil, self-governed, non-commercial organization chartered by the Government of Russia. It combines the members of RAS and scientists employed by institutions, the Academy currently includes around 650 institutions and 55,000 scientific researchers. There are three types of membership in the RAS, full members, corresponding members, and foreign members, Academicians and corresponding members must be citizens of the Russian Federation when elected. However, some academicians and corresponding members were elected before the collapse of the USSR and are now citizens of other countries, Members of RAS are elected based on their scientific contributions – election to membership is considered very prestigious. In the years 2005–2012, the academy had approximately 500 full and 700 corresponding members, but in 2013, after the Russian Academy of Agricultural Sciences and the Russian Academy of Medical Sciences became incorporated into the RAS, a number of the RAS members accordingly increased. As of November 2016, after the last elections, there were 944 full members and 1159 corresponding members in the renewed Russian Academy of Sciences, the RAS consists of 13 specialized scientific divisions, three territorial divisions, sometimes called branches, and 15 regional scientific centers. The Academy has numerous councils, committees, and commissions, all organized for different purposes, Siberian Division of the Russian Academy of Sciences The Siberian Division was established in 1957, with Mikhail Lavrentyev as founding chairman. Research centers are in Novosibirsk, Tomsk, Krasnoyarsk, Irkutsk, Yakutsk, Ulan-Ude, Kemerovo, Tyumen, as of 2005, the Division employed over 33,000 employees,58 of whom were members of the Academy. Ural Division of the Russian Academy of Sciences The Ural Division was established in 1932, research centers are in Yekaterinburg, Perm, Cheliabinsk, Izhevsk, Orenburg, Ufa and Syktyvkar. As of 2007, the Division employed 3,600 scientists,590 full professors,31 full members, started with just three members, The RSSI now has 3,100 members, including 57 from the largest research institutions. Russian universities and technical institutes are not under the supervision of the RAS, the Academy is also increasing its presence in the educational area. In 1990 the Higher Chemical College of the Russian Academy of Sciences was founded, the Academy gives out a number of different prizes, medals and awards among which, Lomonosov Gold Medal Lobachevsky Prize Demidov Prize Kurchatov Medal Pushkin Prize S. V. Expeditions to explore parts of the country had Academy scientists as their leaders or most active participants. A separate organization, called the Russian Academy, was created in 1783 to work on the study of the Russian language, presided over by Princess Yekaterina Dashkova, the Russian Academy was engaged in compiling the six-volume Academic Dictionary of the Russian Language. The Russian Academy was merged into the Imperial Saint Petersburg Academy of Sciences in 1841, in December 1917, Sergey Fedorovich Oldenburg, a leading ethnographer and political activist in the Kadet party, met with Vladimir Lenin to discuss the future of the Academy. They agreed that the expertise of the Academy would be applied to addressing questions of state construction, in 1925 the Soviet government recognized the Russian Academy of Sciences as the highest all-Union scientific institution and renamed it the Academy of Sciences of the USSR. The Soviet Sciences Academy would be affected like all universities by the rules imposed particularly those pertaining to censorship, the Soviet Science Academy ended up with a leader of the philosophy department who was placed there simply to keep the man out of trouble. The government decided to not execute or send the famous writer to the gulag because he had won the Stalin award, doing this would have discredited the Stalin award and thus Stalin the leader of the Communist party himself
37.
Light-second
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The light-second is a unit of length useful in astronomy, telecommunications and relativistic physics. It is defined as the distance light travels in free space in one second. One light-nanosecond is almost 300 millimetres, which limits the speed of transfer between different parts of a large computer. One light-microsecond is about 300 metres, the mean distance, over land, between opposite sides of the Earth is 66.8 light-milliseconds. Communications satellites are typically 1.337 light-milliseconds to 119.4 light-milliseconds from the surface of the Earth, the light-second is a convenient unit for measuring distances in the inner Solar System, because it corresponds very closely to the radiometric data used to determine them.004786385 s. The mean diameter of the Earth is about 0.0425 light-seconds, the average distance from the Earth to the Moon is about 1.282 light-seconds. The diameter of the Sun is about 4.643 light-seconds, the average distance from the Earth to the Sun is 499.0 light-seconds. Multiples of the light-second can be defined, although apart from the light-year they are used in popular science publications than in research works. For example, a light-minute is 60 light-seconds and the distance from the Earth to the Sun is 8.317 light-minutes. Light-year 100 megametres Geometrized unit system
38.
Orders of magnitude (numbers)
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This list contains selected positive numbers in increasing order, including counts of things, dimensionless quantity and probabilities. Mathematics – Writing, Approximately 10−183,800 is a rough first estimate of the probability that a monkey, however, taking punctuation, capitalization, and spacing into account, the actual probability is far lower, around 10−360,783. Computing, The number 1×10−6176 is equal to the smallest positive non-zero value that can be represented by a quadruple-precision IEEE decimal floating-point value, Computing, The number 6. 5×10−4966 is approximately equal to the smallest positive non-zero value that can be represented by a quadruple-precision IEEE floating-point value. Computing, The number 3. 6×10−4951 is approximately equal to the smallest positive non-zero value that can be represented by a 80-bit x86 double-extended IEEE floating-point value. Computing, The number 1×10−398 is equal to the smallest positive non-zero value that can be represented by a double-precision IEEE decimal floating-point value, Computing, The number 4. 9×10−324 is approximately equal to the smallest positive non-zero value that can be represented by a double-precision IEEE floating-point value. Computing, The number 1×10−101 is equal to the smallest positive non-zero value that can be represented by a single-precision IEEE decimal floating-point value, Mathematics, The probability in a game of bridge of all four players getting a complete suit is approximately 4. 47×10−28. ISO, yocto- ISO, zepto- Mathematics, The probability of matching 20 numbers for 20 in a game of keno is approximately 2.83 × 10−19. ISO, atto- Mathematics, The probability of rolling snake eyes 10 times in a row on a pair of dice is about 2. 74×10−16. ISO, micro- Mathematics – Poker, The odds of being dealt a flush in poker are 649,739 to 1 against. Mathematics – Poker, The odds of being dealt a flush in poker are 72,192 to 1 against. Mathematics – Poker, The odds of being dealt a four of a kind in poker are 4,164 to 1 against, for a probability of 2.4 × 10−4. ISO, milli- Mathematics – Poker, The odds of being dealt a full house in poker are 693 to 1 against, for a probability of 1.4 × 10−3. Mathematics – Poker, The odds of being dealt a flush in poker are 507.8 to 1 against, Mathematics – Poker, The odds of being dealt a straight in poker are 253.8 to 1 against, for a probability of 4 × 10−3. Physics, α =0.007297352570, the fine-structure constant, ISO, deci- Mathematics – Poker, The odds of being dealt only one pair in poker are about 5 to 2 against, for a probability of 0.42. Demography, The population of Monowi, a village in Nebraska. Mathematics, √2 ≈1.414213562373095489, the ratio of the diagonal of a square to its side length. Mathematics, φ ≈1.618033988749895848, the golden ratio Mathematics, the number system understood by most computers, human scale, There are 10 digits on a pair of human hands, and 10 toes on a pair of human feet. Mathematics, The number system used in life, the decimal system, has 10 digits,0,1,2,3,4,5,6,7,8,9
39.
