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78-715: USA-66 , also known as GPS IIA-1 , GPS II-10 and GPS SVN-23 , was an American navigation satellite which formed part of the Global Positioning System . It was the first of nineteen Block IIA GPS satellites to be launched, and was the oldest GPS satellite still in operation until its decommissioning on 25 January 2016. Global Positioning System (GPS) was developed by the U.S. Department of Defense to provide all-weather round-the-clock navigation capabilities for military ground, sea, and air forces. Since its implementation, GPS has also become an integral asset in numerous civilian applications and industries around

156-484: A geographic coordinate system as defined in the specification of the ISO 19111 standard. Since there are many different reference ellipsoids , the precise latitude of a feature on the surface is not unique: this is stressed in the ISO standard which states that "without the full specification of the coordinate reference system, coordinates (that is latitude and longitude) are ambiguous at best and meaningless at worst". This

234-524: A line of sight by radio from satellites. The system can be used for providing position, navigation or for tracking the position of something fitted with a receiver (satellite tracking). The signals also allow the electronic receiver to calculate the current local time to a high precision, which allows time synchronisation. These uses are collectively known as Positioning, Navigation and Timing (PNT). Satnav systems operate independently of any telephonic or internet reception, though these technologies can enhance

312-560: A 300-by-300-pixel sphere, so illustrations usually exaggerate the flattening. The graticule on the ellipsoid is constructed in exactly the same way as on the sphere. The normal at a point on the surface of an ellipsoid does not pass through the centre, except for points on the equator or at the poles, but the definition of latitude remains unchanged as the angle between the normal and the equatorial plane. The terminology for latitude must be made more precise by distinguishing: Geographic latitude must be used with care, as some authors use it as

390-496: A constellation of 7 navigational satellites. Three of the satellites are placed in geostationary orbit (GEO) and the remaining 4 in geosynchronous orbit (GSO) to have a larger signal footprint and lower number of satellites to map the region. It is intended to provide an all-weather absolute position accuracy of better than 7.6 metres (25 ft) throughout India and within a region extending approximately 1,500 km (930 mi) around it. An Extended Service Area lies between

468-458: A radio pulse from a known "master" location, followed by a pulse repeated from a number of "slave" stations. The delay between the reception of the master signal and the slave signals allowed the receiver to deduce the distance to each of the slaves, providing a fix . The first satellite navigation system was Transit , a system deployed by the US military in the 1960s. Transit's operation was based on

546-466: A signal that contains orbital data (from which the position of the satellite can be calculated) and the precise time the signal was transmitted. Orbital data include a rough almanac for all satellites to aid in finding them, and a precise ephemeris for this satellite. The orbital ephemeris is transmitted in a data message that is superimposed on a code that serves as a timing reference. The satellite uses an atomic clock to maintain synchronization of all

624-472: A software bug that left the timing of 15 of the remaining GPS satellites off by 13.7 microseconds, causing widespread GPS disruptions. Navigation satellite Satellite-based augmentation systems (SBAS), designed to enhance the accuracy of GNSS, include Japan's Quasi-Zenith Satellite System (QZSS), India's GAGAN and the European EGNOS , all of them based on GPS. Previous iterations of

702-495: A survey but, with the advent of GPS , it has become natural to use reference ellipsoids (such as WGS84 ) with centre at the centre of mass of the Earth and minor axis aligned to the rotation axis of the Earth. These geocentric ellipsoids are usually within 100 m (330 ft) of the geoid. Since latitude is defined with respect to an ellipsoid, the position of a given point is different on each ellipsoid: one cannot exactly specify

780-555: A synonym for geodetic latitude whilst others use it as an alternative to the astronomical latitude . "Latitude" (unqualified) should normally refer to the geodetic latitude. The importance of specifying the reference datum may be illustrated by a simple example. On the reference ellipsoid for WGS84, the centre of the Eiffel Tower has a geodetic latitude of 48° 51′ 29″ N, or 48.8583° N and longitude of 2° 17′ 40″ E or 2.2944°E. The same coordinates on

858-481: A transfer orbit. The satellite raised itself into medium Earth orbit using a Star-37XFP apogee motor . On 30 December 1990, USA-66 was in an orbit with a perigee of 19,935 km (12,387 mi), an apogee of 20,279 km (12,601 mi), a period of 714.8 minutes, and 54.8° of inclination to the equator . It was initially given PRN 23, which it used until its retirement in February 2004; however, it

