Triton is the largest natural satellite of the planet Neptune, the first Neptunian moon to be discovered. The discovery was made on October 1846, by English astronomer William Lassell, it is the only large moon in the Solar System with a retrograde orbit, an orbit in the direction opposite to its planet's rotation. At 2,710 kilometres in diameter, it is the seventh-largest moon in the Solar System, the only satellite of Neptune massive enough to be in hydrostatic equilibrium and the second-largest planetary moon in relation to its primary, after Earth's Moon; because of its retrograde orbit and composition similar to Pluto's, Triton is thought to have been a dwarf planet captured from the Kuiper belt. It has a surface of frozen nitrogen, a water-ice crust, an icy mantle and a substantial core of rock and metal; the core makes up two-thirds of its total mass. The mean density is 2.061 g/cm3, reflecting a composition of 15–35% water ice. Triton is one of the few moons in the Solar System known to be geologically active.
As a consequence, its surface is young, with few obvious impact craters. Intricate cryovolcanic and tectonic terrains suggest a complex geological history. Part of its surface has geysers erupting sublimated nitrogen gas, contributing to a tenuous nitrogen atmosphere less than 1/70,000 the pressure of Earth's atmosphere at sea level. Triton was discovered by British astronomer William Lassell on October 10, 1846, just 17 days after the discovery of Neptune, he discovered Triton with 61 cm telescope. A brewer by trade, Lassell began making mirrors for his amateur telescope in 1820; when John Herschel received news of Neptune's discovery, he wrote to Lassell suggesting he search for possible moons. Lassell discovered Triton eight days later. Lassell claimed to have discovered rings. Although Neptune was confirmed to have rings, they are so faint and dark that it is doubtful that he saw them. Triton is named after the son of Poseidon; the name was first proposed by Camille Flammarion in his 1880 book Astronomie Populaire, was adopted many decades later.
Until the discovery of the second moon Nereid in 1949, Triton was referred to as "the satellite of Neptune". Lassell did not name his own discovery. Triton is unique among all large moons in the Solar System for its retrograde orbit around its planet. Most of the outer irregular moons of Jupiter and Saturn have retrograde orbits, as do some of Uranus's outer moons. However, these moons are all much more distant from their primaries, are small in comparison. Triton's orbit is associated with two tilts, the obliquity of Neptune's spin to Neptune's orbit, 30°, the inclination of Triton's orbit to Neptune's spin, 157°. Triton's orbit precesses forward relative to Neptune's spin with a period of about 678 Earth years, making its Neptune-orbit-relative inclination vary between 127° and 180° and in the past, to 173°; that inclination is 130°. Triton's rotation is tidally locked to be synchronous with its orbit around Neptune: it keeps one face oriented toward the planet at all times, its equator is exactly aligned with its orbital plane.
At the present time, Triton's rotational axis is about 40° from Neptune's orbital plane, hence at some point during Neptune's year each pole points close to the Sun like the poles of Uranus. As Neptune orbits the Sun, Triton's polar regions take turns facing the Sun, resulting in seasonal changes as one pole the other, moves into the sunlight; such changes were observed in 2010. Triton's revolution around Neptune has become a nearly perfect circle with an eccentricity of zero. Viscoelastic damping from tides alone is not thought to be capable of circularizing Triton's orbit in the time since the origin of the system, gas drag from a prograde debris disc is to have played a substantial role. Tidal interactions cause Triton's orbit, closer to Neptune than the Moon's is to Earth, to decay further; this will result in either a collision with Neptune's atmosphere or the breakup of Triton, forming a new ring system similar to that found around Saturn. Moons in retrograde orbits cannot form in the same region of the solar nebula as the planets they orbit, so Triton must have been captured from elsewhere.