Heliocentric gravitational constant
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In celestial mechanics, the standard gravitational parameter μ of a celestial body is the product of the gravitational constant G and the mass M of the body. μ = G M For several objects in the Solar System, the SI units of the standard gravitational parameter are m3 s−2. However, units of km3 s−2 are frequently used in the scientific literature, the central body in an orbital system can be defined as the one whose mass is much larger than the mass of the orbiting body, or M ≫ m. This approximation is standard for planets orbiting the Sun or most moons, conversely, measurements of the smaller bodys orbit only provide information on the product, μ, not G and M separately. This can be generalized for elliptic orbits, μ =4 π2 a 3 / T2 where a is the semi-major axis, for parabolic trajectories rv2 is constant and equal to 2μ. For elliptic and hyperbolic orbits μ = 2a| ε |, where ε is the orbital energy. The value for the Earth is called the gravitational constant. However, the M can be out only by dividing the MG by G. The uncertainty of those measures is 1 to 7000, so M will have the same uncertainty, the value for the Sun is called the heliocentric gravitational constant or geopotential of the Sun and equals 1. 32712440018×1020 m3 s−2. Note that the mass is also denoted by μ. Astronomical system of units Planetary mass
40.
Gravitational constant
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Its measured value is 6. 67408×10−11 m3⋅kg−1⋅s−2. The constant of proportionality, G, is the gravitational constant, colloquially, the gravitational constant is also called Big G, for disambiguation with small g, which is the local gravitational field of Earth. The two quantities are related by g = GME/r2 E. In the general theory of relativity, the Einstein field equations, R μ ν −12 R g μ ν =8 π G c 4 T μ ν, the scaled gravitational constant κ = 8π/c4G ≈2. 071×10−43 s2·m−1·kg−1 is also known as Einsteins constant. The gravitational constant is a constant that is difficult to measure with high accuracy. This is because the force is extremely weak compared with other fundamental forces. In SI units, the 2014 CODATA-recommended value of the constant is. In cgs, G can be written as G ≈6. 674×10−8 cm3·g−1·s−2, in other words, in Planck units, G has the numerical value of 1. In astrophysics, it is convenient to measure distances in parsecs, velocities in kilometers per second, in these units, the gravitational constant is, G ≈4.302 ×10 −3 p c M ⊙ −12. In orbital mechanics, the period P of an object in orbit around a spherical object obeys G M =3 π V P2 where V is the volume inside the radius of the orbit. It follows that P2 =3 π G V M ≈10.896 h r 2 g c m −3 V M. This way of expressing G shows the relationship between the density of a planet and the period of a satellite orbiting just above its surface. Cavendish measured G implicitly, using a torsion balance invented by the geologist Rev. John Michell and he used a horizontal torsion beam with lead balls whose inertia he could tell by timing the beams oscillation. Their faint attraction to other balls placed alongside the beam was detectable by the deflection it caused, cavendishs aim was not actually to measure the gravitational constant, but rather to measure Earths density relative to water, through the precise knowledge of the gravitational interaction. In modern units, the density that Cavendish calculated implied a value for G of 6. 754×10−11 m3·kg−1·s−2, the accuracy of the measured value of G has increased only modestly since the original Cavendish experiment. G is quite difficult to measure, because gravity is weaker than other fundamental forces. Published values of G have varied rather broadly, and some recent measurements of precision are, in fact. This led to the 2010 CODATA value by NIST having 20% increased uncertainty than in 2006, for the 2014 update, CODATA reduced the uncertainty to less than half the 2010 value
41.
Solar mass
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The solar mass is a standard unit of mass in astronomy, equal to approximately 1.99 ×1030 kilograms. It is used to indicate the masses of stars, as well as clusters, nebulae. It is equal to the mass of the Sun, about two kilograms, M☉ = ×1030 kg The above mass is about 332946 times the mass of Earth. Because Earth follows an orbit around the Sun, its solar mass can be computed from the equation for the orbital period of a small body orbiting a central mass. The value he obtained differs by only 1% from the modern value, the diurnal parallax of the Sun was accurately measured during the transits of Venus in 1761 and 1769, yielding a value of 9″. From the value of the parallax, one can determine the distance to the Sun from the geometry of Earth. The first person to estimate the mass of the Sun was Isaac Newton, in his work Principia, he estimated that the ratio of the mass of Earth to the Sun was about 1/28700. Later he determined that his value was based upon a faulty value for the solar parallax and he corrected his estimated ratio to 1/169282 in the third edition of the Principia. The current value for the parallax is smaller still, yielding an estimated mass ratio of 1/332946. As a unit of measurement, the solar mass came into use before the AU, the mass of the Sun has been decreasing since the time it formed. This occurs through two processes in nearly equal amounts, first, in the Suns core, hydrogen is converted into helium through nuclear fusion, in particular the p–p chain, and this reaction converts some mass into energy in the form of gamma ray photons. Most of this energy eventually radiates away from the Sun, second, high-energy protons and electrons in the atmosphere of the Sun are ejected directly into outer space as a solar wind. The original mass of the Sun at the time it reached the main sequence remains uncertain, the early Sun had much higher mass-loss rates than at present, and it may have lost anywhere from 1–7% of its natal mass over the course of its main-sequence lifetime. The Sun gains a small amount of mass through the impact of asteroids. However, as the Sun already contains 99. 86% of the Solar Systems total mass, M☉ G / c2 ≈1.48 km M☉ G / c3 ≈4.93 μs I. -J. A Bright Young Sun Consistent with Helioseismology and Warm Temperatures on Ancient Earth and Mars
42.
