History.

The measurement of longitude is important both to cartography and for ocean navigation. Mariners and explorers for most of history struggled to determine longitude. Finding a method of determining longitude took centuries and required the effort of some of the greatest scientific minds.  Latitude was calculated by observing with quadrant or astrolabe the altitude of the sun or of charted stars above the horizon, but longitude is harder.  Christopher Columbus in 1494 exploited a relatively rare, predicted, astronomical event (a lunar eclipse) to estimate his longitude while at Saona Island (now in the Dominican Republic): "El año de mil cuatrocientos noventa y cuatro estando yo en la isla Saona, que es al cabo Oriental de la isla Española, hubo eclipsis de la luna à catorce de Setiembre, y se fallò que habia diferencia de alli al Càbo de S. Vicente en Portugal cinco horas y mas de media" Translation: "In the year 1494, when I was in Saona Island, which stands at the eastern tip of Española island ["i.e." Hispaniola ], there was a lunar eclipse on September the 14th, and we noticed that there was a difference of more than five hours and a half between there [Saona] and Cape S.Vincente, in Portugal" [of course meaning he had an almanac, foreseeing the lunar eclipse timing when seen from Portugal]. This has obvious implications on Columbus's being finally aware (and the first to prove) that - contrary to his wishes and expectations - he had not reached 'the Indies', after all. Had he actually been there, in fact, he would have been roughly at the antipodes of Europe (see Behaims' globe), and not just 5.5 hours west of it.  Amerigo Vespucci appears to be the first European to offer a solution not depending on rare astronomical occurrences, after devoting a great deal of time and energy studying the problem during his sojourns in the New World: As to longitude, I declare that I found so much difficulty in determining it that I was put to great pains to ascertain the east-west distance I had covered. The final result of my labours was that I found nothing better to do than to watch for and take observations at night of the conjunction of one planet with another, and especially of the conjunction of the moon with the other planets, because the moon is swifter in her course than any other planet. I compared my observations with an almanac. After I had made experiments many nights, one night, the twenty-third of August 1499, there was a conjunction of the moon with Mars, which according to the almanac was to occur at midnight or a half hour before. I found that...at midnight Mars's position was three and a half degrees to the east. That said, Vespucci's writings appear to have been corrupted. (see reference) By comparing the timing of the observed positions of the moon and Mars with the expected timing of their occurrence when seen from Europe (Florence or Nurnberg), Vespucci would actually have been able to deduce his longitude (measured in hours). However, for (t)his method to provide usable results, three conditions should be satisfied: First, it requires waiting for a specific expected astronomical event to occur (in this case, Mars passing through the same right ascension as the moon), and its occurrence to be accurately timed in an astronomical almanac. Second, one needs to know the precise local time, something difficult to ascertain for Vespucci, when travelling especially. Third, it requires a stable viewing platform, rendering the technique useless on the rolling deck of a ship at sea. See Lunar distance (navigation). Due to none of such conditions being fulfilled when Vespucci took his measures (except for the third one, if he was on the ground), there was no possibility for him to accurately esteem his longitude. Notheless he must be credited with having envisioned a correct method to measure longitude (in hours, easily transformed into degrees: 1 hour = 15 degrees). Such a method was to be named the "Lunar distance method" and it became usable by mariners much later, when lunar positions started to be known and published in an accurate enough Almanac: the one issued by astronomer Nevil Maskelyne (1732-1811).see reference  In 1612 Galileo Galilei demonstrated that with sufficiently accurate knowledge of the orbits of the moons of Jupiter one could use their positions as a universal clock and this would make possible the determination of longitude, but the method he devised was impracticable for navigators on ships because of their instability. In 1714 the British government passed the Longitude Act which offered large financial rewards to the first person to demonstrate a practical method for determining the longitude of a ship at sea. These rewards motivated many to search for a solution.  John Harrison, a self-educated English clockmaker, invented the marine chronometer, the key piece in solving the problem of accurately establishing longitude at sea, thus revolutionising and extending the possibility of safe long distance sea travel. A French expedition under Charles-François-César Le Tellier de Montmirail performed the first measurement of longitude aboard "Aurore" in 1767. Though the Board of Longitude rewarded John Harrison for his marine chronometer in 1773, chronometers remained very expensive and the lunar distance method continued to be used for decades. Finally, the combination of the availability of marine chronometers and wireless telegraph time signals put an end to the use of lunars in the 20th century.  Unlike latitude, which has the equator as a natural starting position, there is no natural starting position for longitude. Therefore, a reference meridian had to be chosen. It was a popular practice to use a nation's capital as the starting point, but other locations were also used. While British cartographers had long used the Greenwich meridian in London, other references were used elsewhere, including El Hierro, Rome, Copenhagen, Jerusalem, Saint Petersburg, Pisa, Paris (see the article "Paris meridian"), Philadelphia, and Washington D.C. In 1884 the International Meridian Conference adopted the Greenwich meridian as the "universal Prime Meridian" or "zero point of longitude".