It might therefore have originated in the Kuiper belt, a ring of small icy objects extending from just inside the orbit of Neptune to about 50 AU from the Sun. Thought to be the point of origin for the majority of short-period comets observed from Earth, the belt is home to several large, planet-like bodies including Pluto, now recognized as the largest in a population of Kuiper belt objects locked in orbital step with Neptune. Triton is only larger than Pluto and nearly identical in composition, which has led to the hypothesis that the two share a common origin; the proposed capture of Triton may explain several features of the Neptunian system, including the eccentric orbit of Neptune's moon Nereid and the scarcity of moons as compar
The Eiffel Tower is a wrought-iron lattice tower on the Champ de Mars in Paris, France. It is built the tower. Constructed from 1887 to 1889 as the entrance to the 1889 World's Fair, it was criticised by some of France's leading artists and intellectuals for its design, but it has become a global cultural icon of France and one of the most recognisable structures in the world; the Eiffel Tower is the most-visited paid monument in the world. The tower is 324 metres tall, about the same height as an 81-storey building, the tallest structure in Paris, its base is square. During its construction, the Eiffel Tower surpassed the Washington Monument to become the tallest man-made structure in the world, a title it held for 41 years until the Chrysler Building in New York City was finished in 1930. Due to the addition of a broadcasting aerial at the top of the tower in 1957, it is now taller than the Chrysler Building by 5.2 metres. Excluding transmitters, the Eiffel Tower is the second tallest free-standing structure in France after the Millau Viaduct.
The tower has three levels for visitors, with restaurants on the second levels. The top level's upper platform is 276 m above the ground – the highest observation deck accessible to the public in the European Union. Tickets can be purchased to lift to the first and second levels; the climb from ground level to the first level is over 300 steps, as is the climb from the first level to the second. Although there is a staircase to the top level, it is accessible only by lift; the design of the Eiffel Tower is attributed to Maurice Koechlin and Émile Nouguier, two senior engineers working for the Compagnie des Établissements Eiffel. It was envisioned after discussion about a suitable centrepiece for the proposed 1889 Exposition Universelle, a world's fair to celebrate the centennial of the French Revolution. Eiffel acknowledged that inspiration for a tower came from the Latting Observatory built in New York City in 1853. In May 1884, working at home, Koechlin made a sketch of their idea, described by him as "a great pylon, consisting of four lattice girders standing apart at the base and coming together at the top, joined together by metal trusses at regular intervals".
Eiffel showed little enthusiasm, but he did approve further study, the two engineers asked Stephen Sauvestre, the head of company's architectural department, to contribute to the design. Sauvestre added decorative arches to the base of the tower, a glass pavilion to the first level, other embellishments; the new version gained Eiffel's support: he bought the rights to the patent on the design which Koechlin and Sauvestre had taken out, the design was exhibited at the Exhibition of Decorative Arts in the autumn of 1884 under the company name. On 30 March 1885, Eiffel presented his plans to the Société des Ingénieurs Civils. Little progress was made until 1886, when Jules Grévy was re-elected as president of France and Édouard Lockroy was appointed as minister for trade. A budget for the exposition was passed and, on 1 May, Lockroy announced an alteration to the terms of the open competition being held for a centrepiece to the exposition, which made the selection of Eiffel's design a foregone conclusion, as entries had to include a study for a 300 m four-sided metal tower on the Champ de Mars..
On 12 May, a commission was set up to examine Eiffel's scheme and its rivals, which, a month decided that all the proposals except Eiffel's were either impractical or lacking in details. After some debate about the exact location of the tower, a contract was signed on 8 January 1887; this was signed by Eiffel acting in his own capacity rather than as the representative of his company, granted him 1.5 million francs toward the construction costs: less than a quarter of the estimated 6.5 million francs. Eiffel was to receive all income from the commercial exploitation of the tower during the exhibition and for the next 20 years, he established a separate company to manage the tower, putting up half the necessary capital himself. The proposed tower had been a subject of controversy, drawing criticism from those who did not believe it was feasible and those who objected on artistic grounds; these objections were an expression of a long-standing debate in France about the relationship between architecture and engineering.
It came to a head as work began at the Champ de Mars: a "Committee of Three Hundred" was formed, led by the prominent architect Charles Garnier and including some of the most important figures of the arts, such as Adolphe Bouguereau, Guy de Maupassant, Charles Gounod and Jules Massenet. A petition called "Artists against the Eiffel Tower" was sent to the Minister of Works and Commissioner for the Exposition, Charles Alphand, it was published by Le Temps on 14 February 1887: We, painters, sculptors and passionate devotees of the hitherto untouched beauty of Paris, protest with all our strength, with all our indignation in the name
Hubble Space Telescope
The Hubble Space Telescope is a space telescope, launched into low Earth orbit in 1990 and remains in operation. Although not the first space telescope, Hubble is one of the largest and most versatile and is well known as both a vital research tool and a public relations boon for astronomy; the HST is named after the astronomer Edwin Hubble and is one of NASA's Great Observatories, along with the Compton Gamma Ray Observatory, the Chandra X-ray Observatory and the Spitzer Space Telescope. With a 2.4-meter mirror, Hubble's four main instruments observe in the ultraviolet and near infrared regions of the electromagnetic spectrum. Hubble's orbit outside the distortion of Earth's atmosphere allows it to take high-resolution images, with lower background light than ground-based telescopes. Hubble has recorded some of the most detailed visible light images allowing a deep view into space and time. Many Hubble observations have led to breakthroughs in astrophysics, such as determining the rate of expansion of the universe.