Kepler's Third Law
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In astronomy, Keplers laws of planetary motion are three scientific laws describing the motion of planets around the Sun. The orbit of a planet is an ellipse with the Sun at one of the two foci, a line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time. The square of the period of a planet is proportional to the cube of the semi-major axis of its orbit. Most planetary orbits are circular, and careful observation and calculation are required in order to establish that they are not perfectly circular. Calculations of the orbit of Mars, whose published values are somewhat suspect, from this, Johannes Kepler inferred that other bodies in the Solar System, including those farther away from the Sun, also have elliptical orbits. Keplers work improved the theory of Nicolaus Copernicus, explaining how the planets speeds varied. Isaac Newton showed in 1687 that relationships like Keplers would apply in the Solar System to a approximation, as a consequence of his own laws of motion. Keplers laws are part of the foundation of modern astronomy and physics, Keplers laws improve the model of Copernicus. Keplers corrections are not at all obvious, The planetary orbit is not a circle, the Sun is not at the center but at a focal point of the elliptical orbit. Neither the linear speed nor the speed of the planet in the orbit is constant, but the area speed is constant.015. The calculation is correct when perihelion, the date the Earth is closest to the Sun, the current perihelion, near January 4, is fairly close to the solstice of December 21 or 22. It took nearly two centuries for the current formulation of Keplers work to take on its settled form, voltaires Eléments de la philosophie de Newton of 1738 was the first publication to use the terminology of laws. The Biographical Encyclopedia of Astronomers in its article on Kepler states that the terminology of laws for these discoveries was current at least from the time of Joseph de Lalande. It was the exposition of Robert Small, in An account of the discoveries of Kepler that made up the set of three laws, by adding in the third. Small also claimed, against the history, that these were empirical laws, further, the current usage of Keplers Second Law is something of a misnomer. Kepler had two versions, related in a sense, the distance law and the area law. The area law is what became the Second Law in the set of three, but Kepler did himself not privilege it in that way, Johannes Kepler published his first two laws about planetary motion in 1609, having found them by analyzing the astronomical observations of Tycho Brahe. Keplers third law was published in 1619 and his first law reflected this discovery
43.
General relativity
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General relativity is the geometric theory of gravitation published by Albert Einstein in 1915 and the current description of gravitation in modern physics. General relativity generalizes special relativity and Newtons law of gravitation, providing a unified description of gravity as a geometric property of space and time. In particular, the curvature of spacetime is directly related to the energy and momentum of whatever matter, the relation is specified by the Einstein field equations, a system of partial differential equations. Examples of such differences include gravitational time dilation, gravitational lensing, the redshift of light. The predictions of relativity have been confirmed in all observations. Although general relativity is not the only theory of gravity. Einsteins theory has important astrophysical implications, for example, it implies the existence of black holes—regions of space in which space and time are distorted in such a way that nothing, not even light, can escape—as an end-state for massive stars. The bending of light by gravity can lead to the phenomenon of gravitational lensing, General relativity also predicts the existence of gravitational waves, which have since been observed directly by physics collaboration LIGO. In addition, general relativity is the basis of current cosmological models of an expanding universe. Soon after publishing the special theory of relativity in 1905, Einstein started thinking about how to incorporate gravity into his new relativistic framework. In 1907, beginning with a thought experiment involving an observer in free fall. After numerous detours and false starts, his work culminated in the presentation to the Prussian Academy of Science in November 1915 of what are now known as the Einstein field equations. These equations specify how the geometry of space and time is influenced by whatever matter and radiation are present, the Einstein field equations are nonlinear and very difficult to solve. Einstein used approximation methods in working out initial predictions of the theory, but as early as 1916, the astrophysicist Karl Schwarzschild found the first non-trivial exact solution to the Einstein field equations, the Schwarzschild metric. This solution laid the groundwork for the description of the stages of gravitational collapse. In 1917, Einstein applied his theory to the universe as a whole, in line with contemporary thinking, he assumed a static universe, adding a new parameter to his original field equations—the cosmological constant—to match that observational presumption. By 1929, however, the work of Hubble and others had shown that our universe is expanding and this is readily described by the expanding cosmological solutions found by Friedmann in 1922, which do not require a cosmological constant. Lemaître used these solutions to formulate the earliest version of the Big Bang models, in which our universe has evolved from an extremely hot, Einstein later declared the cosmological constant the biggest blunder of his life
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Frame of reference
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In physics, a frame of reference consists of an abstract coordinate system and the set of physical reference points that uniquely fix the coordinate system and standardize measurements. In n dimensions, n+1 reference points are sufficient to define a reference frame. Using rectangular coordinates, a frame may be defined with a reference point at the origin. In Einsteinian relativity, reference frames are used to specify the relationship between an observer and the phenomenon or phenomena under observation. In this context, the phrase often becomes observational frame of reference, a relativistic reference frame includes the coordinate time, which does not correspond across different frames moving relatively to each other. The situation thus differs from Galilean relativity, where all possible coordinate times are essentially equivalent, the need to distinguish between the various meanings of frame of reference has led to a variety of terms. For example, sometimes the type of system is attached as a modifier. Sometimes the state of motion is emphasized, as in rotating frame of reference, sometimes the way it transforms to frames considered as related is emphasized as in Galilean frame of reference. Sometimes frames are distinguished by the scale of their observations, as in macroscopic and microscopic frames of reference, in this sense, an observational frame of reference allows study of the effect of motion upon an entire family of coordinate systems that could be attached to this frame. On the other hand, a system may be employed for many purposes where the state of motion is not the primary concern. For example, a system may be adopted to take advantage of the symmetry of a system. In a still broader perspective, the formulation of many problems in physics employs generalized coordinates, normal modes or eigenvectors and it seems useful to divorce the various aspects of a reference frame for the discussion below. A coordinate system is a concept, amounting to a choice of language used to describe observations. Consequently, an observer in a frame of reference can choose to employ any coordinate system to describe observations made from that frame of reference. A change in the choice of coordinate system does not change an observers state of motion. This viewpoint can be found elsewhere as well, which is not to dispute that some coordinate systems may be a better choice for some observations than are others. Choice of what to measure and with what observational apparatus is a separate from the observers state of motion. D. Norton, The discussion is taken beyond simple space-time coordinate systems by Brading, extension to coordinate systems using generalized coordinates underlies the Hamiltonian and Lagrangian formulations of quantum field theory, classical relativistic mechanics, and quantum gravity
45.
Stellar system
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A star system or stellar system is a small number of stars that orbit each other, bound by gravitational attraction. A large number of stars bound by gravitation is generally called a cluster or galaxy, although, broadly speaking. Star systems are not to be confused with planetary systems, which include planets, a star system of two stars is known as a binary star, binary star system or physical double star. Examples of binary systems are Sirius, Procyon and Cygnus X-1, the last of which consists of a star. A multiple star system consists of three or more stars that appear from Earth to be close to one another in the sky, physical multiple stars are also commonly called multiple stars or multiple star systems. Most multiple star systems are triple stars, systems with four or more components are less likely to occur. These systems are smaller than open star clusters, which have more complex dynamics, most multiple star systems known are triple, for higher multiplicities, the number of known systems with a given multiplicity decreases exponentially with multiplicity. For example, in the 1999 revision of Tokovinins catalog of physical multiple stars,551 out of the 728 systems described are triple, however, because of selection effects, knowledge of these statistics is very incomplete. Each of these groups must also be hierarchical, which means that they must be divided into smaller subgroups which themselves are hierarchical. Each level of the hierarchy can be treated as a problem by considering close pairs as if they were a single star. In a physical triple star system, each orbits the center of mass of the system. Usually, two of the form a close binary system, and the third orbits this pair at a distance much larger than that of the binary orbit. The reason for this is if the inner and outer orbits are comparable in size. Triple stars that are not all gravitationally bound might comprise a physical binary and a companion, such as Beta Cephei, or rarely. Hierarchical multiple star systems with more than three stars can produce a number of more complicated arrangements, which can be illustrated by what Evans has called a mobile diagram and these are similar to ornamental mobiles hung from the ceiling. Some examples can be seen in the figure to the right, each level of the diagram illustrates the decomposition of the system into two or more systems with smaller size. Evans calls a diagram multiplex if there is a node with more than two children, i. e. if the decomposition of some subsystem involves two or more orbits with comparable size. Because, as we have seen for triple stars, this may be unstable, multiple stars are expected to be simplex
46.