Noting and calculating longitude.

Longitude is given as an angular measurement ranging from 0° at the Prime Meridian to +180° eastward and −180° westward. The Greek letter λ (lambda), is used to denote the location of a place on Earth east or west of the Prime Meridian.  Each degree of longitude is sub-divided into 60 minutes, each of which is divided into 60 seconds. A longitude is thus specified in sexagesimal notation as 23° 27′ 30′′ E. For higher precision, the seconds are specified with a decimal fraction. An alternative representation uses degrees and minutes, where parts of a minute are expressed in decimal notation with a fraction, thus: 23° 27.5′ E. Degrees may also be expressed as a decimal fraction: 23.45833° E. For calculations, the angular measure may be converted to radians, so longitude may also be expressed in this manner as a signed fraction of (pi), or an unsigned fraction of 2.  For calculations, the West/East suffix is replaced by a negative sign in the western hemisphere. The preferred convention—that East is positive—is consistent with a right-handed Cartesian coordinate system, with the North Pole up. A specific longitude may then be combined with a specific latitude (usually positive in the northern hemisphere) to give a precise position on the Earth's surface. Confusingly, the convention of negative for East is also sometimes seen, most commonly in the United States; the Earth System Research Laboratory notes that, while it differs from the international standard, it "make(s) coordinate entry less awkward" for applications confined to the Western Hemisphere.  There is no other physical principle determining longitude directly but with time. Longitude at a point may be determined by calculating the time difference between that at its location and Coordinated Universal Time (UTC). Since there are 24 hours in a day and 360 degrees in a circle, the sun moves across the sky at a rate of 15 degrees per hour (360° ÷ 24 hours = 15° per hour). So if the time zone a person is in is three hours ahead of UTC then that person is near 45° longitude (3 hours × 15° per hour = 45°). The word "near" is used because the point might not be at the center of the time zone; also the time zones are defined politically, so their centers and boundaries often do not lie on meridians at multiples of 15°. In order to perform this calculation, however, a person needs to have a chronometer (watch) set to UTC and needs to determine local time by solar or astronomical observation. The details are more complex than described here: see the articles on Universal Time and on the equation of time for more details.

Singularity and discontinuity of longitude.

Note that the longitude is singular at the Poles and calculations that are sufficiently accurate for other positions may be inaccurate at or near the Poles. Also the discontinuity at the ±180° meridian must be handled with care in calculations. An example is a calculation of east displacement by subtracting two longitudes, which gives the wrong answer if the two positions are on either side of this meridian. To avoid these complexities, consider replacing latitude and longitude with another horizontal position representation in calculation.

Plate movement and longitude.

The Earth's tectonic plates move relative to one another in different directions at speeds on the order of per year. So points on the Earth's surface on different plates are always in motion relative to one another. For example, the longitudinal difference between a point on the Equator in Uganda, on the African Plate, and a point on the Equator in Ecuador, on the South American Plate, is increasing by about 0.0014 arcseconds per year. These tectonic movements likewise affect latitude.  If a global reference frame (such as WGS84, for example) is used, the longitude of a place on the surface will change from year to year. To minimize this change, when dealing just with points on a single plate, a different reference frame can be used, whose coordinates are fixed to a particular plate, such as "NAD83" for North America or "ETRS89" for Europe.

Length of a degree of longitude.