The HST was built by the United States space agency NASA, with contributions from the European Space Agency. The Space Telescope Science Institute selects Hubble's targets and processes the resulting data, while the Goddard Space Flight Center controls the spacecraft. Space telescopes were proposed as early as 1923. Hubble was funded in the 1970s, with a proposed launch in 1983, but the project was beset by technical delays, budget problems, the Challenger disaster; when launched in 1990, Hubble's main mirror was found to have been ground incorrectly, creating a spherical aberration, compromising the telescope's capabilities. The optics were corrected to their intended quality by a servicing mission in 1993. Hubble is the only telescope designed to be serviced in space by astronauts. After launch by Space Shuttle Discovery in 1990, five subsequent Space Shuttle missions repaired and replaced systems on the telescope, including all five of the main instruments; the fifth mission was canceled on safety grounds following the Columbia disaster.
However, after spirited public discussion, NASA administrator Mike Griffin approved the fifth servicing mission, completed in 2009. The telescope is operating as of 2019, could last until 2030–2040. After numerous delays, its successor, the James Webb Space Telescope, is scheduled to be launched in March 2021. In 1923, Hermann Oberth—considered a father of modern rocketry, along with Robert H. Goddard and Konstantin Tsiolkovsky—published Die Rakete zu den Planetenräumen, which mentioned how a telescope could be propelled into Earth orbit by a rocket; the history of the Hubble Space Telescope can be traced back as far as 1946, to the astronomer Lyman Spitzer's paper "Astronomical advantages of an extraterrestrial observatory". In it, he discussed the two main advantages that a space-based observatory would have over ground-based telescopes. First, the angular resolution would be limited only by diffraction, rather than by the turbulence in the atmosphere, which causes stars to twinkle, known to astronomers as seeing.
At that time ground-based telescopes were limited to resolutions of 0.5–1.0 arcseconds, compared to a theoretical diffraction-limited resolution of about 0.05 arcsec for a telescope with a mirror 2.5 m in diameter. Second, a space-based telescope could observe infrared and ultraviolet light, which are absorbed by the atmosphere. Spitzer devoted much of his career to pushing for the development of a space telescope. In 1962, a report by the US National Academy of Sciences recommended the development of a space telescope as part of the space program, in 1965 Spitzer was appointed as head of a committee given the task of defining scientific objectives for a large space telescope. Space-based astronomy had begun on a small scale following World War II, as scientists made use of developments that had taken place in rocket technology; the first ultraviolet spectrum of the Sun was obtained in 1946, the National Aeronautics and Space Administration launched the Orbiting Solar Observatory to obtain UV, X-ray, gamma-ray spectra in 1962.
An orbiting solar telescope was launched in 1962 by the United Kingdom as part of the Ariel space program, in 1966 NASA launched the first Orbiting Astronomical Observatory mission. OAO-1's battery failed after three days, it was followed by OAO-2, which carried out ultraviolet observations of stars and galaxies from its launch in 1968 until 1972, well beyond its original planned lifetime of one year. The OSO and OAO missions demonstrated the important role space-based observations could play in astronomy, in 1968, NASA developed firm plans for a space-based reflecting telescope with a mirror 3 m in diameter, known provisionally as the Large Orbiting Telescope or Large Space Telescope, with a launch slated for 1979; these plans emphasized the need for manned maintenance missions to the telescope to ensure such a costly program had a lengthy working life, the concurrent development of plans for the reusable Space Shuttle indicated that the technology to allow this was soon to become available.
