Meta tags:

Headings (most frequently used words):

in, azimuth, contents, etymology, astronomy, navigation, geodesy, cartography, related, coordinates, other, uses, see, also, references, further, reading, external, links, true, north, based, azimuths, map, projections, right, ascension, polar, coordinate,

Text of the page (most frequently used words):
the (153), #azimuth (53), and (36), from (30), angle (24), edit (19), tan (18), #reference (17), north (17), direction (16), navigation (15), plane (13), are (12), sin (12), for (11), coordinates (11), varphi (11), arabic (10), horizontal (10), orbit (10), can (10), between (10), vector (10), displaystyle (10), wikipedia (9), other (9), point (9), measured (9), right (9), with (8), coordinate (8), astronomy (8), that (8), used (8), alpha (8), cos (8), this (7), system (7), army (7), map (7), orbital (7), degrees (7), south (7), use (6), articles (6), reading (6), see (6), bearing (6), also (6), earth (6), clockwise (6), frac (6), 180 (6), left (6), main (6), toggle (5), page (5), links (5), geodesy (5), sumūt (5), orbits (5), celestial (5), surface (5), true (5), azimuthal (5), projection (5), positive (5), one (5), atan2 (5), east (5), article (5), contents (4), search (4), citation (4), encyclopedia (4), cartography (4), headquarters (4), washington (4), always (4), points (4), sphere (4), two (4), axis (4), relative (4), longitude (4), line (4), than (4), polar (4), hour (4), related (4), projections (4), directions (4), azimuths (4), any (4), defined (4), aligned (4), problem (4), star (4), spheroid (4), usually (4), zero (4), stated (4), observer (4), hide (4), move (4), sidebar (4), view (3), may (3), using (3), was (3), pages (3), different (3), dictionary (3), route (3), finder (3), land (3), samt (3), english (3), equation (3), engineering (3), transfer (3), eccentricity (3), sound (3), declination (3), latitude (3), altitude (3), area (3), tape (3), uses (3), spherical (3), instead (3), along (3), called (3), ascension (3), some (3), when (3), known (3), its (3), swapped (3), normal (3), formula (3), slightly (3), 360 (3), commonly (3), section (3), has (3), our (3), viewpoint (3), geodesic (3), which (3), changes (3), inverse (3), first (3), cardinal (3), interest (3), projected (3), tools (3), subsection (3), add (2), languages (2), table (2), contact (2), about (2), privacy (2), policy (2), text (2), terms (2), wikimedia (2), commons (2), last (2), categories (2), incorporating (2), collier (2), 1911 (2), britannica (2), unsourced (2), statements (2), january (2), 2022 (2), all (2), wayback (2), language (2), recorded (2), short (2), description (2), wikidata (2), org (2), national (2), mathematics (2), new (2), free (2), external (2), rutstrum (2), carl (2), university (2), minnesota (2), press (2), 2000 (2), 8166 (2), 3661 (2), isbn (2), wilderness (2), further (2), war (2), department (2), advanced (2), aerial (2), photograph (2), dept (2), pronounced (2), com (2), lit (2), romanized (2), references (2), gravity (2), efficiency (2), mass (2), fraction (2), body (2), mechanics (2), specific (2), velocity (2), kepler (2), elliptic (2), circular (2), anomaly (2), inclination (2), zenith (2), localization (2), magnetic (2), position (2), angular (2), refers (2), head (2), anticlockwise (2), onto (2), special (2), case (2), rather (2), denoted (2), radians (2), cylindrical (2), horizon (2), angles (2), referenced (2), meridian (2), same (2), there (2), systems (2), long (2), clearly (2), typically (2), begin (2), end (2), distance (2), calculate (2), operatorname (2), above (2), calculated (2), cartographical (2), compass (2), given (2), difference (2), needed (2), chosen (2), then (2), lambda (2), approximation (2), shortest (2), less (2), ellipsoidal (2), geodetic (2), eastward (2), get (2), formulae (2), 270 (2), western (2), side (2), based (2), example (2), west (2), base (2), word (2), medieval (2), version (2), astrolabe (2), astronomical (2), etymology (2), range (2), local (2), appearance (2), upload (2), file (2), history (2), read (2), norsk (2), bahasa (2), log (2), create (2), account (2), donate (2), menu (2), topic, mobile, cookie, statement, statistics, developers, code, conduct, legal, safety, contacts, disclaimers, available, under, additional, apply, site, you, agree, registered, trademark, non, profit, organization, foundation, inc, creative, attribution, sharealike, license, rendered, parsoid, edited, june, 2026, utc, hidden, encyclopaedia, wikisource, webarchive, template, containing, including, pronunciations, phonos, extension, dmy, dates, july, surveying, retrieved, https, index, php, title, oldid, 1358525893, yale, lux, nara, israel, bnf, data, france, united, states, gnd, international, authority, control, databases, science, outer, space, spaceflight, stars, geography, portals, easycalculator, calculator, 