The length of a degree of longitude (east-west distance) depends only on the radius of a circle of latitude. For a sphere of radius that radius at latitude is, and the length of a one-degree (or radian) arc along a circle of latitude is When the Earth is modelled by an ellipsoid this arc length becomes where, the eccentricity of the ellipsoid, is related to the major and minor axes (the equatorial and polar radii respectively) by  An alternative formula is  Cos decreases from 1 at the equator to 0 at the poles, which measures how circles of latitude shrink from the equator to a point at the pole, so the length of a degree of longitude decreases likewise. This contrasts with the small (1%) increase in the length of a degree of latitude (north-south distance), equator to pole. The table shows both for the WGS84 ellipsoid with = and =. Note that the distance between two points 1 degree apart on the same circle of latitude, measured along that circle of latitude, is slightly more than the shortest (geodesic) distance between those points (unless on the equator, where these are equal); the difference is less than.  A geographical mile is defined to be the length of one minute of arc along the equator (one equatorial minute of longitude), therefore a degree of longitude along the equator is exactly 60 geographical miles or 111.3 kilometers, as there are 60 minutes in a degree. The length of 1 minute of longitude along the equator is 1 geographical mile or, while the length of 1 second of it is 0.016 geographical mile or.

Longitude on bodies other than Earth.

Planetary co-ordinate systems are defined relative to their mean axis of rotation and various definitions of longitude depending on the body. The longitude systems of most of those bodies with observable rigid surfaces have been defined by references to a surface feature such as a crater. The north pole is that pole of rotation that lies on the north side of the invariable plane of the solar system (near the ecliptic). The location of the prime meridian as well as the position of the body's north pole on the celestial sphere may vary with time due to precession of the axis of rotation of the planet (or satellite). If the position angle of the body's prime meridian increases with time, the body has a direct (or prograde) rotation; otherwise the rotation is said to be retrograde.  In the absence of other information, the axis of rotation is assumed to be normal to the mean orbital plane; Mercury and most of the satellites are in this category. For many of the satellites, it is assumed that the rotation rate is equal to the mean orbital period. In the case of the giant planets, since their surface features are constantly changing and moving at various rates, the rotation of their magnetic fields is used as a reference instead. In the case of the Sun, even this criterion fails (because its magnetosphere is very complex and does not really rotate in a steady fashion), and an agreed-upon value for the rotation of its equator is used instead.  For "planetographic longitude", west longitudes (i.e., longitudes measured positively to the west) are used when the rotation is prograde, and east longitudes (i.e., longitudes measured positively to the east) when the rotation is retrograde. In simpler terms, imagine a distant, non-orbiting observer viewing a planet as it rotates. Also suppose that this observer is within the plane of the planet's equator. A point on the Equator that passes directly in front of this observer later in time has a higher planetographic longitude than a point that did so earlier in time.  However, "planetocentric longitude" is always measured positively to the east, regardless of which way the planet rotates. "East" is defined as the counter-clockwise direction around the planet, as seen from above its north pole, and the north pole is whichever pole more closely aligns with the Earth's north pole. Longitudes traditionally have been written using "E" or "W" instead of "+" or "−" to indicate this polarity. For example, −91°, 91°W, +269° and 269°E all mean the same thing.  The reference surfaces for some planets (such as Earth and Mars) are ellipsoids of revolution for which the equatorial radius is larger than the polar radius, such that they are oblate spheroids. Smaller bodies (Io, Mimas, etc.) tend to be better approximated by triaxial ellipsoids; however, triaxial ellipsoids would render many computations more complicated, especially those related to map projections. Many projections would lose their elegant and popular properties. For this reason spherical reference surfaces are frequently used in mapping programs.  The modern standard for maps of Mars (since about 2002) is to use planetocentric coordinates. Guided by the works of historical astronomers, Merton E. Davies established the meridian of Mars at Airy-0 crater. For Mercury, the only other planet with a solid surface visible from Earth, a thermocentric coordinate is used: the prime meridian runs through the point on the equator where the planet is hottest (due to the planet's rotation and orbit, the sun briefly retrogrades at noon at this point during perihelion, giving it more sun). By convention, this meridian is defined as exactly twenty degrees of longitude east of Hun Kal.  Tidally-locked bodies have a natural reference longitude passing through the point nearest to their parent body: 0° the center of the primary-facing hemisphere, 90° the center of the leading hemisphere, 180° the center of the anti-primary hemisphere, and 270° the center of the trailing hemisphere. However, libration due to non-circular orbits or axial tilts causes this point to move around any fixed point on the celestial body like an analemma.