The continuing success of the OAO program encouraged strong consensus within the astronomical community that the LST should be a major goal. In 1970, NASA established two committees, one to plan the engineering side of the space telescope project, the other to determine the scientific goals of the mission. Once these had been established, the next hurdle for NASA was to obtain funding for the instrument, which would be far more costly than any Earth-bas
Navigation is a field of study that focuses on the process of monitoring and controlling the movement of a craft or vehicle from one place to another. The field of navigation includes four general categories: land navigation, marine navigation, aeronautic navigation, space navigation, it is the term of art used for the specialized knowledge used by navigators to perform navigation tasks. All navigational techniques involve locating the navigator's position compared to known locations or patterns. Navigation, in a broader sense, can refer to any skill or study that involves the determination of position and direction. In this sense, navigation includes pedestrian navigation. In the European medieval period, navigation was considered part of the set of seven mechanical arts, none of which were used for long voyages across open ocean. Polynesian navigation is the earliest form of open-ocean navigation, it was based on memory and observation recorded on scientific instruments like the Marshall Islands Stick Charts of Ocean Swells.
Early Pacific Polynesians used the motion of stars, the position of certain wildlife species, or the size of waves to find the path from one island to another. Maritime navigation using scientific instruments such as the mariner's astrolabe first occurred in the Mediterranean during the Middle Ages. Although land astrolabes were invented in the Hellenistic period and existed in classical antiquity and the Islamic Golden Age, the oldest record of a sea astrolabe is that of Majorcan astronomer Ramon Llull dating from 1295; the perfecting of this navigation instrument is attributed to Portuguese navigators during early Portuguese discoveries in the Age of Discovery. The earliest known description of how to make and use a sea astrolabe comes from Spanish cosmographer Martín Cortés de Albacar's Arte de Navegar published in 1551, based on the principle of the archipendulum used in constructing the Egyptian pyramids. Open-seas navigation using the astrolabe and the compass started during the Age of Discovery in the 15th century.
The Portuguese began systematically exploring the Atlantic coast of Africa from 1418, under the sponsorship of Prince Henry. In 1488 Bartolomeu Dias reached the Indian Ocean by this route. In 1492 the Spanish monarchs funded Christopher Columbus's expedition to sail west to reach the Indies by crossing the Atlantic, which resulted in the Discovery of the Americas. In 1498, a Portuguese expedition commanded by Vasco da Gama reached India by sailing around Africa, opening up direct trade with Asia. Soon, the Portuguese sailed further eastward, to the Spice Islands in 1512, landing in China one year later; the first circumnavigation of the earth was completed in 1522 with the Magellan-Elcano expedition, a Spanish voyage of discovery led by Portuguese explorer Ferdinand Magellan and completed by Spanish navigator Juan Sebastián Elcano after the former's death in the Philippines in 1521. The fleet of seven ships sailed from Sanlúcar de Barrameda in Southern Spain in 1519, crossed the Atlantic Ocean and after several stopovers rounded the southern tip of South America.
Some ships were lost, but the remaining fleet continued across the Pacific making a number of discoveries including Guam and the Philippines. By only two galleons were left from the original seven; the Victoria led by Elcano sailed across the Indian Ocean and north along the coast of Africa, to arrive in Spain in 1522, three years after its departure. The Trinidad sailed east from the Philippines, trying to find a maritime path back to the Americas, but was unsuccessful; the eastward route across the Pacific known as the tornaviaje was only discovered forty years when Spanish cosmographer Andrés de Urdaneta sailed from the Philippines, north to parallel 39°, hit the eastward Kuroshio Current which took its galleon across the Pacific. He arrived in Acapulco on October 8, 1565; the term stems from the 1530s, from Latin navigationem, from navigatus, pp. of navigare "to sail, sail over, go by sea, steer a ship," from navis "ship" and the root of agere "to drive". The latitude of a place on Earth is its angular distance north or south of the equator.
Latitude is expressed in degrees ranging from 0° at the Equator to 90° at the North and South poles. The latitude of the North Pole is 90° N, the latitude of the South Pole is 90° S. Mariners calculated latitude in the Northern Hemisphere by sighting the North Star Polaris with a sextant and using sight reduction tables to correct for height of eye and atmospheric refraction; the height of Polaris in degrees above the horizon is the latitude of the observer, within a degree or so. Similar to latitude, the longitude of a place on Earth is the angular distance east or west of the prime meridian or Greenwich meridian. Longitude is expressed in degrees ranging from 0° at the Greenwich meridian to 180° east and west. Sydney, for example, has a longitude of about 151° east. New York City has a longitude of 74° west. For most of history, mariners struggled to determine longitude. Longitude can be calculated. Lacking that, one can use a sextant to take a lunar distance that, with a nautical almanac, can be used to calculate the time at zero longitude.
