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IERS Reference Meridian

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The IERS Reference Meridian ( IRM ), also called the International Reference Meridian , is the prime meridian (0° longitude) maintained by the International Earth Rotation and Reference Systems Service (IERS). It passes about 5.3 arcseconds east of George Biddell Airy 's 1851 transit circle which is 102 metres (335 ft) at the latitude of the Royal Observatory, Greenwich . Thus it differs slightly from the historical Greenwich Meridian .

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69-737: It is the reference meridian of the Global Positioning System (GPS) operated by the United States Space Force , and of WGS 84 and its two formal versions, the ideal International Terrestrial Reference System (ITRS) and its realization, the International Terrestrial Reference Frame (ITRF). The most important reason for the 5.3 seconds of longitude offset between the IERS Reference Meridian and

138-408: A moving map display , or recorded or used by some other system, such as a vehicle guidance system. Although usually not formed explicitly in the receiver processing, the conceptual time differences of arrival (TDOAs) define the measurement geometry. Each TDOA corresponds to a hyperboloid of revolution (see Multilateration ). The line connecting the two satellites involved (and its extensions) forms

207-705: A deliberate error introduced into the GPS data that military receivers could correct for. As civilian GPS usage grew, there was increasing pressure to remove this error. The SA system was temporarily disabled during the Gulf War , as a shortage of military GPS units meant that many US soldiers were using civilian GPS units sent from home. In the 1990s, Differential GPS systems from the US Coast Guard , Federal Aviation Administration , and similar agencies in other countries began to broadcast local GPS corrections, reducing

276-450: A directive making GPS freely available for civilian use, once it was sufficiently developed, as a common good. The first Block II satellite was launched on February 14, 1989, and the 24th satellite was launched in 1994. The GPS program cost at this point, not including the cost of the user equipment but including the costs of the satellite launches, has been estimated at US$ 5 billion (equivalent to $ 10 billion in 2023). Initially,

345-635: A few centimetres. The IERS system is not quite fixed to any point attached to the Earth. For example, all points on the European portion of the Eurasian plate, including the Royal Observatory, are moving northeast at about 2.5 cm per year relative to it. The IRM is the weighted average (in the least squares sense) of the reference meridians of the hundreds of ground stations contributing to

414-517: A full complement of 24 satellites in 2027. The GPS project was launched in the United States in 1973 to overcome the limitations of previous navigation systems, combining ideas from several predecessors, including classified engineering design studies from the 1960s. The U.S. Department of Defense developed the system, which originally used 24 satellites, for use by the United States military, and became fully operational in 1993. Civilian use

483-429: A liaison. The U.S. Department of Defense is required by law to "maintain a Standard Positioning Service (as defined in the federal radio navigation plan and the standard positioning service signal specification) that will be available on a continuous, worldwide basis" and "develop measures to prevent hostile use of GPS and its augmentations without unduly disrupting or degrading civilian uses". USA-203 from Block IIR-M

552-563: A manageable level to permit accurate navigation. During Labor Day weekend in 1973, a meeting of about twelve military officers at the Pentagon discussed the creation of a Defense Navigation Satellite System (DNSS) . It was at this meeting that the real synthesis that became GPS was created. Later that year, the DNSS program was named Navstar. Navstar is often erroneously considered an acronym for "NAVigation System using Timing And Ranging" but

621-461: A minimum, four satellites must be in view of the receiver for it to compute four unknown quantities (three position coordinates and the deviation of its own clock from satellite time). Each GPS satellite continually broadcasts a signal ( carrier wave with modulation ) that includes: Conceptually, the receiver measures the TOAs (according to its own clock) of four satellite signals. From the TOAs and

690-466: A one-way time transfer system are the clock on a church or town building and the ringing of their time-indication bells; time balls , radio clock signals such as LORAN , DCF77 and MSF ; and finally the Global Positioning System which uses multiple one-way time transfers from different satellites, with positional information and other advanced means of delay compensations to allow receiver compensation of time and position information in real time. In

759-530: A period of time, and exact time synchronization is determined retrospectively. In particular, time synchronization has been accomplished by using pairs of radio telescopes to listen to a pulsar , with the time transfer accomplished by comparing time offsets of the received pulsar signal. Examples of time and frequency transfer techniques include: In a one-way time transfer system, one end transmits its current time over some communication channel to one or more receivers. The receivers will, at reception, decode