Longitude (, ), is a geographic coordinate that specifies the east–west position of a point on the Earth's surface, or the surface of a celestial body. It is an angular measurement, usually expressed in degrees and denoted by the Greek letter lambda (λ). Meridians (lines running from pole to pole) connect points with the same longitude. The Prime Meridian, which passes near the Royal Observatory, Greenwich, England, is defined as 0° longitude by convention. Positive longitudes are east of the Prime Meridian, and negative ones are west.

La longitude est une coordonnée géographique représentée par une valeur angulaire, expression du positionnement est-ouest d'un point sur Terre (ou sur une autre sphère). La longitude de référence sur Terre est le méridien de Greenwich.Tous les points de même longitude appartiennent à une ligne épousant la courbure terrestre, coupant l'équateur à angle droit et reliant le pôle Nord au pôle Sud. Cette ligne est appelée « méridien ». À la différence de la latitude (position nord-sud), qui bénéficie de l'équateur et des pôles comme références, il n’existe aucune référence naturelle pour la longitude. La longitude, généralement notée λ, est donc une mesure angulaire sur 360° par rapport à un méridien de référence, avec une étendue de —180°, vers l'ouest, à +180°, vers l'est. Par convention, le méridien de référence, à la longitude 0°, est le méridien de Greenwich.


Gameplay.

Blizzard Entertainment's use of three distinct races in "StarCraft" is widely credited with revolutionizing the real-time strategy genre. All units are unique to their respective races, and while rough comparisons can be drawn between certain types of units in the technology tree, every unit performs differently and requires different tactics for a player to succeed.  The psionic and technologically adept Protoss have access to powerful units and machinery and advanced technologies such as energy shields and localized warp capabilities, powered by their psionic traits. However, their forces have lengthy and expensive manufacturing processes, encouraging players to follow a strategy of the quality of their units over the quantity. The insectoid Zerg possess entirely organic units and structures, which can be produced quickly and at a far cheaper cost to resources, but are accordingly weaker, relying on sheer numbers and speed to overwhelm enemies. The humanoid Terrans provide a middle ground between the other two races, providing units that are versatile and flexible. They have access to a range of more ballistic military technologies and machinery, such as tanks and nuclear weapons.  Although each race is unique in its composition, no race has an innate advantage over the other. Each species is balanced out so that while they have different strengths, powers, and abilities, their overall strength is the same. The balance stays complete via infrequent patches (game updates) provided by Blizzard.  "StarCraft" features artificial intelligence that scales in difficulty, although the player cannot change the difficulty level in the single-player campaigns. Each campaign starts with enemy factions running easy AI modes, scaling through the course of the campaign to the hardest AI modes. In the level editor provided with the game, a designer has access to four levels of AI difficulties: "easy", "medium", "hard", and "insane", each setting differing in the units and technologies allowed to an AI faction and the extent of the AI's tactical and strategic planning. The single-player campaign consists of thirty missions, split into ten for each race.

Resource management.

Each race relies on two resources to sustain their game economies and to build their forces: minerals and vespene gas. Minerals are needed for all units and structures, and they are obtained by using a worker unit to harvest the resource directly from mineral nodes scattered around the battlefield. Players require vespene gas to construct advanced units and buildings, and they acquire it by constructing a gas extraction building on top of a geyser and using worker units to extract the gas from it. In addition, players need to regulate the supplies for their forces to ensure that they can construct the number of units they need. Although the nature of the supply differs between the races—Terrans use physical supplies held in depots, Protoss use psionic energy channeled from their homeworld via pylons, and Zerg are regulated by the number of controlling overlord units present—the supply mechanic essentially works in exactly the same way for each race (just with differing impacts on gameplay), allowing players to create new units when there are sufficient resources to sustain them.

Base construction.

Protoss and Zerg building construction is limited to specific locations: Protoss buildings need to be linked to a power grid, while almost every Zerg structure must be placed on a carpet of biomass, called "creep", that is produced by certain structures. Terran buildings are far less limited, with certain primary base structures possessing the ability to take off and fly slowly to a new location. Terran buildings, however, require the worker unit to continue construction on the building until it is completed. Also, once a Terran building has taken a certain amount of damage, it will catch fire and can eventually burn to the ground without further enemy action if repairs are not performed by a worker unit. The Protoss, by contrast, only require a worker unit to begin the process of transporting a building to the theater of operations via warp, and their buildings' shields (but not their structure) are regenerative. The Zerg worker unit physically transforms into the structure created, which is capable of slowly healing itself.