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936-411: Is also used in the current literature. The parametric latitude is related to the geodetic latitude by: The alternative name arises from the parameterization of the equation of the ellipse describing a meridian section. In terms of Cartesian coordinates p , the distance from the minor axis, and z , the distance above the equatorial plane, the equation of the ellipse is: The Cartesian coordinates of

1014-484: Is determined by the shape of the ellipse which is rotated about its minor (shorter) axis. Two parameters are required. One is invariably the equatorial radius, which is the semi-major axis , a . The other parameter is usually (1) the polar radius or semi-minor axis , b ; or (2) the (first) flattening , f ; or (3) the eccentricity , e . These parameters are not independent: they are related by Many other parameters (see ellipse , ellipsoid ) appear in

1092-453: Is determined with the meridian altitude method. More precise measurement of latitude requires an understanding of the gravitational field of the Earth, either to set up theodolites or to determine GPS satellite orbits. The study of the figure of the Earth together with its gravitational field is the science of geodesy . The graticule is formed by the lines of constant latitude and constant longitude, which are constructed with reference to

1170-466: Is of great importance in accurate applications, such as a Global Positioning System (GPS), but in common usage, where high accuracy is not required, the reference ellipsoid is not usually stated. In English texts, the latitude angle, defined below, is usually denoted by the Greek lower-case letter phi ( ϕ or φ ). It is measured in degrees , minutes and seconds or decimal degrees , north or south of

1248-451: Is the angle between the equatorial plane and the normal to the surface at that point: the normal to the surface of the sphere is along the radial vector. The latitude, as defined in this way for the sphere, is often termed the spherical latitude, to avoid ambiguity with the geodetic latitude and the auxiliary latitudes defined in subsequent sections of this article. Besides the equator, four other parallels are of significance: The plane of

1326-421: Is the meridional radius of curvature . The quarter meridian distance from the equator to the pole is For WGS84 this distance is 10 001 .965 729  km . The evaluation of the meridian distance integral is central to many studies in geodesy and map projection. It can be evaluated by expanding the integral by the binomial series and integrating term by term: see Meridian arc for details. The length of

1404-607: Is the world's most utilized satellite navigation system. First launch year: 1982 The formerly Soviet , and now Russian , Glo bal'naya Na vigatsionnaya S putnikovaya S istema , (GLObal NAvigation Satellite System or GLONASS), is a space-based satellite navigation system that provides a civilian radionavigation-satellite service and is also used by the Russian Aerospace Defence Forces. GLONASS has full global coverage since 1995 and with 24 active satellites. First launch year: 2000 BeiDou started as

1482-752: Is – according to Article 1.45 of the International Telecommunication Union's (ITU) Radio Regulations (RR) – defined as « A radionavigation-satellite service in which earth stations are located on board ships .» ITU Radio Regulations (article 1) classifies radiocommunication services as: The allocation of radio frequencies is provided according to Article 5 of the ITU Radio Regulations (edition 2012). To improve harmonisation in spectrum utilisation, most service allocations are incorporated in national Tables of Frequency Allocations and Utilisations within

1560-522: The Philosophiæ Naturalis Principia Mathematica , in which he proved that a rotating self-gravitating fluid body in equilibrium takes the form of an oblate ellipsoid. (This article uses the term ellipsoid in preference to the older term spheroid .) Newton's result was confirmed by geodetic measurements in the 18th century. (See Meridian arc .) An oblate ellipsoid is the three-dimensional surface generated by

1638-459: The Doppler effect : the satellites travelled on well-known paths and broadcast their signals on a well-known radio frequency . The received frequency will differ slightly from the broadcast frequency because of the movement of the satellite with respect to the receiver. By monitoring this frequency shift over a short time interval, the receiver can determine its location to one side or the other of

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1716-670: The Multi-functional Satellite Augmentation System , Differential GPS , GPS-aided GEO augmented navigation (GAGAN) and inertial navigation systems . The Quasi-Zenith Satellite System (QZSS) is a four-satellite regional time transfer system and enhancement for GPS covering Japan and the Asia-Oceania regions. QZSS services were available on a trial basis as of January 12, 2018, and were started in November 2018. The first satellite

1794-580: The zenith ). On map projections there is no universal rule as to how meridians and parallels should appear. The examples below show the named parallels (as red lines) on the commonly used Mercator projection and the Transverse Mercator projection . On the former the parallels are horizontal and the meridians are vertical, whereas on the latter there is no exact relationship of parallels and meridians with horizontal and vertical: both are complicated curves. \ In 1687 Isaac Newton published