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828-422: A phone moves from one cell to another. Multiple techniques have been developed, often transferring reference clock synchronization from one point to another, often over long distances. Accuracy approaching one nanosecond worldwide is economically practical for many applications. Radio-based navigation systems are frequently used as time transfer systems. In some cases, multiple measurements are made over

897-431: A receiver start-up situation. Most receivers have a track algorithm , sometimes called a tracker , that combines sets of satellite measurements collected at different times—in effect, taking advantage of the fact that successive receiver positions are usually close to each other. After a set of measurements are processed, the tracker predicts the receiver location corresponding to the next set of satellite measurements. When

966-429: A two-way time transfer system, the two peers will both transmit and receive each other's messages, thus performing two one-way time transfers to determine the difference between the remote clock and the local clock. The sum of these time differences is the round-trip delay between the two nodes. It is often assumed that this delay is evenly distributed between the directions between the peers. Under this assumption, half

1035-399: Is available from many commercial GNSS receivers . Its initial system design expected general timing precision better than 340 nanoseconds using low-grade "coarse mode" and 200 ns in precision mode. A GPS receiver functions by precisely measuring the transit time of signals received from several satellites. These distances combined geometrically with precise orbital information identify

1104-458: Is notionally based on the prime meridian. Because of changes in the rate of Earth's rotation, standard international time UTC can differ from the mean observed solar time at noon on the prime meridian by up to 0.9 of a second. Leap seconds are inserted from time to time, to keep UTC close to Earth's angular position relative to the Sun; see mean solar time . Download coordinates as: Starting at

1173-410: Is one of the global navigation satellite systems (GNSS) that provide geolocation and time information to a GPS receiver anywhere on or near the Earth where there is an unobstructed line of sight to four or more GPS satellites. It does not require the user to transmit any data, and operates independently of any telephone or Internet reception, though these technologies can enhance the usefulness of

1242-527: Is owned and operated by the United States government as a national resource. The Department of Defense is the steward of GPS. The Interagency GPS Executive Board (IGEB) oversaw GPS policy matters from 1996 to 2004. After that, the National Space-Based Positioning, Navigation and Timing Executive Committee was established by presidential directive in 2004 to advise and coordinate federal departments and agencies on matters concerning

1311-808: Is unhealthy For a more complete list, see List of GPS satellites On February 10, 1993, the National Aeronautic Association selected the GPS Team as winners of the 1992 Robert J. Collier Trophy , the US's most prestigious aviation award. This team combines researchers from the Naval Research Laboratory, the U.S. Air Force, the Aerospace Corporation , Rockwell International Corporation, and IBM Federal Systems Company. The citation honors them "for

1380-503: The Doppler effect , they could pinpoint where the satellite was along its orbit. The Director of the APL gave them access to their UNIVAC I computer to perform the heavy calculations required. Early the next year, Frank McClure, the deputy director of the APL, asked Guier and Weiffenbach to investigate the inverse problem: pinpointing the user's location, given the satellite's. (At the time,

1449-535: The North Pole and heading south to the South Pole , the IERS Reference Meridian passes through eight countries and three oceans (Arctic Ocean, Atlantic Ocean and Southern Ocean): Global Positioning System The Global Positioning System ( GPS ), originally Navstar GPS , is a satellite-based radio navigation system owned by the United States Space Force and operated by Mission Delta 31 . It

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1518-504: The navigation equations gives the position of the receiver along with the difference between the time kept by the receiver's on-board clock and the true time-of-day, thereby eliminating the need for a more precise and possibly impractical receiver based clock. Applications for GPS such as time transfer , traffic signal timing, and synchronization of cell phone base stations , make use of this cheap and highly accurate timing. Some GPS applications use this time for display, or, other than for

1587-754: The Airy transit circle is that the observations with the transit circle were based on the local vertical , while the IERS Reference is a geodetic longitude , that is, the plane of the meridian contains the center of mass of the Earth. The International Hydrographic Organization adopted an early version of the IRM in 1983 for all nautical charts. It was adopted for air navigation by the International Civil Aviation Organization on 3 March 1989. Tectonic plates slowly move over