Multiplayer.

Multiplayer on "StarCraft" is powered through Blizzard Entertainment's Battle.net Internet service. Through this, a maximum of eight players can compete in a variety of game modes, including simply destroying all other players (which may be competitive, as in Ladder play, or non-ranked, as in melee play), to king of the hill and capture the flag objective-based games. In addition, the game incorporates a variety of specialized scenarios for different types of game, such as simulating a football game, using the Terran hoverbike unit to conduct a bike race, or hosting a Zerg hunting competition. "StarCraft" is also one of the few games that include a spawn installation, which allows for limited multiplayer. It must be installed from a disc, and requires a product key to work just as the full version does. However, one product key can support up to eight spawned installations with access to Battle.net. Limitations of a spawned installation include the inability to play single-player missions, create multiplayer games, or use the campaign editor. Newer releases of the game available through Battle.net or discs that include the Windows Vista label don't support the spawn installation.

Synopsis.

Setting.

"StarCraft" takes place in a science fiction universe created by Chris Metzen and James Phinney for Blizzard Entertainment. According to the story presented in the game's manual, the overpopulation of Earth in the early 24th century has caused the international governing body, known as United Powers League (which was later succeeded by United Earth Directorate), to exile certain members of the human race, such as criminals, the cybernetically enhanced, and genetic mutants, to colonize the far reaches of the galaxy. An attempt to colonize a nearby solar system goes wrong, resulting in humanity's arrival in the Koprulu Sector. In the distant Koprulu Sector of the galaxy, the exiles form several governments, but quickly fall into conflict with each other. One government, the Confederacy of Man, eventually emerges as the strongest faction, but its oppressive nature and brutal methods of suppressing dissidents stir up major rebel opposition in the form of a terrorist group called the Sons of Korhal. Just prior to the beginning of the game, in December 2499, an alien race possessing advanced technology and psionic power, the Protoss, makes first contact with humanity by destroying a Confederate colony world without any prior warning. Soon after this, the Terrans discover that a second alien race, the insectoid Zerg, has been stealthily infesting the surface of several of the Terran colonies, and that the Protoss are destroying the planets to prevent the Zerg from spreading. With the Confederacy threatened by two alien races and internal rebellion, it begins to crumble.

Characters.

The player assumes the role of three nameless characters over the course of the game. In the first act, the player acts as the Confederate magistrate of an outlying colony world of Mar Sara, threatened by both the Zerg and the Protoss, and is forced through events to join the rebel Sons of Korhal under its leader Arcturus Mengsk. Mengsk's campaign is accompanied by Jim Raynor, a morally conscious law enforcement officer from Mar Sara, and Sarah Kerrigan, a psychic assassin and Mengsk's second-in-command. The second episode of the game sees the player as a cerebrate, a commander within the Zerg Swarm. The player is ruled over by the Zerg Overmind — the manifestation of the collective consciousness of the Swarm and the game's primary antagonist — and is given advice from other cerebrates of higher rank and status while accomplishing the objectives of the Swarm. In the final part of "StarCraft", the player is a newly appointed Executor within the Protoss military reporting to Aldaris, a representative of the Protoss government. Aldaris is at odds with Tassadar — the former occupant of the player's position — over his association with Zeratul, a member of a heretical group known as dark templar.

Story.