Cosmic distance ladder
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The cosmic distance ladder is the succession of methods by which astronomers determine the distances to celestial objects. A real direct distance measurement of an object is possible only for those objects that are close enough to Earth. The techniques for determining distances to more distant objects are all based on various measured correlations between methods that work at distances and methods that work at larger distances. Several methods rely on a candle, which is an astronomical object that has a known luminosity. The ladder analogy arises because no single technique can measure distances at all ranges encountered in astronomy, instead, one method can be used to measure nearby distances, a second can be used to measure nearby to intermediate distances, and so on. Each rung of the ladder provides information that can be used to determine the distances at the next higher rung, at the base of the ladder are fundamental distance measurements, in which distances are determined directly, with no physical assumptions about the nature of the object in question. The precise measurement of stellar positions is part of the discipline of astrometry, direct distance measurements are based upon the astronomical unit, which is the distance between the Earth and the Sun. Historically, observations of transits of Venus were crucial in determining the AU, in the first half of the 20th century, observations of asteroids were also important. Keplers laws provide precise ratios of the sizes of the orbits of objects orbiting the Sun, radar is used to measure the distance between the orbits of the Earth and of a second body. From that measurement and the ratio of the two sizes, the size of Earths orbit is calculated. The Earths orbit is known with a precision of a few meters, the most important fundamental distance measurements come from trigonometric parallax. As the Earth orbits the Sun, the position of stars will appear to shift slightly against the more distant background. These shifts are angles in a triangle, with 2 AU making the base leg of the triangle. The amount of shift is small, measuring 1 arcsecond for an object at the 1 parsec distance of the nearest stars. Astronomers usually express distances in units of parsecs, light-years are used in popular media, because parallax becomes smaller for a greater stellar distance, useful distances can be measured only for stars whose parallax is larger than a few times the precision of the measurement. Parallax measurements typically have an accuracy measured in milliarcseconds, the Hubble telescope WFC3 now has the potential to provide a precision of 20 to 40 microarcseconds, enabling reliable distance measurements up to 5,000 parsecs for small numbers of stars. By the early 2020s, the GAIA space mission will provide similarly accurate distances to all bright stars. Stars have a velocity relative to the Sun that causes proper motion, for a group of stars with the same spectral class and a similar magnitude range, a mean parallax can be derived from statistical analysis of the proper motions relative to their radial velocities
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Arcsecond
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A minute of arc, arcminute, 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 also 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 also 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 also 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″
48.
Archimedes
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Archimedes of Syracuse was a Greek mathematician, physicist, engineer, inventor, and astronomer. Although few details of his life are known, he is regarded as one of the scientists in classical antiquity. He was also one of the first to apply mathematics to physical phenomena, founding hydrostatics and statics and he is credited with designing innovative machines, such as his screw pump, compound pulleys, and defensive war machines to protect his native Syracuse from invasion. Archimedes died during the Siege of Syracuse when he was killed by a Roman soldier despite orders that he should not be harmed. Cicero describes visiting the tomb of Archimedes, which was surmounted by a sphere and a cylinder, unlike his inventions, the mathematical writings of Archimedes were little known in antiquity. Archimedes was born c.287 BC in the city of Syracuse, Sicily, at that time a self-governing colony in Magna Graecia. The date of birth is based on a statement by the Byzantine Greek historian John Tzetzes that Archimedes lived for 75 years, in The Sand Reckoner, Archimedes gives his fathers name as Phidias, an astronomer about whom nothing is known. Plutarch wrote in his Parallel Lives that Archimedes was related to King Hiero II, a biography of Archimedes was written by his friend Heracleides but this work has been lost, leaving the details of his life obscure. It is unknown, for instance, whether he married or had children. During his youth, Archimedes may have studied in Alexandria, Egypt and he referred to Conon of Samos as his friend, while two of his works have introductions addressed to Eratosthenes. Archimedes died c.212 BC during the Second Punic War, according to the popular account given by Plutarch, Archimedes was contemplating a mathematical diagram when the city was captured. A Roman soldier commanded him to come and meet General Marcellus but he declined, the soldier was enraged by this, and killed Archimedes with his sword. Plutarch also gives an account of the death of Archimedes which suggests that he may have been killed while attempting to surrender to a Roman soldier. According to this story, Archimedes was carrying mathematical instruments, and was killed because the thought that they were valuable items. General Marcellus was reportedly angered by the death of Archimedes, as he considered him a valuable asset and had ordered that he not be harmed. Marcellus called Archimedes a geometrical Briareus, the last words attributed to Archimedes are Do not disturb my circles, a reference to the circles in the mathematical drawing that he was supposedly studying when disturbed by the Roman soldier. This quote is given in Latin as Noli turbare circulos meos. The phrase is given in Katharevousa Greek as μὴ μου τοὺς κύκλους τάραττε
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Aristarchus of Samos
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Aristarchus of Samos was an ancient Greek astronomer and mathematician who presented the first known model that placed the Sun at the center of the known universe with the Earth revolving around it. He was influenced by Philolaus of Croton, but he identified the central fire with the Sun, like Anaxagoras before him, he suspected that the stars were just other bodies like the Sun, albeit further away from Earth. His astronomical ideas were rejected in favor of the geocentric theories of Aristotle and Ptolemy. Nicolaus Copernicus had attributed the theory to Aristarchus. This is the account as you have heard from astronomers. Since stellar parallax is only detectable with telescopes, his accurate speculation was unprovable at the time and it is a common misconception that the heliocentric view was held as sacrilegious by the contemporaries of Aristarchus. This is due to Gilles Ménages translation of a passage from Plutarchs On the Apparent Face in the Orb of the Moon. Plutarch reported that Cleanthes as a worshipper of the Sun and opponent to the model, was jokingly told by Aristarchus that he should be charged with impiety. Gilles Ménage, shortly after the trials of Galileo and Giordano Bruno, amended an accusative with a nominative, the resulting misconception of an isolated and persecuted Aristarchus is still transmitted today. In his Naturalis Historia, Pliny the Elder later wondered whether errors in the predictions about the heavens could be attributed to a displacement of the Earth from its central position. Pliny and Seneca referred to planets retrograde motion as an apparent phenomenon, still, no stellar parallax was observed, and Plato, Aristotle and Ptolemy preferred the geocentric model, which was held as true throughout the Middle Ages. The heliocentric theory was revived by Copernicus, after which Johannes Kepler described planetary motions with greater accuracy with his three laws, isaac Newton later gave a theoretical explanation based on laws of gravitational attraction and dynamics. The only surviving work attributed to Aristarchus, On the Sizes and Distances of the Sun. The discrepancy may come from a misinterpretation of what unit of measure was meant by a certain Greek term in Aristarchus text, Aristarchus claimed that at half moon, the angle between the Sun and Moon was 87°. He might have proposed 87° as a bound, since gauging the lunar terminators deviation from linearity to 1° accuracy is beyond the unaided human ocular limit. Aristarchus is known to have also studied light and vision, using correct geometry, but the insufficiently accurate 87° datum, Aristarchus concluded that the Sun was between 18 and 20 times farther away than the Moon. The implicit false solar parallax of slightly under 3° was used by astronomers up to and including Tycho Brahe, Aristarchus inequality Belief Perseverance Heath, Sir Thomas. Gomez, A. G. Aristarchos of Samos, the Polymath, online Galleries, History of Science Collections, University of Oklahoma Libraries High resolution images of works by Aristarchus of Samos in. jpg and. tiff format