1656-524: The Earth's center) and the offset of the receiver clock relative to the GPS time are computed simultaneously, using the navigation equations to process the TOFs. The receiver's Earth-centered solution location is usually converted to latitude , longitude and height relative to an ellipsoidal Earth model. The height may then be further converted to height relative to the geoid , which is essentially mean sea level. These coordinates may be displayed, such as on

1725-664: The GPS and related systems. The executive committee is chaired jointly by the Deputy Secretaries of Defense and Transportation. Its membership includes equivalent-level officials from the Departments of State, Commerce, and Homeland Security, the Joint Chiefs of Staff and NASA . Components of the executive office of the president participate as observers to the executive committee, and the FCC chairman participates as

1794-411: The GPS positioning information. It provides critical positioning capabilities to military, civil, and commercial users around the world. Although the United States government created, controls, and maintains the GPS system, it is freely accessible to anyone with a GPS receiver. The GPS project was started by the U.S. Department of Defense in 1973. The first prototype spacecraft was launched in 1978 and

1863-668: The GPS service, including new signals for civil use and increased accuracy and integrity for all users, all the while maintaining compatibility with existing GPS equipment. Modernization of the satellite system has been an ongoing initiative by the U.S. Department of Defense through a series of satellite acquisitions to meet the growing needs of the military, civilians, and the commercial market. As of early 2015, high-quality Standard Positioning Service (SPS) GPS receivers provided horizontal accuracy of better than 3.5 meters (11 ft), although many factors such as receiver and antenna quality and atmospheric issues can affect this accuracy. GPS

1932-740: The Global Positioning System (GPS) its 60th Anniversary Award, nominated by IAF member, the American Institute for Aeronautics and Astronautics (AIAA). The IAF Honors and Awards Committee recognized the uniqueness of the GPS program and the exemplary role it has played in building international collaboration for the benefit of humanity. On December 6, 2018, Gladys West was inducted into the Air Force Space and Missile Pioneers Hall of Fame in recognition of her work on an extremely accurate geodetic Earth model, which

2001-514: The IERS network. The network includes GPS stations, satellite laser ranging (SLR) stations, lunar laser ranging (LLR) stations, and the highly accurate very long baseline interferometry (VLBI) stations. All stations' coordinates are adjusted annually to remove net rotation relative to the major tectonic plates. If earth had only two hemispherical plates moving relative to each other around any axis which intersects their centres or their junction, then

2070-561: The Internet, based on Java applets loaded by each client. The two-way satellite time and frequency transfer (TWSTFT) system being used in comparison among some time laboratories uses a satellite for a common link between the laboratories. The Network Time Protocol uses packet-based messages over an IP network. Historically, the telegraphic determination of longitude was an important way to connect two points. It could be used one-way or two-way, with each observatory potentially correcting

2139-480: The Navy TRANSIT system were too slow for the high speeds of Air Force operation. The Naval Research Laboratory (NRL) continued making advances with their Timation (Time Navigation) satellites, first launched in 1967, second launched in 1969, with the third in 1974 carrying the first atomic clock into orbit and the fourth launched in 1977. Another important predecessor to GPS came from a different branch of

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2208-582: The Navy was developing the submarine-launched Polaris missile, which required them to know the submarine's location.) This led them and APL to develop the TRANSIT system. In 1959, ARPA (renamed DARPA in 1972) also played a role in TRANSIT. TRANSIT was first successfully tested in 1960. It used a constellation of five satellites and could provide a navigational fix approximately once per hour. In 1967,

2277-604: The SLBM situation. In 1960, the Air Force proposed a radio-navigation system called MOSAIC (MObile System for Accurate ICBM Control) that was essentially a 3-D LORAN System. A follow-on study, Project 57, was performed in 1963 and it was "in this study that the GPS concept was born". That same year, the concept was pursued as Project 621B, which had "many of the attributes that you now see in GPS" and promised increased accuracy for U.S. Air Force bombers as well as ICBMs. Updates from

2346-524: The TOTs, the receiver forms four time of flight (TOF) values, which are (given the speed of light) approximately equivalent to receiver-satellite ranges plus time difference between the receiver and GPS satellites multiplied by speed of light, which are called pseudo-ranges. The receiver then computes its three-dimensional position and clock deviation from the four TOFs. In practice the receiver position (in three dimensional Cartesian coordinates with origin at