The story of "StarCraft" is presented through its instruction manual, the briefings to each mission, and conversations within the missions themselves, along with the use of cinematic cutscenes at key points. The game itself is split into three episodes, one for the player to command each race. In the first segment of the game, the player and Jim Raynor are attempting to control the colony of Mar Sara in the wake of the Zerg attacks on other Terran worlds. After the Confederacy arrests Raynor for destroying Confederate property, despite the fact that it had been infested by the Zerg, the player joins Arcturus Mengsk and the Sons of Korhal. Raynor, who is freed by Mengsk's troops, also joins and frequently accompanies the player on missions. Mengsk then begins to use Confederate technology captured on Mar Sara to lure the Zerg to Confederate installations and further his own goals. After forcing Confederate general Edmund Duke to join him, Mengsk sacrifices his own second-in-command, Sarah Kerrigan, to ensure the destruction of the Confederacy by luring the Zerg to the Confederate capital Tarsonis. Raynor is outraged by Mengsk's true aims of obtaining power at any cost and deserts, taking with him a small army of the former colonial militia of Mar Sara. Mengsk reorganizes what remains of the Terran population into the Terran Dominion, crowning himself as emperor.  The second campaign reveals that Kerrigan was not killed by the Zerg, but rather is captured and infested in an effort to incorporate her psionic traits into the Zerg gene pool. She emerges with far more psionic powers and physical strength, her DNA completely altered. Meanwhile, the Protoss commander Tassadar discovers that the Zerg's cerebrates cannot be killed by conventional means, but that they can be harmed by the powers wielded by the heretical dark templar. Tassadar allies himself with the dark templar prelate Zeratul, who assassinates Zasz, one of the Zerg's cerebrates in their hive clusters on Char. The cerebrate's death results in its forces running amok through the Zerg hives, but briefly links the minds of Zeratul and the Zerg Overmind, allowing the Overmind to finally learn the location of the Protoss homeworld Aiur, which the Overmind has been seeking for millennia. The main Zerg swarm promptly invades Aiur, while Kerrigan is dispatched to deal with Tassadar, and despite facing heavy Protoss resistance, the Overmind is able to embed itself into the crust of the planet.  The final episode of the game sees Aldaris and the Protoss government branding Tassadar a traitor and a heretic for conspiring with the dark templar. The player (later hinted to be Artanis) initially serves Aldaris in defending Aiur from the Zerg invasion, but while on a mission to arrest Tassadar, the player joins him instead. A Protoss civil war erupts, pitting Tassadar, Zeratul, and their allies against the Protoss establishment. The dark templar prove their worth when they use their energies to slay two more of the Zerg cerebrates on Aiur, and the Conclave reconciles with them. Aided by Raynor's forces—who sided with Tassadar back on Char—the Protoss break through the Overmind's weakened defenses and destroy the Overmind's outer shell, but take heavy casualties in the process. Tassadar channels his own psionic energies in combination with those of the dark templar through the hull of his command ship and crashes it into the Overmind, sacrificing himself in order to destroy it.

Development.

Blizzard Entertainment began development on "StarCraft" in 1995, shortly after the release of highly successful "". Using the "Tides of Darkness" game engine as a base, "StarCraft" made its debut at E3 1996. The version of the game displayed, assembled by the team's lead programmer Bob Fitch, received a rather weak response from the convention and was criticized by many for being ""Warcraft" in space." As a consequence the entire project was overhauled, bringing the focus onto creating three distinct species. Bill Roper, one of the game's producers, stated this would be a major departure from the "Warcraft" approach, comparing its two equal sides to those of chess and stating that "StarCraft" would allow players to "develop very unique strategies based on which species is being played, and will require players to think of different strategies to combat the other two species." The hand-drawn graphics seen in the E3 version were also replaced with rendered graphics. In early 1997, the new version of "StarCraft" was unveiled, receiving a far more positive response. However, the game was still marred by technical difficulties, so Bob Fitch completely redesigned the "Warcraft II" engine within two months to ensure that many of the features desired by the designers, such as the abilities for units to burrow and cloak, could be implemented. Later improvements to the game included pre-rendered sprites and backgrounds, constructed using 3D Studio Max. An isometric in-game view was also adopted, in contrast to "Warcraft II"s 3/4s birdseye perspective. In addition, the game utilized high quality music, composed by Blizzard's resident composers, and professional voice actors were hired.  Despite the progress, "StarCraft" was slow to emerge. The continual delays inspired a group of "StarCraft" fans on the official forums who labeled themselves "Operation: Can't Wait Any Longer" to write a series of fictional stories in which the members of Operation CWAL attempted to retrieve the beta version of "StarCraft" from Blizzard's headquarters in Irvine, California. To pay homage to their presence on the forums and enthusiasm for the game, Blizzard Entertainment later incorporated the group's name into "StarCraft" as a cheat code to speed up the production of units and gave the group thanks in the game's credits. The game was released for Windows on March 31, 1998, with the Classic Mac OS version following a year later in 1999. Development on a Nintendo 64 version, "StarCraft 64", began in 1999, converted from PC by Mass Media Interactive Entertainment—a subsidiary of THQ—and published by Nintendo. "StarCraft 64" was released on June 13, 2000 in the US and Europe. It was also released in Australia on May 25, 2001.