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On the Sizes and Distances of the Sun and Moon
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On the Sizes and Distances is widely accepted as the only extant work written by Aristarchus of Samos, an ancient Greek astronomer who lived circa 310–230 BC. This work calculates the sizes of the Sun and Moon, as well as their distances from the Earth in terms of Earths radius, the book was presumably preserved by students of Pappus of Alexandrias course in mathematics, although there is no evidence of this. The editio princeps was published by John Wallis in 1688, using medieval manuscripts compiled by Sir Henry Savile. The earliest Latin translation was made by Giorgio Valla in 1488, there is also a 1572 Latin translation and commentary by Frederico Commandino. The works method relied on observations, The apparent size of the Sun. The size of the Earths shadow in relation to the Moon during a lunar eclipse The angle between the Sun and Moon during a moon is very close to 90°. The rest of the details a reconstruction of Aristarchus method. The reconstruction uses the variables, Aristarchus began with the premise that, during a half moon. By observing the angle between the Sun and Moon, φ, the ratio of the distances to the Sun, from the diagram and trigonometry, we can calculate that S L =1 cos φ = sec φ. The diagram is greatly exaggerated, because in reality, S =390 L, Aristarchus determined φ to be a thirtieth of a quadrant less than a right angle, in current terminology, 87°. Trigonometric functions had not yet invented, but using geometrical analysis in the style of Euclid. In other words, the distance to the Sun was somewhere between 18 and 20 times greater than the distance to the Moon and this value was accepted by astronomers for the next two thousand years, until the invention of the telescope permitted a more precise estimate of solar parallax. Aristarchus then used another construction based on an eclipse, By similarity of the triangles. The appearance of these equations can be simplified using n = d/ℓ, ℓ t =1 + x x s t =1 + x 1 + n The above equations give the radii of the Moon and Sun entirely in terms of observable quantities. The following formulae give the distances to the Sun and Moon in terrestrial units, L t = S t = where θ is the apparent radius of the Moon and Sun measured in degrees. It is unlikely that Aristarchus used these exact formulae, yet these formulae are likely an approximation to those of Aristarchus. The above formulae can be used to reconstruct the results of Aristarchus, the following table shows the results of a long-standing reconstruction using n =2, x =19.1 and θ = 1°, alongside the modern day accepted values. The error in this calculation comes primarily from the values for x and θ
51.
Lunar distance (astronomy)
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Lunar distance is as a unit of measure in astronomy. It is the distance from the center of Earth to the center of the Moon. More technically, it is the mean semi-major axis of the lunar orbit. It may also refer to the distance between the centers of the Earth and the Moon, or less commonly, the instantaneous Earth-Moon distance. The lunar distance is approximately a quarter of a million miles, Lunar distance is also called Earth-Moon distance, Earth–Moon characteristic distance, or distance to the Moon, and commonly indicated with LD or Δ ⊕ L. The mean semi-major axis has a value of 384,402 km, the time-averaged distance between Earth and Moon centers is 385,000.6 km. The actual distance varies over the course of the orbit of the Moon, from 356,500 km at the perigee to 406,700 km at apogee, Lunar distance is commonly used to express the distance to near-Earth object encounters. The measurement is useful in characterizing the lunar radius, the mass of the Sun. Millimeter-precision measurements of the distance are made by measuring the time taken for light to travel between LIDAR stations on the Earth and retroreflectors placed on the Moon. The Moon is spiraling away from the Earth at a rate of 3.8 cm per year. By coincidence, the diameter of corner cubes in retroreflectors on the Moon is also 3.8 cm, the instantaneous lunar distance is constantly changing. In fact the distance between the Moon and Earth can change by as much as 75 m/s, or more than 1,000 kilometers in just 6 hours. There are other effects that influence the lunar distance. Some factors are described in this section, the distance to the Moon can be measured to an accuracy of 2 mm over a 1-hour sampling period, which results in an overall uncertainty of 2–3 cm for the average distance. However, due to its orbit with varying eccentricity, the instantaneous distance varies with monthly periodicity. Furthermore, the distance is perturbed by the effects of various astronomical bodies - most significantly the Sun. Other forces responsible for minuscule perturbations are other planets in the system, asteroids, tidal forces. The effect of pressure from the sun contributes an amount of ±3.6 mm to the lunar distance
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Lunar phase
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The lunar phase or phase of the moon is the shape of the illuminated portion of the Moon as seen by an observer on Earth. The lunar phases change cyclically as the Moon orbits the Earth, according to the positions of the Moon. The Moons rotation is locked by the Earths gravity, therefore the same lunar surface always faces Earth. This face is variously sunlit depending on the position of the Moon in its orbit, therefore, the portion of this hemisphere that is visible to an observer on Earth can vary from about 100% to 0%. The lunar terminator is the boundary between the illuminated and darkened hemispheres, each of the four intermediate lunar phases is roughly seven days but this varies slightly due to the elliptical shape of the Moons orbit. Aside from some craters near the lunar poles such as Shoemaker, all parts of the Moon see around 14.77 days of sunlight, in Western culture, the four principal lunar phases are new moon, first quarter, full moon, and third quarter. These are the instants when the Moons apparent geocentric celestial longitude minus the Suns apparent geocentric longitude is 0°, 90°, 180° and 270°. Each of these phases is instantaneous, lasting theoretically zero time, during the intervals between principal phases, the Moon appears either crescent-shaped or gibbous. These shapes, and the periods of time when the Moon shows them, are called the intermediate phases. They last, on average, one-quarter of a month, roughly 7.38 days, but their durations vary slightly because the Moons orbit is slightly elliptical. The descriptor waxing is used for a phase when the Moons apparent size is increasing, from new moon toward full moon. As the moon waxes, the lunar phases progress through new moon, crescent moon, first-quarter moon, gibbous moon, the moon is then said to wane as it passes through the gibbous moon, third-quarter moon, crescent moon and back to new moon. The terms old moon and new moon are not interchangeable, the old moon is a waning sliver until the moment it aligns with the sun and begins to wax, at which point it becomes new again. Half moon is used to mean the first- and third-quarter moons, while the term quarter refers to the extent of the moons cycle around the Earth. When a crescent Moon occurs, the phenomenon of earthshine may be apparent, in the Northern Hemisphere, if the left side of the Moon is dark then the light part is growing, and the Moon is referred to as waxing. If the right side of the Moon is dark then the part is shrinking. Assuming that the viewer is in the hemisphere, the right portion of the Moon is the part that is always growing. Nearer the Equator the Moon with its terminator will appear apparently horizontal during the morning and evening, the crescent Moon can open upward or downward, with the horns of the crescent pointing up or down, respectively
53.