2415-607: The U.S. Navy developed the Timation satellite, which proved the feasibility of placing accurate clocks in space, a technology required for GPS. In the 1970s, the ground-based OMEGA navigation system, based on phase comparison of signal transmission from pairs of stations, became the first worldwide radio navigation system. Limitations of these systems drove the need for a more universal navigation solution with greater accuracy. Although there were wide needs for accurate navigation in military and civilian sectors, almost none of those

2484-442: The U.S. Secretary of Defense, William Perry , in view of the widespread growth of differential GPS services by private industry to improve civilian accuracy. Moreover, the U.S. military was developing technologies to deny GPS service to potential adversaries on a regional basis. Selective Availability was removed from the GPS architecture beginning with GPS-III. Since its deployment, the U.S. has implemented several improvements to

2553-416: The US government announced that the next generation of GPS satellites would not include the feature at all. Advances in technology and new demands on the existing system have now led to efforts to modernize the GPS and implement the next generation of GPS Block III satellites and Next Generation Operational Control System (OCX) which was authorized by the U.S. Congress in 2000. When Selective Availability

2622-512: The United States military. In 1964, the United States Army orbited its first Sequential Collation of Range ( SECOR ) satellite used for geodetic surveying. The SECOR system included three ground-based transmitters at known locations that would send signals to the satellite transponder in orbit. A fourth ground-based station, at an undetermined position, could then use those signals to fix its location precisely. The last SECOR satellite

2691-451: The axis of the hyperboloid. The receiver is located at the point where three hyperboloids intersect. It is sometimes incorrectly said that the user location is at the intersection of three spheres. While simpler to visualize, this is the case only if the receiver has a clock synchronized with the satellite clocks (i.e., the receiver measures true ranges to the satellites rather than range differences). There are marked performance benefits to

2760-502: The basic position calculations, do not use it at all. Time transfer Time and frequency transfer is a scheme where multiple sites share a precise reference time or frequency. The technique is commonly used for creating and distributing standard time scales such as International Atomic Time (TAI). Time transfer solves problems such as astronomical observatories correlating observed flashes or other phenomena with each other, as well as cell phone towers coordinating handoffs as

2829-648: The clocks on GPS satellites, as observed by those on Earth, run 38 microseconds faster per day than those on the Earth. The design of GPS corrects for this difference; because without doing so, GPS calculated positions would accumulate errors of up to 10 kilometers per day (6 mi/d). When the Soviet Union launched its first artificial satellite ( Sputnik 1 ) in 1957, two American physicists, William Guier and George Weiffenbach, at Johns Hopkins University 's Applied Physics Laboratory (APL) monitored its radio transmissions. Within hours they realized that, because of

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2898-496: The distance from the satellite to the ground station. With the distance information collected from multiple ground stations, the location coordinates of any satellite at any time can be calculated with great precision. Each GPS satellite carries an accurate record of its own position and time, and broadcasts that data continuously. Based on data received from multiple GPS satellites , an end user's GPS receiver can calculate its own four-dimensional position in spacetime ; However, at

2967-451: The distance traveled between two position measurements drops below or near the random error of position measurement. GPS units can use measurements of the Doppler shift of the signals received to compute velocity accurately. More advanced navigation systems use additional sensors like a compass or an inertial navigation system to complement GPS. GPS requires four or more satellites to be visible for accurate navigation. The solution of

3036-407: The effect of both SA degradation and atmospheric effects (that military receivers also corrected for). The U.S. military had also developed methods to perform local GPS jamming, meaning that the ability to globally degrade the system was no longer necessary. As a result, United States President Bill Clinton signed a bill ordering that Selective Availability be disabled on May 1, 2000; and, in 2007 ,

3105-428: The full constellation of 24 satellites became operational in 1993. After Korean Air Lines Flight 007 was shot down when it mistakenly entered Soviet airspace, President Ronald Reagan announced that the GPS system would be made available for civilian use as of September 16, 1983; however, initially this civilian use was limited to an average accuracy of 100 meters (330 ft) by use of Selective Availability (SA),

3174-407: The highest-quality signal was reserved for military use, and the signal available for civilian use was intentionally degraded, in a policy known as Selective Availability . This changed on May 1, 2000, with U.S. President Bill Clinton signing a policy directive to turn off Selective Availability to provide the same accuracy to civilians that was afforded to the military. The directive was proposed by