Reliable marine chronometers were unavailable until the late 18th century and not affordable until the 19th century. For about a hundred years, from about 1767 until about 1850, mariners lacking a chronometer used the method of lunar distances to determine Greenwich time to find their longitude. A mariner with a chronometer could check its reading using a lunar determination of Greenwich tim
The Moon is an astronomical body that orbits planet Earth and is Earth's only permanent natural satellite. It is the fifth-largest natural satellite in the Solar System, the largest among planetary satellites relative to the size of the planet that it orbits; the Moon is after Jupiter's satellite Io the second-densest satellite in the Solar System among those whose densities are known. The Moon is thought to have formed not long after Earth; the most accepted explanation is that the Moon formed from the debris left over after a giant impact between Earth and a Mars-sized body called Theia. The Moon is in synchronous rotation with Earth, thus always shows the same side to Earth, the near side; the near side is marked by dark volcanic maria that fill the spaces between the bright ancient crustal highlands and the prominent impact craters. After the Sun, the Moon is the second-brightest visible celestial object in Earth's sky, its surface is dark, although compared to the night sky it appears bright, with a reflectance just higher than that of worn asphalt.
Its gravitational influence produces the ocean tides, body tides, the slight lengthening of the day. The Moon's average orbital distance is 1.28 light-seconds. This is about thirty times the diameter of Earth; the Moon's apparent size in the sky is the same as that of the Sun, since the star is about 400 times the lunar distance and diameter. Therefore, the Moon covers the Sun nearly during a total solar eclipse; this matching of apparent visual size will not continue in the far future because the Moon's distance from Earth is increasing. The Moon was first reached in September 1959 by an unmanned spacecraft; the United States' NASA Apollo program achieved the only manned lunar missions to date, beginning with the first manned orbital mission by Apollo 8 in 1968, six manned landings between 1969 and 1972, with the first being Apollo 11. These missions returned lunar rocks which have been used to develop a geological understanding of the Moon's origin, internal structure, the Moon's history. Since the Apollo 17 mission in 1972, the Moon has been visited only by unmanned spacecraft.
Both the Moon's natural prominence in the earthly sky and its regular cycle of phases as seen from Earth have provided cultural references and influences for human societies and cultures since time immemorial. Such cultural influences can be found in language, lunar calendar systems and mythology; the usual English proper name for Earth's natural satellite is "the Moon", which in nonscientific texts is not capitalized. The noun moon is derived from Old English mōna, which stems from Proto-Germanic *mēnô, which comes from Proto-Indo-European *mḗh₁n̥s "moon", "month", which comes from the Proto-Indo-European root *meh₁- "to measure", the month being the ancient unit of time measured by the Moon; the name "Luna" is used. In literature science fiction, "Luna" is used to distinguish it from other moons, while in poetry, the name has been used to denote personification of Earth's moon; the modern English adjective pertaining to the Moon is lunar, derived from the Latin word for the Moon, luna. The adjective selenic is so used to refer to the Moon that this meaning is not recorded in most major dictionaries.
It is derived from the Ancient Greek word for the Moon, σελήνη, from, however derived the prefix "seleno-", as in selenography, the study of the physical features of the Moon, as well as the element name selenium. Both the Greek goddess Selene and the Roman goddess Diana were alternatively called Cynthia; the names Luna and Selene are reflected in terminology for lunar orbits in words such as apolune and selenocentric. The name Diana comes from the Proto-Indo-European *diw-yo, "heavenly", which comes from the PIE root *dyeu- "to shine," which in many derivatives means "sky and god" and is the origin of Latin dies, "day"; the Moon formed 4.51 billion years ago, some 60 million years after the origin of the Solar System. Several forming mechanisms have been proposed, including the fission of the Moon from Earth's crust through centrifugal force, the gravitational capture of a pre-formed Moon, the co-formation of Earth and the Moon together in the primordial accretion disk; these hypotheses cannot account for the high angular momentum of the Earth–Moon system.