1921, 11th, encyclopædia, look, wiktionary, torge, müller, 2012, gruyter, 248, december, 1944, september, 1941, march, 1956, 1993, 194, azimut, written, pronunciation, machine, 2014, archived, englishwordsofarabicancestry, wordpress, brill, islam, centre, ressources, textuelles, lexicales, historical, principles, online, unabridged, singular, form, noun, السَّمْت, insertion, maneuver, propulsive, maneuvers, oberth, effect, assist, measures, tsiolkovsky, rocket, propellant, payload, ratio, preflight, lyapunov, lissajous, halo, lagrangian, influence, perturbations, hill, barycenter, gravitational, influences, vis, viva, energy, period, laws, planetary, motion, escape, dynamical, friction, equations, decaying, radial, hyperbolic, parabolic, hohmann, types, semi, major, nodes, mean, argument, periapsis, apsis, elements, astrodynamics, part, series, solar, sextant, panning, camera, course, clock, recording, equidistant, quantum, number, angzarr, displacement, rotated, horizontally, propeller, shipbuilding, thruster, experiments, literature, source, makes, compared, imaginary, straight, drawn, within, through, eyes, drives, component, although, normally, measuring, vernal, equinox, equator, comparison, centred, scale, ordered, radii, click, detail, wide, variety, they, have, property, central, preserved, however, serve, everyone, identification, azid, especially, applications, radar, triangulation, opposite, occurs, another, note, contrast, input, order, would, easier, remark, axes, counterclockwise, mathematical, why, becomes, negative, decimal, flat, grid, standard, brunton, geo, geologists, surveyors, measure, sun, location, modify, replace, change, sign, since, westward, where, flattening, wgs84, 298, 257, 563, 223, sqrt, follows, better, assumes, squashed, least, very, meanings, whose, perpendicular, path, negligible, arc, second, distances, 100, theodolite, oblate, standing, want, find, fair, assuming, 141, miller, orthographic, melbourne, cape, town, geographical, vincenty, paths, 337, nnw, 315, 292, wnw, 247, wsw, 225, 202, ssw, 157, sse, 135, 112, ese, ene, nne, eastern, quite, bearings, either, might, described, turn, thirty, toward, words, brackets, omitted, abbreviated, s30, 150, turning, them, happens, exactly, notation, due, today, though, units, moving, degree, circle, exceptions, mil, grad, been, more, generally, fixed, easily, established, marker, mount, allen, southern, california, sandstone, peak, sometimes, elevation, installation, modern, nearly, sat, satellite, dish, originates, meaning, plural, entered, late, context, particular, instrument, 1390s, record, spanish, 1270s, book, largely, derived, sources, commissioned, castile, king, alfonso, libros, del, saber, astronomía, treatise, geoffrey, chaucer, latin, السمت, السموت, signed, concept, ballistics, mining, mapping, radius, around, sea, level, sky, object, mathematically, perpendicularly, origin, most, centric, اَلسُّمُوت, formed, orthogonal, disambiguation, item, projects, printable, download, pdf, print, export, switch, legacy, parser, shortened, url, cite, information, permanent, link, what, here, general, actions, talk, tiếng, việt, oʻzbekcha, ўзбекча, اردو, українська, татарча, tatarça, türkçe, tagalog, ไทย, тоҷикӣ, தமிழ், svenska, српски, srpski, shqip, slovenščina, srpskohrvatski, српскохрватски, سنڌي, саха, тыла, русский, română, português, پښتو, piemontèis, polski, bokmål, nynorsk, nederlands, melayu, монгол, മലയാളം, македонски, мокшень, latviešu, lietuvių, lëtzebuergesch, кыргызча, 한국어, қазақша, ქართული, 日本語, italiano, íslenska, ido, indonesia, հայերեն, magyar, hrvatski, हिन्दी, עברית, galego, gaeilge, français, suomi, فارسی, estremeñu, euskara, eesti, español, esperanto, ελληνικά, deutsch, словѣньскъ, ⱄⰾⱁⰲⱑⱀⱐⱄⰽⱏ, kaszëbsczi, čeština, کوردی, català, বাংলা, български, беларуская, башҡортса, azərbaycanca, asturianu, العربية, alemannisch, afrikaans, top, personal, recent, community, portal, learn, help, contribute, random, current, events, jump, content,

Text of the page (random words):