1872-477: The BeiDou navigation system and the present Indian Regional Navigation Satellite System (IRNSS), operationally known as NavIC, are examples of stand-alone operating regional navigation satellite systems ( RNSS ). Satellite navigation devices determine their location ( longitude , latitude , and altitude / elevation ) to high precision (within a few centimeters to meters) using time signals transmitted along

1950-450: The Earth's orbit about the Sun is called the ecliptic , and the plane perpendicular to the rotation axis of the Earth is the equatorial plane. The angle between the ecliptic and the equatorial plane is called variously the axial tilt, the obliquity, or the inclination of the ecliptic, and it is conventionally denoted by i . The latitude of the tropical circles is equal to i and the latitude of

2028-1097: The Internet. One main use of the system is in aviation . According to specifications, horizontal position accuracy when using EGNOS-provided corrections should be better than seven metres. In practice, the horizontal position accuracy is at the metre level. Similar service is provided in North America by the Wide Area Augmentation System (WAAS), in Russia by the System for Differential Corrections and Monitoring (SDCM), and in Asia, by Japan's Multi-functional Satellite Augmentation System (MSAS) and India's GPS-aided GEO augmented navigation (GAGAN). 27 operational + 3 spares Currently: 26 in orbit 24 operational 2 inactive 6 to be launched Using multiple GNSS systems for user positioning increases

2106-691: The Sun is overhead at some point of the Tropic of Capricorn . The south polar latitudes below the Antarctic Circle are in daylight, whilst the north polar latitudes above the Arctic Circle are in night. The situation is reversed at the June solstice, when the Sun is overhead at the Tropic of Cancer. Only at latitudes in between the two tropics is it possible for the Sun to be directly overhead (at

2184-490: The U.S. Air force, the spacecraft measured 5.3 m across with solar panels deployed and had a design life of 7.5 years. USA-66 was launched at 21:39:01 UTC on 26 November 1990, atop a Delta II launch vehicle , flight number D201, flying in the 7925-9.5 configuration. The launch took place from Launch Complex 17A (LC-17A) at the Cape Canaveral Air Force Station (CCAFS), and placed USA-66 into

2262-571: The WGS84 spheroid is The variation of this distance with latitude (on WGS84 ) is shown in the table along with the length of a degree of longitude (east–west distance): A calculator for any latitude is provided by the U.S. Government's National Geospatial-Intelligence Agency (NGA). The following graph illustrates the variation of both a degree of latitude and a degree of longitude with latitude. There are six auxiliary latitudes that have applications to special problems in geodesy, geophysics and

2340-453: The accuracy of positions to centimetric precision (and to millimetric precision for altimetric application and also allows monitoring very tiny seasonal changes of Earth rotation and deformations), in order to build a much more precise geodesic reference system. The two current operational low Earth orbit (LEO) satellite phone networks are able to track transceiver units with accuracy of a few kilometres using doppler shift calculations from

2418-425: The angle subtended at the centre by the meridian arc from the equator to the point concerned. If the meridian distance is denoted by m ( ϕ ) then where R denotes the mean radius of the Earth. R is equal to 6,371 km or 3,959 miles. No higher accuracy is appropriate for R since higher-precision results necessitate an ellipsoid model. With this value for R the meridian length of 1 degree of latitude on

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2496-638: The centre of the Earth and perpendicular to the rotation axis intersects the surface at a great circle called the Equator . Planes parallel to the equatorial plane intersect the surface in circles of constant latitude; these are the parallels. The Equator has a latitude of 0°, the North Pole has a latitude of 90° North (written 90° N or +90°), and the South Pole has a latitude of 90° South (written 90° S or −90°). The latitude of an arbitrary point

2574-408: The datum ED50 define a point on the ground which is 140 metres (460 feet) distant from the tower. A web search may produce several different values for the latitude of the tower; the reference ellipsoid is rarely specified. The length of a degree of latitude depends on the figure of the Earth assumed. On the sphere the normal passes through the centre and the latitude ( ϕ ) is therefore equal to

2652-529: The definitions of latitude and longitude. In the first step the physical surface is modeled by the geoid , a surface which approximates the mean sea level over the oceans and its continuation under the land masses. The second step is to approximate the geoid by a mathematically simpler reference surface. The simplest choice for the reference surface is a sphere , but the geoid is more accurately modeled by an ellipsoid of revolution . The definitions of latitude and longitude on such reference surfaces are detailed in