3243-535: The location of the receiver. Precise timing is fundamental to an accurate GPS location. The time from an atomic clock onboard each satellite is encoded into the radio signal; the receiver determines how much later it received the signal than it was sent. To do this, a local clock is corrected to the GPS atomic clock time by solving for three dimensions and time based on four or more satellite signals. Improvements in algorithms lead many modern low-cost GPS receivers to achieve better than 10-meter accuracy, which implies

3312-461: The longitudes (around any other rotation axis) of any two, diametrically opposite, stations must move in opposite directions by the same amount. The 180th meridian (the meridian at 180° both east and west of the Prime Meridian ) is opposite the IERS Reference Meridian and forms a great circle with it dividing the earth into Western Hemisphere and Eastern Hemisphere . Universal Time

3381-479: The message, and either just report the time, or adjust a local clock which can provide hold-over time reports in between the reception of messages. The advantage of one-way systems is that they can be technically simple and serve many receivers, as the transmitter is unaware of the receivers. The principal drawback of the one-way time transfer system is that propagation delays of the communication channel remain uncompensated except in some advanced systems. Examples of

3450-543: The most significant development for safe and efficient navigation and surveillance of air and spacecraft since the introduction of radio navigation 50 years ago". Two GPS developers received the National Academy of Engineering Charles Stark Draper Prize for 2003: GPS developer Roger L. Easton received the National Medal of Technology on February 13, 2006. Francis X. Kane (Col. USAF, ret.)

3519-440: The new measurements are collected, the receiver uses a weighting scheme to combine the new measurements with the tracker prediction. In general, a tracker can (a) improve receiver position and time accuracy, (b) reject bad measurements, and (c) estimate receiver speed and direction. The disadvantage of a tracker is that changes in speed or direction can be computed only with a delay, and that derived direction becomes inaccurate when

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3588-487: The nuclear triad, also had requirements for a more accurate and reliable navigation system. The U.S. Navy and U.S. Air Force were developing their own technologies in parallel to solve what was essentially the same problem. To increase the survivability of ICBMs, there was a proposal to use mobile launch platforms (comparable to the Soviet SS-24 and SS-25 ) and so the need to fix the launch position had similarity to

3657-440: The other's time or position. Telegraphy methods of the 19th century established many of the same techniques used in modern times, including round-trip time delay calculations and time synchronization in the 15 to 25 millisecond range. The time difference between two clocks may be determined by simultaneously comparing each clock to a common reference signal that may be received at both sites. As long as both end stations receive

3726-524: The precision needed for GPS. The design of GPS is based partly on similar ground-based radio-navigation systems, such as LORAN and the Decca Navigator System , developed in the early 1940s. In 1955, Friedwardt Winterberg proposed a test of general relativity —detecting time slowing in a strong gravitational field using accurate atomic clocks placed in orbit inside artificial satellites. Special and general relativity predicted that

3795-652: The reason for the ultra-secrecy at that time. The nuclear triad consisted of the United States Navy's submarine-launched ballistic missiles (SLBMs) along with United States Air Force (USAF) strategic bombers and intercontinental ballistic missiles (ICBMs). Considered vital to the nuclear deterrence posture, accurate determination of the SLBM launch position was a force multiplier . Precise navigation would enable United States ballistic missile submarines to get an accurate fix of their positions before they launched their SLBMs. The USAF, with two thirds of

3864-408: The reference atomic clocks at the ground control stations; any drift of the clocks aboard the satellites from the reference time maintained on the ground stations is corrected regularly. Since the speed of radio waves ( speed of light ) is constant and independent of the satellite speed, the time delay between when the satellite transmits a signal and the ground station receives it is proportional to

3933-410: The round-trip delay is the propagation delay to be compensated. A drawback is that the two-way propagation delay must be measured and used to calculate a delay correction. That function can be implemented in the reference source, in which case the source capacity limits the number of clients that can be served, or by software in each client. The NIST provides a time reference service to computer users on

4002-422: The same satellite signal at the same time, the accuracy of the signal source is not important. The nature of the received signal is not important, although widely available timing and navigation systems such as GPS or LORAN are convenient. The accuracy of time transferred in this way is typically 1–10 ns. Since the advent of GPS and other satellite navigation systems, highly precise, yet affordable timing