The prevailing hypothesis is that the Earth–Moon system formed after an impact of a Mars-sized body with the proto-Earth. The impact blasted material into Earth's orbit and the material accreted and formed the Moon; the Moon's far side has a crust, 30 mi thicker than that of the near side. This is thought to be; this hypothesis, although not perfect best explains the evidence. Eighteen months prior to an October 1984 conference on lunar origins, Bill Hartmann, Roger Phillips, Jeff Taylor challenged fellow lunar scientists: "You have eighteen months. Go back to your Apollo data, go back to your computer, do whatever you have to, but make up your mind. Don't come to our conference unless you have something to say about the Moon's birth." At the 1984 conference at Kona, the giant impact hypothesis emerged as the most consensual theory. Before the conference, there were parti
A milliradian called a mil or mrad, is an SI derived unit for angular measurement, defined as a thousandth of a radian. Mils are used in adjustment of firearm sights by adjusting the angle of the sight compared to the barrel. Mils are used for comparing shot groupings, or to compare the difficulty of hitting different sized shooting targets at different distances; when using a scope with both mil adjustment and a reticle with mil markings, the shooter can use the reticle as a "ruler" to count the number of mils a shot was off target which directly translates to the sight adjustment needed to hit the target with a follow up shot. Optics with mil markings in the reticle can be used to make a range estimation of a known size target, or vice versa to determine a target size if the distance is known, a practice called "milling". Milliradians are used for small angles, which allows for precise mathematical simplifications to more calculate back and forth between the angular separation observed in an optic, linear subtension on target and range.
In such applications it is useful to use a unit for target size, a thousandth of the unit for range, for instance by using the metric units millimeters for target size and meters for range. This coincides with the definition of the milliradian where the arc length is defined as 1/1000 of the radius. A common adjustment value in firearm sights is 1 cm at 100 meters which equals 10 mm/100 m = 1/10 mil; the true definition of a milliradian is based on a unit circle with a radius of one and an arc divided into 1000 mils per radian, hence 2000π or 6283.185 milliradians in one turn, rifle scope adjustments and reticles are calibrated to this definition. There are other definitions used for land mapping and artillery which are rounded to more be divided into smaller parts for use with compasses. For instance there are artillery sights and compasses with 6400 NATO mils, 6000 Warsaw Pact mils or 6300 Swedish "streck" per turn instead of 360° or 2000π, achieving higher resolution than a 360° compass while being easier to divide into parts than if true milliradians were used.
The milliradian was first used in the mid nineteenth century by Charles-Marc Dapples, a Swiss engineer and professor at the University of Lausanne. Degrees and minutes were the usual units of angular measurement but others were being proposed, with "grads" under various names having considerable popularity in much of northern Europe. However, Imperial Russia used a different approach, dividing a circle into equilateral triangles and hence 600 units to a circle. Around the time of the start of World War I, France was experimenting with the use of milliemes for use with artillery sights instead of decigrades; the United Kingdom was trialing them to replace degrees and minutes. They were adopted by France although decigrades remained in use throughout World War I. Other nations used decigrades; the United States, which copied many French artillery practices, adopted mils. Before 2007 the Swedish defence forces used "streck", closer to the milliradian but changed to NATO mils. After the Bolshevik Revolution and the adoption of the metric system of measurement the Red Army expanded the 600 unit circle into a 6000 mil one.
Hence the Russian mil has a somewhat different origin than those derived from French artillery practices. In the 1950s, NATO adopted metric units of measurement for general use. Mils and kilograms became standard, although degrees remained in use for naval and air purposes, reflecting civil practices. Use of the milliradian is practical because it is concerned with small angles, when using radians the small angle approximation shows that the angle approximates to the sine of the angle, sin θ ≃ θ; this allows a user to dispense with trigonometry and use simple ratios to determine size and distance with high accuracy for rifle and short distance artillery calculations by using the handy property of subtension: One mil subtends one meter at a distance of one thousand meters. More in detail, because subtension ≃ arc length, instead of finding the angular distance denoted by θ by using the tangent function θ trig = arctan subtension range, one can instead make a good approximation by using the definition of a radian and the simplified formula: θ rad = subtension range Since a radian is mathematically defined as the angle formed when the length of a circular arc equals the radius of the circle, a milliradian, is the angle formed when the length of a circular arc equals 1/1000 of the radius of the circle.