2730-493: The delivery of weapons to targets, greatly increasing their lethality whilst reducing inadvertent casualties from mis-directed weapons. (See Guided bomb ). Satellite navigation also allows forces to be directed and to locate themselves more easily, reducing the fog of war . Now a global navigation satellite system, such as Galileo , is used to determine users location and the location of other people or objects at any given moment. The range of application of satellite navigation in

2808-402: The ellipsoid to that point Q on the surrounding sphere (of radius a ) which is the projection parallel to the Earth's axis of a point P on the ellipsoid at latitude ϕ . It was introduced by Legendre and Bessel who solved problems for geodesics on the ellipsoid by transforming them to an equivalent problem for spherical geodesics by using this smaller latitude. Bessel's notation, u ( ϕ ) ,

2886-517: The equator. For navigational purposes positions are given in degrees and decimal minutes. For instance, The Needles lighthouse is at 50°39.734′ N 001°35.500′ W. This article relates to coordinate systems for the Earth: it may be adapted to cover the Moon, planets and other celestial objects ( planetographic latitude ). For a brief history, see History of latitude . In celestial navigation , latitude

2964-452: The equator. Latitude and longitude are used together as a coordinate pair to specify a location on the surface of the Earth. On its own, the term "latitude" normally refers to the geodetic latitude as defined below. Briefly, the geodetic latitude of a point is the angle formed between the vector perpendicular (or normal ) to the ellipsoidal surface from the point, and the plane of the equator . Two levels of abstraction are employed in

3042-438: The following sections. Lines of constant latitude and longitude together constitute a graticule on the reference surface. The latitude of a point on the actual surface is that of the corresponding point on the reference surface, the correspondence being along the normal to the reference surface, which passes through the point on the physical surface. Latitude and longitude together with some specification of height constitute

3120-610: The four major global satellite navigation systems consisting of MEO satellites, the SISRE of the BDS-3 MEO satellites was slightly inferior to 0.4 m of Galileo, slightly superior to 0.59 m of GPS, and remarkably superior to 2.33 m of GLONASS. The SISRE of BDS-3 IGSO was 0.90 m, which was on par with the 0.92 m of QZSS IGSO. However, as the BDS-3 GEO satellites were newly launched and not completely functioning in orbit, their average SISRE

3198-774: The future is enormous, including both the public and private sectors across numerous market segments such as science, transport, agriculture, insurance, energy, etc. The ability to supply satellite navigation signals is also the ability to deny their availability. The operator of a satellite navigation system potentially has the ability to degrade or eliminate satellite navigation services over any territory it desires. In order of first launch year: First launch year: 1978 The United States' Global Positioning System (GPS) consists of up to 32 medium Earth orbit satellites in six different orbital planes . The exact number of satellites varies as older satellites are retired and replaced. Operational since 1978 and globally available since 1994, GPS

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3276-519: The future version 3.0. EGNOS consists of 40 Ranging Integrity Monitoring Stations, 2 Mission Control Centres, 6 Navigation Land Earth Stations, the EGNOS Wide Area Network (EWAN), and 3 geostationary satellites . Ground stations determine the accuracy of the satellite navigation systems data and transfer it to the geostationary satellites; users may freely obtain this data from those satellites using an EGNOS-enabled receiver, or over

3354-399: The geocentric latitude ( θ ) and the geodetic latitude ( ϕ ) is: For points not on the surface of the ellipsoid, the relationship involves additionally the ellipsoidal height h : where N is the prime vertical radius of curvature. The geodetic and geocentric latitudes are equal at the equator and at the poles but at other latitudes they differ by a few minutes of arc. Taking the value of

3432-552: The global public. The first two generations of China's BeiDou navigation system were designed to provide regional coverage. GNSS augmentation is a method of improving a navigation system's attributes, such as accuracy, reliability, and availability, through the integration of external information into the calculation process, for example, the Wide Area Augmentation System , the European Geostationary Navigation Overlay Service ,