navigation subsection 3 1 true north based azimuths 4 in geodesy 5 in cartography toggle in cartography subsection 5 1 map projections 6 related coordinates toggle related coordinates subsection 6 1 right ascension 6 2 polar coordinate 7 other uses 8 see also 9 references 10 further reading 11 external links toggle the table of contents azimuth 78 languages afrikaans alemannisch العربية asturianu azərbaycanca башҡортса беларуская български বাংলা català کوردی čeština kaszëbsczi словѣньскъ ⱄⰾⱁⰲⱑⱀⱐⱄⰽⱏ deutsch ελληνικά esperanto español eesti euskara estremeñu فارسی suomi français gaeilge galego עברית हिन्दी hrvatski magyar հայերեն bahasa indonesia ido íslenska italiano 日本語 ქართული қазақша 한국어 кыргызча lëtzebuergesch lietuvių latviešu мокшень македонски മലയാളം монгол bahasa melayu nederlands norsk nynorsk norsk bokmål polski piemontèis پښتو português română русский саха тыла سنڌي srpskohrvatski српскохрватски slovenščina shqip српски srpski svenska தமிழ் тоҷикӣ ไทย tagalog türkçe татарча tatarça українська اردو oʻzbekcha ўзбекча tiếng việt 吴语 文言 粵語 中文 edit links article talk english read edit view history tools tools move to sidebar hide actions read edit view history general what links here related changes upload file permanent link page information cite this page get shortened url switch to legacy parser print export download as pdf printable version in other projects wikimedia commons wikidata item appearance move to sidebar hide from wikipedia the free encyclopedia horizontal angle from north or other reference cardinal direction for other uses see azimuth disambiguation the azimuth is the angle formed between a reference direction in this example north and a line from the observer to a point of interest projected on the same plane as the reference direction orthogonal to the zenith an azimuth ˈ æ z ə m ə θ ⓘ from arabic اَلسُّمُوت romanized as sumūt lit the directions 1 is the horizontal angle from a cardinal direction most commonly north in a local or observer centric spherical coordinate system mathematically the relative position vector from an observer origin to a point of interest is projected perpendicularly onto a reference plane the horizontal plane the angle between the projected vector and a reference vector on the reference plane is called the azimuth when used as a celestial coordinate the azimuth is the horizontal direction of a star or other astronomical object in the sky the star is the point of interest the reference plane is the local area e g a circular area with a 5 km radius at sea level around an observer on earth s surface and the reference vector points to true north the azimuth is the angle between the north vector and the star s vector on the horizontal plane 2 azimuth is usually measured in degrees in the positive range 0 to 360 or in the signed range 180 to 180 the concept is used in navigation astronomy engineering mapping geodesy mining and ballistics etymology edit the word azimuth originates from medieval arabic السموت al sumūt pronounced as sumūt meaning the directions plural of arabic السمت al samt the direction the arabic word entered late medieval latin in an astronomical context and in particular in the use of the arabic version of the astrolabe astronomy instrument its first recorded use in english is in the 1390s in geoffrey chaucer s a treatise on the astrolabe the first known record in any western language is in spanish in the 1270s in an astronomy book that was largely derived from arabic sources the libros del saber de astronomía commissioned by king alfonso x of castile 3 in astronomy edit main article horizontal coordinate system in the horizontal coordinate system used in celestial navigation azimuth is one of the two coordinates 4 the other is altitude sometimes called elevation above the horizon it is also used for satellite dish installation see also sat finder in modern astronomy azimuth is nearly always measured from the north in navigation edit main article azimuth navigation azimuth marker mount allen sandstone peak southern california u s in land navigation azimuth is usually denoted alpha α and defined as a horizontal angle measured clockwise from a north base line or meridian 5 6 azimuth has also been more generally defined as a horizontal angle measured clockwise from any fixed reference plane or easily established base direction line 7 8 9 today the reference plane for an azimuth is typically true north measured as a 0 azimuth though other angular units grad mil can be used moving clockwise on a 360 degree circle east has azimuth 90 south 180 and west 270 there are exceptions some navigation systems use south as the reference vector any direction can be the reference vector as long as it is clearly defined quite commonly azimuths or compass bearings are stated in a system in which either north or south can be the zero and the angle may be measured clockwise or anticlockwise from the zero for example a bearing might be described as from south turn thirty degrees toward the east the words in brackets are usually omitted abbreviated s30 e which is the bearing 30 degrees in the eastward direction from south i e the bearing 150 degrees clockwise from north the reference direction stated first is always north or south and the turning direction stated last is east or west the directions are chosen so that the angle stated between them is positive between zero and 90 degrees if the