Eusebius of Caesarea
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Eusebius of Caesarea, also known as Eusebius Pamphili, was a Greek historian of Christianity, exegete, and Christian polemicist. He became the bishop of Caesarea Maritima about 314 AD, together with Pamphilus, he was a scholar of the Biblical canon and is regarded as an extremely well learned Christian of his time. He wrote Demonstrations of the Gospel, Preparations for the Gospel, as Father of Church History he produced the Ecclesiastical History, On the Life of Pamphilus, the Chronicle and On the Martyrs. Little is known about the life of Eusebius and his successor at the See of Caesarea, Acacius, wrote a Life of Eusebius, a work that has since been lost. Eusebius own surviving works probably only represent a portion of his total output. Beyond notices in his extant writings, the sources are the 5th-century ecclesiastical historians Socrates, Sozomen, and Theodoret. There are assorted notices of his activities in the writings of his contemporaries Athanasius, Arius, Eusebius of Nicomedia, Eusebius pupil, Eusebius of Emesa, provides some incidental information. In his Ecclesiastical History, Eusebius writes of Dionysius of Alexandria as his contemporary, if this is true, Eusebius birth must have been before Dionysius death in autumn 264, most modern scholars date the birth to some point in the five years between 260 and 265. He was presumably born in the town in which he lived for most of his adult life and he was baptized and instructed in the city, and lived in Palestine in 296, when Diocletians army passed through the region. Eusebius was made presbyter by Agapius of Caesarea, S. Wallace-Hadrill, deem the phrase too ambiguous to support the contention. By the 3rd century, Caesarea had a population of about 100,000 and it had been a pagan city since Pompey had given control of the city to the gentiles during his command of the eastern provinces in the 60s BC. The gentiles retained control of the city for the three centuries to follow, despite Jewish petitions for joint governorship, gentile government was strengthened by the citys refoundation under Herod the Great, when it had taken on the name of Augustus Caesar. In addition to the settlers, Caesarea had large Jewish. Eusebius was probably born into the Christian contingent of the city.46 states that Zacchaeus was the first bishop, through the activities of the theologian Origen and the school of his follower Pamphilus, Caesarea became a center of Christian learning. Origen was largely responsible for the collection of information, or which churches were using which gospels. On his deathbed, Origen had made a bequest of his library to the Christian community in the city. Together with the books of his patron Ambrosius, Origens library formed the core of the collection that Pamphilus established, Pamphilus also managed a school that was similar to that of Origen. Pamphilus was compared to Demetrius of Phalerum and Pisistratus, for he had gathered Bibles from all parts of the world, like his model Origen, Pamphilus maintained close contact with his students
54.
Eratosthenes
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Eratosthenes of Cyrene was a Greek mathematician, geographer, poet, astronomer, and music theorist. He was a man of learning, becoming the librarian at the Library of Alexandria. He invented the discipline of geography, including the terminology used today and he is best known for being the first person to calculate the circumference of the Earth, which he did by applying a measuring system using stadia, a standard unit of measure during that time period. He was also the first to calculate the tilt of the Earths axis, additionally, he may have accurately calculated the distance from the Earth to the Sun and invented the leap day. He created the first map of the world, incorporating parallels, Eratosthenes was the founder of scientific chronology, he endeavored to revise the dates of the chief literary and political events from the conquest of Troy. In number theory, he introduced the sieve of Eratosthenes, an efficient method of identifying prime numbers and he was a figure of influence in many fields. According to an entry in the Suda, his critics scorned him, nonetheless, his devotees nicknamed him Pentathlos after the Olympians who were well rounded competitors, for he had proven himself to be knowledgeable in every area of learning. Eratosthenes yearned to understand the complexities of the entire world, the son of Aglaos, Eratosthenes was born in 276 BC in Cyrene. Alexander the Great conquered Cyrene in 332 BC, and following his death in 323 BC, its rule was given to one of his generals, Ptolemy I Soter, the founder of the Ptolemaic Kingdom. Under Ptolemaic rule the economy prospered, based largely on the export of horses and silphium, Cyrene became a place of cultivation, where knowledge blossomed. Eratosthenes went to Athens to further his studies, there he was taught Stoicism by its founder, Zeno of Citium, in philosophical lectures on living a virtuous life. He then studied under Ariston of Chios, who led a more cynical school of philosophy and he also studied under the head of the Platonic Academy, who was Arcesilaus of Pitane. His interest in Plato led him to write his very first work at a level, Platonikos. Eratosthenes was a man of many perspectives and investigated the art of poetry under Callimachus and he was a talented and imaginative poet. He wrote poems, one in hexameters called Hermes, illustrating the life history. He wrote Chronographies, a text that scientifically depicted dates of importance and this work was highly esteemed for its accuracy. George Syncellus was later able to preserve from Chronographies a list of 38 kings of the Egyptian Thebes, Eratosthenes also wrote Olympic Victors, a chronology of the winners of the Olympic Games. It is not known when he wrote his works, but they highlighted his abilities and these works and his great poetic abilities led the pharaoh Ptolemy III Euergetes to seek to place him as a librarian at the Library of Alexandria in the year 245 BC
55.