Just like the radian, the milliradian is dimensionless, but unlike the radian where the same unit must be used for radius and arc length, the milliradian needs to have a ratio between the units where the subtension is a thousandth of the radius when using the simplified formula. The approximation error by using the simplified linear form
Astronomy is a natural science that studies celestial objects and phenomena. It applies mathematics and chemistry in an effort to explain the origin of those objects and phenomena and their evolution. Objects of interest include planets, stars, nebulae and comets. More all phenomena that originate outside Earth's atmosphere are within the purview of astronomy. A related but distinct subject is physical cosmology, the study of the Universe as a whole. Astronomy is one of the oldest of the natural sciences; the early civilizations in recorded history, such as the Babylonians, Indians, Nubians, Chinese and many ancient indigenous peoples of the Americas, performed methodical observations of the night sky. Astronomy has included disciplines as diverse as astrometry, celestial navigation, observational astronomy, the making of calendars, but professional astronomy is now considered to be synonymous with astrophysics. Professional astronomy is split into theoretical branches. Observational astronomy is focused on acquiring data from observations of astronomical objects, analyzed using basic principles of physics.
Theoretical astronomy is oriented toward the development of computer or analytical models to describe astronomical objects and phenomena. The two fields complement each other, with theoretical astronomy seeking to explain observational results and observations being used to confirm theoretical results. Astronomy is one of the few sciences in which amateurs still play an active role in the discovery and observation of transient events. Amateur astronomers have made and contributed to many important astronomical discoveries, such as finding new comets. Astronomy means "law of the stars". Astronomy should not be confused with astrology, the belief system which claims that human affairs are correlated with the positions of celestial objects. Although the two fields share a common origin, they are now distinct. Both of the terms "astronomy" and "astrophysics" may be used to refer to the same subject. Based on strict dictionary definitions, "astronomy" refers to "the study of objects and matter outside the Earth's atmosphere and of their physical and chemical properties," while "astrophysics" refers to the branch of astronomy dealing with "the behavior, physical properties, dynamic processes of celestial objects and phenomena."
In some cases, as in the introduction of the introductory textbook The Physical Universe by Frank Shu, "astronomy" may be used to describe the qualitative study of the subject, whereas "astrophysics" is used to describe the physics-oriented version of the subject. However, since most modern astronomical research deals with subjects related to physics, modern astronomy could be called astrophysics; some fields, such as astrometry, are purely astronomy rather than astrophysics. Various departments in which scientists carry out research on this subject may use "astronomy" and "astrophysics" depending on whether the department is affiliated with a physics department, many professional astronomers have physics rather than astronomy degrees; some titles of the leading scientific journals in this field include The Astronomical Journal, The Astrophysical Journal, Astronomy and Astrophysics. In early historic times, astronomy only consisted of the observation and predictions of the motions of objects visible to the naked eye.
In some locations, early cultures assembled massive artifacts that had some astronomical purpose. In addition to their ceremonial uses, these observatories could be employed to determine the seasons, an important factor in knowing when to plant crops and in understanding the length of the year. Before tools such as the telescope were invented, early study of the stars was conducted using the naked eye; as civilizations developed, most notably in Mesopotamia, Persia, China and Central America, astronomical observatories were assembled and ideas on the nature of the Universe began to develop. Most early astronomy consisted of mapping the positions of the stars and planets, a science now referred to as astrometry. From these observations, early ideas about the motions of the planets were formed, the nature of the Sun and the Earth in the Universe were explored philosophically; the Earth was believed to be the center of the Universe with the Sun, the Moon and the stars rotating around it. This is known as the geocentric model of the Ptolemaic system, named after Ptolemy.
A important early development was the beginning of mathematical and scientific astronomy, which began among the Babylonians, who laid the foundations for the astronomical traditions that developed in many other civilizations. The Babylonians discovered. Following the Babylonians, significant advances in astronomy were made in ancient Greece and the Hellenistic world. Greek astronomy is characterized from the start by seeking a rational, physical explanation for celestial phenomena. In the 3rd century BC, Aristarchus of Samos estimated the size and distance of the Moon and Sun, he proposed a model of the Solar System where the Earth and planets rotated around the Sun, now called the heliocentric model. In the 2nd century BC, Hipparchus discovered precession, calculated the size and distance of the Moon and inven