bearing happens to be exactly in the direction of one of the cardinal points a different notation e g due east is used instead true north based azimuths edit from north eastern side direction azimuth n 0 nne 22 5 ne 45 ene 67 5 e 90 ese 112 5 se 135 sse 157 5 from north western side direction azimuth s 180 ssw 202 5 sw 225 wsw 247 5 w 270 wnw 292 5 nw 315 nnw 337 5 in geodesy edit main article inverse geodetic problem see also earth section paths inverse problem vincenty s formulae inverse problem and geographical distance ellipsoidal surface formulae the azimuth between cape town and melbourne along the geodesic the shortest route changes from 141 to 42 azimuthal orthographic projection and miller cylindrical projection we are standing at latitude φ 1 displaystyle varphi _ 1 longitude zero we want to find the azimuth from our viewpoint to point 2 at latitude φ 2 displaystyle varphi _ 2 longitude l positive eastward we can get a fair approximation by assuming the earth is a sphere in which case the azimuth α is given by tan α sin l cos φ 1 tan φ 2 sin φ 1 cos l displaystyle tan alpha frac sin l cos varphi _ 1 tan varphi _ 2 sin varphi _ 1 cos l a better approximation assumes the earth is a slightly squashed sphere an oblate spheroid azimuth then has at least two very slightly different meanings normal section azimuth is the angle measured at our viewpoint by a theodolite whose axis is perpendicular to the surface of the spheroid geodetic azimuth or geodesic azimuth is the angle between north and the ellipsoidal geodesic the shortest path on the surface of the spheroid from our viewpoint to point 2 the difference is usually negligible less than 0 03 arc second for distances less than 100 km 10 normal section azimuth can be calculated as follows citation needed e 2 f 2 f 1 e 2 1 f 2 λ 1 e 2 tan φ 2 tan φ 1 e 2 1 1 e 2 tan φ 2 2 1 1 e 2 tan φ 1 2 tan α sin l λ cos l sin φ 1 displaystyle begin aligned e 2 f 2 f 1 e 2 1 f 2 lambda left 1 e 2 right frac tan varphi _ 2 tan varphi _ 1 e 2 sqrt frac 1 left 1 e 2 right left tan varphi _ 2 right 2 1 left 1 e 2 right left tan varphi _ 1 right 2 tan alpha frac sin l lambda cos l sin varphi _ 1 end aligned where f is the flattening and e the eccentricity for the chosen spheroid e g 1 298 257 223 563 for wgs84 if φ 1 0 then tan α sin l 1 e 2 tan φ 2 displaystyle tan alpha frac sin l left 1 e 2 right tan varphi _ 2 to calculate the azimuth of the sun or a star given its declination and hour angle at a specific location modify the formula for a spherical earth replace φ 2 with declination and longitude difference with hour angle and change the sign since the hour angle is positive westward instead of east citation needed in cartography edit a standard brunton geo compass commonly used by geologists and surveyors to measure azimuth the cartographical azimuth or grid azimuth in decimal degrees can be calculated when the coordinates of two points are known in a flat plane cartographical coordinates α 180 π atan2 x 2 x 1 y 2 y 1 displaystyle alpha frac 180 pi operatorname atan2 x_ 2 x_ 1 y_ 2 y_ 1 remark that the reference axes are swapped relative to the counterclockwise mathematical polar coordinate system and that the azimuth is clockwise relative to the north this is why the x and y axis in the above formula are swapped if the azimuth becomes negative one can always add 360 the formula in radians would be slightly easier α atan2 x 2 x 1 y 2 y 1 displaystyle alpha operatorname atan2 x_ 2 x_ 1 y_ 2 y_ 1 note the swapped x y displaystyle x y in contrast to the normal y x displaystyle y x atan2 input order the opposite problem occurs when the coordinates x 1 y 1 of one point the distance d and the azimuth α to another point x 2 y 2 are known one can calculate its coordinates x 2 x 1 d sin α y 2 y 1 d cos α displaystyle begin aligned x_ 2 x_ 1 d sin alpha y_ 2 y_ 1 d cos alpha end aligned this is typically used in triangulation and azimuth identification azid especially in radar applications map projections edit there is a wide variety of azimuthal map projections they all have the property that directions the azimuths from a central point are preserved some navigation systems use south as the reference plane however any direction can serve as the plane of reference as long as it is clearly defined for everyone using that system comparison of some azimuthal projections centred on 90 n at the same scale ordered by projection altitude in earth radii click for detail related coordinates edit right ascension edit if instead of measuring from and along the horizon the angles are measured from and along the celestial equator the angles are called right ascension if referenced to the vernal equinox or hour angle if referenced to the celestial meridian polar coordinate edit