3510-927: The globe, including recreational used (e.g., boating, aircraft, hiking), corporate vehicle fleet tracking, and surveying. GPS employs 24 spacecraft in 20,200 km circular orbits inclined at 55.0°. These vehicles are placed in 6 orbit planes with four operational satellites in each plane. GPS Block 2 was the operational system, following the demonstration system composed of Block 1 (Navstar 1 - 11) spacecraft. These spacecraft were 3-axis stabilized , nadir pointing using reaction wheels . Dual solar arrays supplied 710 watts of power. They used S-band (SGLS) communications for control and telemetry and Ultra high frequency (UHF) cross-link between spacecraft. The payload consisted of two L-band navigation signals at 1575.42 MHz (L1) and 1227.60 MHz (L2). Each spacecraft carried 2 rubidium and 2 Cesium clocks and nuclear detonation detection sensors. Built by Rockwell Space Systems for

3588-473: The ionosphere, and this slowing varies with the receiver's angle to the satellite, because that changes the distance through the ionosphere. The basic computation thus attempts to find the shortest directed line tangent to four oblate spherical shells centred on four satellites. Satellite navigation receivers reduce errors by using combinations of signals from multiple satellites and multiple correlators, and then using techniques such as Kalman filtering to combine

3666-775: The last of which was launched in December 2021. The main modulation used in Galileo Open Service signal is the Composite Binary Offset Carrier (CBOC) modulation. The NavIC (acronym for Navigation with Indian Constellation ) is an autonomous regional satellite navigation system developed by the Indian Space Research Organisation (ISRO). The Indian government approved the project in May 2006. It consists of

3744-451: The latitude and longitude of a geographical feature without specifying the ellipsoid used. Many maps maintained by national agencies are based on older ellipsoids, so one must know how the latitude and longitude values are transformed from one ellipsoid to another. GPS handsets include software to carry out datum transformations which link WGS84 to the local reference ellipsoid with its associated grid. The shape of an ellipsoid of revolution

3822-538: The meridian arc between two given latitudes is given by replacing the limits of the integral by the latitudes concerned. The length of a small meridian arc is given by When the latitude difference is 1 degree, corresponding to ⁠ π / 180 ⁠ radians, the arc distance is about The distance in metres (correct to 0.01 metre) between latitudes ϕ {\displaystyle \phi }  − 0.5 degrees and ϕ {\displaystyle \phi }  + 0.5 degrees on

3900-525: The navigation system, systems can be classified as: As many of the global GNSS systems (and augmentation systems) use similar frequencies and signals around L1, many "Multi-GNSS" receivers capable of using multiple systems have been produced. While some systems strive to interoperate with GPS as well as possible by providing the same clock, others do not. Ground-based radio navigation is decades old. The DECCA , LORAN , GEE and Omega systems used terrestrial longwave radio transmitters which broadcast

3978-440: The noisy, partial, and constantly changing data into a single estimate for position, time, and velocity. Einstein 's theory of general relativity is applied to GPS time correction, the net result is that time on a GPS satellite clock advances faster than a clock on the ground by about 38 microseconds per day. The original motivation for satellite navigation was for military applications. Satellite navigation allows precision in

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4056-455: The now-decommissioned Beidou-1, an Asia-Pacific local network on the geostationary orbits. The second generation of the system BeiDou-2 became operational in China in December 2011. The BeiDou-3 system is proposed to consist of 30 MEO satellites and five geostationary satellites (IGSO). A 16-satellite regional version (covering Asia and Pacific area) was completed by December 2012. Global service

4134-466: The number of visible satellites, improves precise point positioning (PPP) and shortens the average convergence time. The signal-in-space ranging error (SISRE) in November 2019 were 1.6 cm for Galileo, 2.3 cm for GPS, 5.2 cm for GLONASS and 5.5 cm for BeiDou when using real-time corrections for satellite orbits and clocks. The average SISREs of the BDS-3 MEO, IGSO, and GEO satellites were 0.52 m, 0.90 m and 1.15 m, respectively. Compared to

4212-407: The polar circles is its complement (90° - i ). The axis of rotation varies slowly over time and the values given here are those for the current epoch . The time variation is discussed more fully in the article on axial tilt . The figure shows the geometry of a cross-section of the plane perpendicular to the ecliptic and through the centres of the Earth and the Sun at the December solstice when

4290-460: The primary service area and a rectangle area enclosed by the 30th parallel south to the 50th parallel north and the 30th meridian east to the 130th meridian east , 1,500–6,000 km beyond borders. A goal of complete Indian control has been stated, with the space segment , ground segment and user receivers all being built in India. The constellation was in orbit as of 2018, and the system