Inflection
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An inflection expresses one or more grammatical categories with a prefix, suffix or infix, or another internal modification such as a vowel change. For example, the Latin verb ducam, meaning I will lead, includes the suffix -am, expressing person, number, the use of this suffix is an inflection. In contrast, in the English clause I will lead, the lead is not inflected for any of person, number, or tense. The inflected form of a word contains both one or more free morphemes, and one or more bound morphemes. These two morphemes together form the inflected word cars and its categories can be determined only from its context. Requiring the forms or inflections of more than one word in a sentence to be compatible with each other according to the rules of the language is known as concord or agreement. For example, in the choir sings, choir is a singular noun, languages that have some degree of inflection are synthetic languages. These can be inflected, or weakly inflected. Languages that are so inflected that a sentence can consist of a highly inflected word are called polysynthetic languages. Languages such as Mandarin Chinese that never use inflections are called analytic or isolating, in English most nouns are inflected for number with the inflectional plural affix -s, and most English verbs are inflected for tense with the inflectional past tense affix -ed. English also inflects verbs by affixation to mark the person singular in the present tense. English short adjectives are inflected to mark comparative and superlative forms, in addition, English also shows inflection by ablaut and umlaut, as well as long-short vowel alternation. For example, Write, wrote, written Sing, sang, sung Foot, feet Mouse, mice Child, children For details, see English plural, English verbs, and English irregular verbs. When a given word class is subject to inflection in a particular language, words which follow such a standard pattern are said to be regular, those that inflect differently are called irregular. For instance, many languages that feature verb inflection have both regular verbs and irregular verbs, in English, regular verbs form their past tense and past participle with the ending -d, thus verbs like play, arrive and enter are regular. However, there are a few hundred verbs which follow different patterns, such as sing–sang–sung and keep–kept–kept, irregular verbs often preserve patterns which were regular in past forms of the language, but which have now become anomalous. Example, Latin dīcō, dīcere, dīxī, dictum > Spanish digo, decir, dije, strong vs. weak inflection—Sometimes two inflection systems exist, conventionally classified as strong and weak. Ancient Greek verbs are likewise said to have had a first aorist, suppletion—The irregular form was originally derived from a different root
56.
Hipparchus
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Hipparchus of Nicaea was a Greek astronomer, geographer, and mathematician. He is considered the founder of trigonometry but is most famous for his discovery of precession of the equinoxes. Hipparchus was born in Nicaea, Bithynia, and probably died on the island of Rhodes and he is known to have been a working astronomer at least from 162 to 127 BC. Hipparchus is considered the greatest ancient astronomical observer and, by some and he was the first whose quantitative and accurate models for the motion of the Sun and Moon survive. For this he made use of the observations and perhaps the mathematical techniques accumulated over centuries by the Babylonians. He developed trigonometry and constructed trigonometric tables, and he solved problems of spherical trigonometry. With his solar and lunar theories and his trigonometry, he may have been the first to develop a method to predict solar eclipses. Relatively little of Hipparchuss direct work survives into modern times, although he wrote at least fourteen books, only his commentary on the popular astronomical poem by Aratus was preserved by later copyists. There is a tradition that Hipparchus was born in Nicaea, in the ancient district of Bithynia. His birth date was calculated by Delambre based on clues in his work, Hipparchus must have lived some time after 127 BC because he analyzed and published his observations from that year. Hipparchus obtained information from Alexandria as well as Babylon, but it is not known when or if he visited these places and he is believed to have died on the island of Rhodes, where he seems to have spent most of his later life. It is not known what Hipparchuss economic means were nor how he supported his scientific activities and his appearance is likewise unknown, there are no contemporary portraits. In the 2nd and 3rd centuries coins were made in his honour in Bithynia that bear his name and show him with a globe, this supports the tradition that he was born there. As an astronomer of antiquity his influence, supported by ideas from Aristotle, held sway for nearly 2000 years, Hipparchuss only preserved work is Τῶν Ἀράτου καὶ Εὐδόξου φαινομένων ἐξήγησις. This is a critical commentary in the form of two books on a popular poem by Aratus based on the work by Eudoxus. Hipparchus also made a list of his works, which apparently mentioned about fourteen books. His famous star catalog was incorporated into the one by Ptolemy, the first trigonometric table was apparently compiled by Hipparchus, who is now consequently known as the father of trigonometry. There are a variety of mis-steps in the more ambitious 2005 paper, According to one book review, both of these claims have been rejected by other scholars
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Pappus of Alexandria
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Pappus of Alexandria was one of the last great Alexandrian mathematicians of Antiquity, known for his Synagoge or Collection, and for Pappuss hexagon theorem in projective geometry. Nothing is known of his life, other than, that he had a son named Hermodorus, Collection, his best-known work, is a compendium of mathematics in eight volumes, the bulk of which survives. It covers a range of topics, including geometry, recreational mathematics, doubling the cube, polygons. Pappus flourished in the 4th century AD, in a period of general stagnation in mathematical studies, he stands out as a remarkable exception. In this respect the fate of Pappus strikingly resembles that of Diophantus, in his surviving writings, Pappus gives no indication of the date of the authors whose works he makes use of, or of the time at which he himself wrote. If no other information were available, all that could be known would be that he was later than Ptolemy, whom he quotes, and earlier than Proclus. The Suda states that Pappus was of the age as Theon of Alexandria. A different date is given by a note to a late 10th-century manuscript, which states, next to an entry on Emperor Diocletian. This works out as October 18,320 AD, and so Pappus must have flourished c.320 AD. The great work of Pappus, in eight books and titled Synagoge or Collection, has not survived in complete form, the first book is lost, and the rest have suffered considerably. The Suda enumerates other works of Pappus, Χωρογραφία οἰκουμενική, commentary on the 4 books of Ptolemys Almagest, Ποταμοὺς τοὺς ἐν Λιβύῃ, Pappus himself mentions another commentary of his own on the Ἀνάλημμα of Diodorus of Alexandria. Pappus also wrote commentaries on Euclids Elements, and on Ptolemys Ἁρμονικά and these discoveries form, in fact, a text upon which Pappus enlarges discursively. Heath considered the systematic introductions to the books as valuable, for they set forth clearly an outline of the contents. From these introductions one can judge of the style of Pappuss writing, heath also found his characteristic exactness made his Collection a most admirable substitute for the texts of the many valuable treatises of earlier mathematicians of which time has deprived us. The portions of Collection which has survived can be summarized as follows and we can only conjecture that the lost Book I, like Book II, was concerned with arithmetic, Book III being clearly introduced as beginning a new subject. The whole of Book II discusses a method of multiplication from a book by Apollonius of Perga. The final propositions deal with multiplying together the values of Greek letters in two lines of poetry, producing two very large numbers approximately equal to 2*1054 and 2*1038. Book III contains geometrical problems, plane and solid, on the arithmetic, geometric and harmonic means between two straight lines, and the problem of representing all three in one and the same geometrical figure
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Zhoubi Suanjing