in mathematics the azimuth angle of a point in cylindrical coordinates or spherical coordinates is the anticlockwise angle between the positive x axis and the projection of the vector onto the xy plane a special case of an azimuth angle is the angle in polar coordinates of the component of the vector in the xy plane although this angle is normally measured in radians rather than degrees and denoted by θ rather than φ other uses edit for magnetic tape drives azimuth refers to the angle between the tape head s and tape in sound localization experiments and literature the azimuth refers to the angle the sound source makes compared to the imaginary straight line that is drawn from within the head through the area between the eyes an azimuth thruster in shipbuilding is a propeller that can be rotated horizontally see also edit altitude astronomy angular displacement angzarr azimuthal quantum number azimuthal equidistant projection azimuth recording bearing navigation clock position course navigation inclination longitude latitude magnetic declination panning camera relative bearing sextant solar azimuth angle sound localization zenith part of a series on astrodynamics orbital mechanics orbital elements apsis argument of periapsis eccentricity inclination mean anomaly orbital nodes semi major axis true anomaly types of two body orbits by eccentricity circular orbit elliptic orbit transfer orbit hohmann transfer orbit bi elliptic transfer orbit parabolic orbit hyperbolic orbit radial orbit decaying orbit equations dynamical friction escape velocity kepler s equation kepler s laws of planetary motion orbital period orbital velocity surface gravity specific orbital energy vis viva equation celestial mechanics gravitational influences barycenter hill sphere perturbations sphere of influence n body orbits lagrangian points halo orbits lissajous orbits lyapunov orbits engineering and efficiency preflight engineering mass ratio payload fraction propellant mass fraction tsiolkovsky rocket equation efficiency measures gravity assist oberth effect propulsive maneuvers orbital maneuver orbit insertion v t e references edit the singular form of the noun is arabic السَّمْت romanized as samt lit the direction azimuth dictionary com unabridged online n d azimuth at new english dictionary on historical principles azimut at centre national de ressources textuelles et lexicales al samt at brill s encyclopedia of islam azimuth at englishwordsofarabicancestry wordpress com archived january 2 2014 at the wayback machine in arabic the written al sumūt is always pronounced as sumūt see pronunciation of al in arabic rutstrum carl the wilderness route finder university of minnesota press 2000 isbn 0 8166 3661 3 p 194 u s army map reading and land navigation fm 21 26 headquarters dept of the army washington d c 7 may 1993 ch 6 p 2 u s army map reading and land navigation fm 21 26 headquarters dept of the army washington d c 28 march 1956 ch 3 p 63 u s army ch 6 p 2 u s army advanced map and aerial photograph reading headquarters war department washington d c 17 september 1941 pp 24 25 u s army advanced map and aerial photograph reading headquarters war department washington d c 23 december 1944 p 15 torge müller 2012 geodesy de gruyter eq 6 70 p 248 further reading edit rutstrum carl the wilderness route finder university of minnesota press 2000 isbn 0 8166 3661 3 external links edit look up azimuth in wiktionary the free dictionary azimuth encyclopædia britannica 11th ed 1911 azimuth collier s new encyclopedia 1921 azimuth calculator easycalculator org portals geography mathematics astronomy stars spaceflight outer space science authority control databases international gnd national united states france bnf data israel other nara yale lux retrieved from https en wikipedia org w index php title azimuth oldid 1358525893 categories angle navigation surveying horizontal coordinate system geodesy cartography hidden categories articles with short description short description is different from wikidata use dmy dates from july 2022 pages using the phonos extension pages including recorded pronunciations articles containing arabic language text webarchive template wayback links all articles with unsourced statements articles with unsourced statements from january 2022 wikipedia articles incorporating a citation from the 1911 encyclopaedia britannica with wikisource reference wikipedia articles incorporating a citation from collier s encyclopedia this page was last edited on 9 june 2026 at 06 55 utc page was rendered with parsoid text is available under the creative commons attribution sharealike 4 0 license additional terms may apply by using this site you agree to the terms of use and privacy policy wikipedia is a registered tradem...