Music.

The musical score to "StarCraft" was composed by Blizzard Entertainment's composers. Glenn Stafford composed the Terran and Protoss in-game themes, while Derek Duke, who was a contracted composer at the time, wrote all the in-game music for the Zerg. The cinematic scores were composed by Stafford and Hayes. Hayes also collaborated with Stafford on one of the Protoss in-game tracks. Tracy W. Bush provided additional support in composing. The musical score of the game was received well by reviewers, who have described it as "appropriately melodic and dark" and "impressive", with one reviewer noting that some of the music owed much of its inspiration to Jerry Goldsmith's score for the film "Alien". The first official game soundtrack, "StarCraft: Game Music Vol. 1", was released in 2000, comprising tracks from both "StarCraft" and "", as well as a sizable portion of remix tracks and music inspired by "StarCraft", created by several South Korean disc jockeys. The soundtrack was distributed by Net Vision Entertainment. In September 2008, Blizzard Entertainment announced that a second soundtrack, "StarCraft Original Soundtrack", had been released on iTunes. This soundtrack consisted entirely of the original music from "StarCraft" and "Brood War", both from in-game themes to music used in the cinematic cut scenes.

Expansions and versions.

Computer expansions.

Before the release of "StarCraft", Blizzard Entertainment released a free-to-download game demo entitled "Loomings", comprising three missions and a tutorial. The prequel was made available for the full game in October 1999 as a custom map campaign, adding two extra missions and hosting it on Battle.net. In addition, the full release of "StarCraft" included a secondary campaign entitled "Enslavers". Consisting of five missions played as both the Terrans and the Protoss, "Enslavers" is set in the second campaign in "StarCraft" and follows the story of a Terran smuggler who manages to take control of a Zerg cerebrate and is pursued by both the Protoss and Terran Dominion. "Enslavers" acts as an exemplar single-player campaign for the game's level editor, highlighting how to use the features of the program. "StarCraft"s first expansion, Insurrection, was released for Windows on July 31, 1998. The expansion was developed by Aztech New Media and authorized by Blizzard Entertainment. Its story focused on a separate Confederate colony alluded to in the manual to "StarCraft", following a group of Terran colonists and a Protoss fleet in their fight against the Zerg and a rising local insurgency. "Insurrection" was not received well, being criticized by reviewers for lacking the quality of the original game. "Insurrection" was followed within a few months by a second expansion, Retribution. Developed by Stardock, published by WizardWorks and authorized by Blizzard Entertainment, "Retribution" follows all three races attempting to seize control of a powerful crystal on a Terran Dominion colony. The expansion was not received with critical support, instead being regarded as average but at least challenging. After the release of "Retribution", Blizzard Entertainment announced a new official expansion pack that would continue on the story of "StarCraft". "" was consequently created, developed jointly by Blizzard Entertainment and Saffire Corporation. "Brood War" continues the story of "StarCraft" from days after its conclusion, and was released for both Windows and Mac to critical praise on December 18, 1998 in the US and in March 1999 in Europe.  Before Insurrection, an unauthorized expansion pack, called Stellar Forces, was published by Micro Star but was recalled weeks later when Blizzard won the court case against it. It consisted of 22 single player maps and 32 multi-player maps which are considered to be rather plain.

Nintendo 64 version.

In 2000, "StarCraft 64" was released In North America for the Nintendo 64, co-developed by Blizzard Entertainment and Mass Media Inc. and published by Nintendo. The game featured all of the missions from both "StarCraft" and the expansion "Brood War", as well as some exclusive missions, such as two different tutorials and a new secret mission, "Resurrection IV". Blizzard Entertainment had previously considered a PlayStation port of the game, but it was decided that the game would instead be released on the Nintendo 64. "Resurrection IV" is set after the conclusion of "Brood War", and follows Jim Raynor embarking on a mission to rescue the "Brood War" character Alexei Stukov, a vice admiral from Earth who has been captured by the Zerg. The "Brood War" missions required the use of a Nintendo 64 memory Expansion Pak to run. In addition, "StarCraft 64" features a split screen cooperative mode, also requiring the expansion pak, allowing two players to control one force in-game. "StarCraft 64" lacked the online multiplayer capabilities and speech in mission briefings. In addition, cut scenes were shortened.