4368-572: The purpose of radionavigation . This service may also include feeder links necessary for its operation". RNSS is regarded as a safety-of-life service and an essential part of navigation which must be protected from interferences . Aeronautical radionavigation-satellite ( ARNSS ) is – according to Article 1.47 of the International Telecommunication Union's (ITU) Radio Regulations (RR) – defined as « A radionavigation service in which earth stations are located on board aircraft .» Maritime radionavigation-satellite service ( MRNSS )

4446-509: The reference ellipsoid to the plane or in calculations of geodesics on the ellipsoid. Their numerical values are not of interest. For example, no one would need to calculate the authalic latitude of the Eiffel Tower. The expressions below give the auxiliary latitudes in terms of the geodetic latitude, the semi-major axis, a , and the eccentricity, e . (For inverses see below .) The forms given are, apart from notational variants, those in

4524-461: The responsibility of the appropriate national administration. Allocations are: Latitude In geography , latitude is a coordinate that specifies the north – south position of a point on the surface of the Earth or another celestial body. Latitude is given as an angle that ranges from −90° at the south pole to 90° at the north pole, with 0° at the Equator . Lines of constant latitude , or parallels , run east–west as circles parallel to

4602-473: The rotation axis of the Earth. The primary reference points are the poles where the axis of rotation of the Earth intersects the reference surface. Planes which contain the rotation axis intersect the surface at the meridians ; and the angle between any one meridian plane and that through Greenwich (the Prime Meridian ) defines the longitude: meridians are lines of constant longitude. The plane through

4680-417: The rotation of an ellipse about its shorter axis (minor axis). "Oblate ellipsoid of revolution" is abbreviated to 'ellipsoid' in the remainder of this article. (Ellipsoids which do not have an axis of symmetry are termed triaxial .) Many different reference ellipsoids have been used in the history of geodesy . In pre-satellite days they were devised to give a good fit to the geoid over the limited area of

4758-553: The satellite, and several such measurements combined with a precise knowledge of the satellite's orbit can fix a particular position. Satellite orbital position errors are caused by radio-wave refraction , gravity field changes (as the Earth's gravitational field is not uniform), and other phenomena. A team, led by Harold L Jury of Pan Am Aerospace Division in Florida from 1970 to 1973, found solutions and/or corrections for many error sources. Using real-time data and recursive estimation,

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4836-407: The satellite. The coordinates are sent back to the transceiver unit where they can be read using AT commands or a graphical user interface . This can also be used by the gateway to enforce restrictions on geographically bound calling plans. The International Telecommunication Union (ITU) defines a radionavigation-satellite service ( RNSS ) as "a radiodetermination-satellite service used for

4914-524: The satellites in the constellation. The receiver compares the time of broadcast encoded in the transmission of three (at sea level) or four (which allows an altitude calculation also) different satellites, measuring the time-of-flight to each satellite. Several such measurements can be made at the same time to different satellites, allowing a continual fix to be generated in real time using an adapted version of trilateration : see GNSS positioning calculation for details. Each distance measurement, regardless of

4992-519: The semi-major axis and the inverse flattening, ⁠ 1 / f ⁠ . For example, the defining values for the WGS84 ellipsoid, used by all GPS devices, are from which are derived The difference between the semi-major and semi-minor axes is about 21 km (13 miles) and as fraction of the semi-major axis it equals the flattening; on a computer monitor the ellipsoid could be sized as 300 by 299 pixels. This would barely be distinguishable from

5070-420: The sphere is 111.2 km (69.1 statute miles) (60.0 nautical miles). The length of one minute of latitude is 1.853 km (1.151 statute miles) (1.00 nautical miles), while the length of 1 second of latitude is 30.8 m or 101 feet (see nautical mile ). In Meridian arc and standard texts it is shown that the distance along a meridian from latitude ϕ to the equator is given by ( ϕ in radians) where M ( ϕ )

5148-403: The squared eccentricity as 0.0067 (it depends on the choice of ellipsoid) the maximum difference of ϕ − θ {\displaystyle \phi {-}\theta } may be shown to be about 11.5 minutes of arc at a geodetic latitude of approximately 45° 6′. The parametric latitude or reduced latitude , β , is defined by the radius drawn from the centre of

5226-458: The standard reference for map projections, namely "Map projections: a working manual" by J. P. Snyder. Derivations of these expressions may be found in Adams and online publications by Osborne and Rapp. The geocentric latitude is the angle between the equatorial plane and the radius from the centre to a point of interest. When the point is on the surface of the ellipsoid, the relation between