4071-649: The surface of Earth, so most countries have adopted for their maps an IRM version fixed relative to their own tectonic plate as it existed at the beginning of a specific year. Examples include the North American Datum 1983 (NAD83), the European Terrestrial Reference Frame 1989 (ETRF89), and the Geocentric Datum of Australia 1994 (GDA94). Versions fixed to a tectonic plate differ from the global version by at most

4140-403: The user carrying a clock synchronized with the satellites. Foremost is that only three satellites are needed to compute a position solution. If it were an essential part of the GPS concept that all users needed to carry a synchronized clock, a smaller number of satellites could be deployed, but the cost and complexity of the user equipment would increase. The description above is representative of

4209-579: Was allowed from the 1980s. Roger L. Easton of the Naval Research Laboratory , Ivan A. Getting of The Aerospace Corporation , and Bradford Parkinson of the Applied Physics Laboratory are credited with inventing it. The work of Gladys West on the creation of the mathematical geodetic Earth model is credited as instrumental in the development of computational techniques for detecting satellite positions with

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4278-420: Was concerned with the curving of the paths of radio waves ( atmospheric refraction ) traversing the ionosphere from NavSTAR satellites. After Korean Air Lines Flight 007 , a Boeing 747 carrying 269 people, was shot down by a Soviet interceptor aircraft after straying in prohibited airspace because of navigational errors, in the vicinity of Sakhalin and Moneron Islands , President Ronald Reagan issued

4347-490: Was destroyed in a launch failure). The effect of the ionosphere on radio transmission was investigated in a geophysics laboratory of Air Force Cambridge Research Laboratory , renamed to Air Force Geophysical Research Lab (AFGRL) in 1974. AFGRL developed the Klobuchar model for computing ionospheric corrections to GPS location. Of note is work done by Australian space scientist Elizabeth Essex-Cohen at AFGRL in 1974. She

4416-703: Was discontinued, GPS was accurate to about 5 meters (16 ft). GPS receivers that use the L5 band have much higher accuracy of 30 centimeters (12 in), while those for high-end applications such as engineering and land surveying are accurate to within 2 cm ( 3 ⁄ 4  in) and can even provide sub-millimeter accuracy with long-term measurements. Consumer devices such as smartphones can be accurate to 4.9 m (16 ft) or better when used with assistive services like Wi-Fi positioning . As of July 2023 , 18 GPS satellites broadcast L5 signals, which are considered pre-operational prior to being broadcast by

4485-625: Was inducted into the U.S. Air Force Space and Missile Pioneers Hall of Fame at Lackland A.F.B., San Antonio, Texas, March 2, 2010, for his role in space technology development and the engineering design concept of GPS conducted as part of Project 621B. In 1998, GPS technology was inducted into the Space Foundation Space Technology Hall of Fame . On October 4, 2011, the International Astronautical Federation (IAF) awarded

4554-626: Was launched in 1969. With these parallel developments in the 1960s, it was realized that a superior system could be developed by synthesizing the best technologies from 621B, Transit, Timation, and SECOR in a multi-service program. Satellite orbital position errors, induced by variations in the gravity field and radar refraction among others, had to be resolved. A team led by Harold L. Jury of Pan Am Aerospace Division in Florida from 1970 to 1973, used real-time data assimilation and recursive estimation to do so, reducing systematic and residual errors to

4623-549: Was never considered as such by the GPS Joint Program Office (TRW may have once advocated for a different navigational system that used that acronym). With the individual satellites being associated with the name Navstar (as with the predecessors Transit and Timation), a more fully encompassing name was used to identify the constellation of Navstar satellites, Navstar-GPS . Ten " Block I " prototype satellites were launched between 1978 and 1985 (an additional unit

4692-530: Was seen as justification for the billions of dollars it would cost in research, development, deployment, and operation of a constellation of navigation satellites. During the Cold War arms race , the nuclear threat to the existence of the United States was the one need that did justify this cost in the view of the United States Congress. This deterrent effect is why GPS was funded. It is also

4761-529: Was ultimately used to determine the orbit of the GPS constellation. On February 12, 2019, four founding members of the project were awarded the Queen Elizabeth Prize for Engineering with the chair of the awarding board stating: "Engineering is the foundation of civilisation; ...They've re-written, in a major way, the infrastructure of our world." The GPS satellites carry very stable atomic clocks that are synchronized with one another and with

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