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The Zhoubi Suanjing, or Chou Pei Suan Ching, is one of the oldest Chinese mathematical texts. Zhou refers to the ancient dynasty Zhou c, 1046-771 BCE, Bi means thigh and according to the book, it refers to the gnomon of the sundial. The book is dedicated to astronomical observation and calculation, Suan Jing or classic of arithmetic were appended in later time to honor the achievement of the book in mathematics. This book dates from the period of the Zhou Dynasty, yet its compilation and addition of materials continued into the Han Dynasty and it is an anonymous collection of 246 problems encountered by the Duke of Zhou and his astronomer and mathematician, Shang Gao. Each question has stated their numerical answer and corresponding arithmetic algorithm and this book contains one of the first recorded proofs of the Pythagorean Theorem. Commentators such as Liu Hui, Zu Geng, Li Chunfeng and Yang Hui have expanded on this text, tsinghua Bamboo Slips Boyer, Carl B. A History of Mathematics, John Wiley & Sons, Inc, full text of the Zhoubi Suanjing, including diagrams - Chinese Text Project. Full text of the Zhoubi Suanjing, at Project Gutenberg Christopher Cullen, astronomy and Mathematics in Ancient China, The Zhou Bi Suan Jing, Cambridge University Press,2007
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Li (length)
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The li, also known as the Chinese mile, is a traditional Chinese unit of distance. The li has varied considerably over time but was usually about a third as long as the English mile and this is then divided into 1,500 chi or Chinese feet. The character 里 combines the characters for field and earth, since it was considered to be about the length of a single village. As late as the 1940s, a li did not represent a fixed measure, there is also another li that indicates a unit of length 1/1000 of a chi, but it is used much less commonly. This li is used in the Peoples Republic of China as the equivalent of the prefix in metric units. This traditional unit, in terms of usage and distance proportion. The basic Chinese traditional unit of distance was the chi, as its value changed over time, so did the lis. In addition, the number of chi per li was sometimes altered, to add further complexity, under the Qin Dynasty, the li was set at 360 paces but the number of chi per bu was subsequently changed from 6 to 5, shortening the li by 1⁄6. Thus, the Qin li of about 576 meters became the Han li, the basic units of measurement fortunately remained stable over the Qin and Han periods. A bronze imperial standard measure, dated AD9, had been preserved at the Imperial Palace in Beijing and this has allowed very accurate conversions to modern measurements, which has provided a new and extremely useful additional tool in the identification of place names and routes. These measurements have confirmed in many ways including the discovery of a number of rulers found at archaeological sites. The Han li was calculated by Dubs to be 415.8 metres and all indications are that this is a precise, under the Tang Dynasty, the li was approximately 323 meters. In the late Manchu or Qing Dynasty, the number of chi was increased from 1,500 per li to 1,800 and this had a value of 2115 feet or 644.6 meters. In addition, the Qing added a longer unit called the tu and these changes were undone by the Republic of China of Chiang Kai-shek, who adopted the metric system in 1928. The Republic of China continues not to use the li at all, under Mao Zedong, the Peoples Republic of China reinstituted the traditional units as a measure of anti-imperialism and cultural pride before officially adopting the metric system in 1984. A place was made within this for the units, which were restandardized to metric values. A modern li is thus set at half a kilometer. However, unlike the jin which is frequently preferred in daily use over the kilogram
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Solar parallax
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The term is derived from the Greek word παράλλαξις, meaning alternation. Due to foreshortening, nearby objects have a larger parallax than more distant objects when observed from different positions, astronomers use the principle of parallax to measure distances to the closer stars. Here, the parallax is the semi-angle of inclination between two sight-lines to the star, as observed when the Earth is on opposite sides of the Sun in its orbit. Parallax also affects optical instruments such as rifle scopes, binoculars, microscopes, many animals, including humans, have two eyes with overlapping visual fields that use parallax to gain depth perception, this process is known as stereopsis. In computer vision the effect is used for stereo vision, and there is a device called a parallax rangefinder that uses it to find range. A simple everyday example of parallax can be seen in the dashboard of motor vehicles that use a needle-style speedometer gauge. When viewed from directly in front, the speed may show exactly 60, as the eyes of humans and other animals are in different positions on the head, they present different views simultaneously. This is the basis of stereopsis, the process by which the brain exploits the parallax due to the different views from the eye to gain depth perception, animals also use motion parallax, in which the animals move to gain different viewpoints. For example, pigeons bob their heads up and down to see depth, the motion parallax is exploited also in wiggle stereoscopy, computer graphics which provide depth cues through viewpoint-shifting animation rather than through binocular vision. Parallax arises due to change in viewpoint occurring due to motion of the observer, of the observed, what is essential is relative motion. By observing parallax, measuring angles, and using geometry, one can determine distance, astronomers also use the word parallax as a synonym for distance measurent by other methods, see parallax #Astronomy. In a geostatic model, the movement of the star would have to be taken as real with the star oscillating across the sky with respect to the background stars, the parsec is defined as the distance for which the annual parallax is 1 arcsecond. Annual parallax is measured by observing the position of a star at different times of the year as the 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. Stellar parallax remains the standard for calibrating other measurement methods, accurate calculations of distance based on stellar parallax require a measurement of the distance from the Earth to the Sun, now based on radar reflection off the surfaces of planets. 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, the fact that stellar parallax was so small that it was unobservable at the time was used as the main scientific argument against heliocentrism during the early modern age. In 1989, the satellite Hipparcos was launched primarily for obtaining improved parallaxes and proper motions for over 100,000 nearby stars, increasing the reach of the method tenfold
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Earth radii
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Earth radius is the distance from the Earths center to its surface, about 6,371 km. This length is used as a unit of distance, especially in astronomy and geology. This article deals primarily with spherical and ellipsoidal models of the Earth, see Figure of the Earth for a more complete discussion of the models. The Earth is only approximately spherical, so no single value serves as its natural radius, distances from points on the surface to the center range from 6,353 km to 6,384 km. Several different ways of modeling the Earth as a sphere each yield a mean radius of 6,371 km. It can also mean some kind of average of such distances, Aristotle, writing in On the Heavens around 350 BC, reports that the mathematicians guess the circumference of the Earth to be 400,000 stadia. Due to uncertainty about which stadion variant Aristotle meant, scholars have interpreted Aristotles figure to be anywhere from highly accurate to almost double the true value, the first known scientific measurement and calculation of the radius of the Earth was performed by Eratosthenes about 240 BC. Estimates of the accuracy of Eratosthenes’s measurement range from within 0. 5% to within 17%, as with Aristotles report, uncertainty in the accuracy of his measurement is due to modern uncertainty over which stadion definition he used. Earths rotation, internal density variations, and external tidal forces cause its shape to deviate systematically from a perfect sphere, local topography increases the variance, resulting in a surface of profound complexity. Our descriptions of the Earths surface must be simpler than reality in order to be tractable, hence, we create models to approximate characteristics of the Earths surface, generally relying on the simplest model that suits the need. Each of the models in use involve some notion of the geometric radius. Strictly speaking, spheres are the solids to have radii. In the case of the geoid and ellipsoids, the distance from any point on the model to the specified center is called a radius of the Earth or the radius of the Earth at that point. It is also common to refer to any mean radius of a model as the radius of the earth. When considering the Earths real surface, on the hand, it is uncommon to refer to a radius. Rather, elevation above or below sea level is useful, regardless of the model, any radius falls between the polar minimum of about 6,357 km and the equatorial maximum of about 6,378 km. Hence, the Earth deviates from a sphere by only a third of a percent. While specific values differ, the concepts in this article generalize to any major planet