5304-472: The study of geodesy, geophysics and map projections but they can all be expressed in terms of one or two members of the set a , b , f and e . Both f and e are small and often appear in series expansions in calculations; they are of the order ⁠ 1 / 298 ⁠ and 0.0818 respectively. Values for a number of ellipsoids are given in Figure of the Earth . Reference ellipsoids are usually defined by

5382-407: The system being used, places the receiver on a spherical shell at the measured distance from the broadcaster. By taking several such measurements and then looking for a point where they meet, a fix is generated. However, in the case of fast-moving receivers, the position of the signal moves as signals are received from several satellites. In addition, the radio signals slow slightly as they pass through

5460-461: The system of 30 MEO satellites was originally scheduled to be operational in 2010. The original year to become operational was 2014. The first experimental satellite was launched on 28 December 2005. Galileo is expected to be compatible with the modernized GPS system. The receivers will be able to combine the signals from both Galileo and GPS satellites to greatly increase the accuracy. The full Galileo constellation consists of 24 active satellites,

5538-641: The systematic and residual errors were narrowed down to accuracy sufficient for navigation. Part of an orbiting satellite's broadcast includes its precise orbital data. Originally, the US Naval Observatory (USNO) continuously observed the precise orbits of these satellites. As a satellite's orbit deviated, the USNO sent the updated information to the satellite. Subsequent broadcasts from an updated satellite would contain its most recent ephemeris . Modern systems are more direct. The satellite broadcasts

5616-407: The theory of map projections: The definitions given in this section all relate to locations on the reference ellipsoid but the first two auxiliary latitudes, like the geodetic latitude, can be extended to define a three-dimensional geographic coordinate system as discussed below . The remaining latitudes are not used in this way; they are used only as intermediate constructs in map projections of

5694-556: The usefulness of the positioning information generated. Global coverage for each system is generally achieved by a satellite constellation of 18–30 medium Earth orbit (MEO) satellites spread between several orbital planes . The actual systems vary, but all use orbital inclinations of >50° and orbital periods of roughly twelve hours (at an altitude of about 20,000 kilometres or 12,000 miles). GNSS systems that provide enhanced accuracy and integrity monitoring usable for civil navigation are classified as follows: By their roles in

5772-501: Was available for public use in early 2018. NavIC provides two levels of service, the "standard positioning service", which will be open for civilian use, and a "restricted service" (an encrypted one) for authorized users (including military). There are plans to expand NavIC system by increasing constellation size from 7 to 11. India plans to make the NavIC global by adding 24 more MEO satellites. The Global NavIC will be free to use for

5850-752: Was completed by December 2018. On 23 June 2020, the BDS-3 constellation deployment is fully completed after the last satellite was successfully launched at the Xichang Satellite Launch Center . First launch year: 2011 The European Union and European Space Agency agreed in March 2002 to introduce their own alternative to GPS, called the Galileo positioning system . Galileo became operational on 15 December 2016 (global Early Operational Capability, EOC). At an estimated cost of €10 billion,

5928-712: Was launched in September 2010. An independent satellite navigation system (from GPS) with 7 satellites is planned for 2023. The European Geostationary Navigation Overlay Service (EGNOS) is a satellite-based augmentation system (SBAS) developed by the European Space Agency and EUROCONTROL on behalf of the European Commission . Currently, it supplements GPS by reporting on the reliability and accuracy of their positioning data and sending out corrections. The system will supplement Galileo in

6006-556: Was marginally worse than the 0.91 m of the QZSS GEO satellites. Doppler Orbitography and Radio-positioning Integrated by Satellite (DORIS) is a French precision navigation system. Unlike other GNSS systems, it is based on static emitting stations around the world, the receivers being on satellites, in order to precisely determine their orbital position. The system may be used also for mobile receivers on land with more limited usage and coverage. Used with traditional GNSS systems, it pushes

6084-508: Was subsequently reactivated broadcasting PRN 32 and in February 2008 it rejoined the operational constellation. It is located in slot 5 of plane E of the GPS constellation. The satellite has a mass of 840 kg (1,850 lb). It had a design life of 7.5 years, but remained in service for over 25 years. On 25 January 2016, USA-66 was decommissioned, and removed from the GPS constellation. When engineers took it offline, its disappearance triggered

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