Remaster.

A remastered edition of the game, "", released August 14, 2017, preserves the gameplay of the original while adding support for ultra-high-definition graphics, Blizzard's modern online features, and re-recorded audio (soundtrack and sound effects).

"StarCraft: Cartooned".

On June 8, 2019, as part of the grand finals of the third season of the KSL, Blizzard announced a graphics overhaul pack for the game by Carbot Animations, the producers of multiple Blizzard-related parody animations, including their first and longest-running one, the "StarCrafts" series. As a graphical overhaul, its effect applies to all game modes and menus in "StarCraft: Remastered". It was released on July 10, 2019 as "StarCraft: Cartooned" alongside an announcer pack featuring South Korean YouTuber and children's television host Hyejin "Hey Jini" Kang.

Cultural impact.

Reception.

"StarCraft" was released internationally on March 31, 1998 and became the best-selling PC game for that year, selling over 1.5 million copies worldwide. In the United States, it was the best-selling computer game of 1998, with 746,365 units sold. It was the country's 14th best-selling release of the period between 1993 and 1999, selling 916,000 copies. By April 1999, South Korean players had purchased almost 300,000 units of the game. "StarCraft"s worldwide sales reached 4 million units by July 2001; South Korea accounted for 50% of these copies. By May 2007, "StarCraft" had sold over 9.5 million copies across the globe, with 4.5 million of these being sold in South Korea. Since the initial release of "StarCraft", Blizzard Entertainment reported that its Battle.net online multiplayer service grew by 800 percent.  Generally, "StarCraft" was received positively by critics, with many contemporary reviewers noting that while the game may not have deviated significantly from the status quo of most real-time strategy games, it was one of the best to have applied the formula. In addition, "StarCraft"s pioneering use of three distinct, unique, and balanced races over two equal sides was praised by critics, with GameSpot commenting that this helped the game to "avoid the problem that has plagued every other game in the genre". Many critics also praised the strength of the story accompanying the game, with some reviewers being impressed by how well the story was folded into the gameplay. The game's voice acting in particular was praised; GameSpot later hailed the voice work in the game as one of the ten best in the industry at the time. Equally, the multiplayer aspects of the game were positively received. "StarCraft" has received multiple awards, including being named as one of the best games of all time by GameSpot, IGN, and "Game Informer". According to Blizzard Entertainment, "StarCraft" has won 37 awards and has received a star on the floor of the Metreon as part of the Walk of Game in San Francisco in early 2006.  "Next Generation" reviewed the PC version of the game, rating it five stars out of five, and stated that "The quality of the play balancing and the elegance of the design mean that "StarCraft" sets a new high watermark for all real-time strategy games."  The reviewer from the online second volume of "Pyramid" stated that "One of the most hotly anticipated computer games of the last two years, Blizzard Entertainment's "Starcraft" has had a tremendous amount of hype to live up to. The fact that it "does" live up to the high expectations set for it may be the only recommendation it needs."  Although at the time "StarCraft"s graphics and audio were praised by critics, later reviews have noted that the graphics do not compare to more modern games. The capacity for the game's artificial intelligence to navigate units to waypoints also faced some heavy criticism, with "PC Zone" stating that the inability for developers to make an effective pathfinding system was "the single most infuriating element of the real-time strategy genre". In addition, several reviewers expressed concern over some familiarities between the unit structures of each race, as well as over the potential imbalance of players using rushing tactics early in multiplayer games. Blizzard Entertainment has strived to balance rush tactics in later updates. The Nintendo 64 version of the game was not received as positively by reviewers, and was criticized for poor graphics in comparison to the PC version. However, critics did praise the game and Mass Media for using effective controls on the gamepad and maintaining the high quality audio.  "Starcraft" won the Origins Award for Best Strategy Computer Game of 1998.  In 1998, "PC Gamer" declared it the 5th-best computer game ever released, and the editors called it "a strategy game that continues to evolve and surprise many months after its release, and that currently represents the state of the genre's art".  With more than 11 million copies sold worldwide by February 2009, "StarCraft" became one of the best-selling games for the personal computer. It has been praised for pioneering the use of unique "factions" in RTS gameplay, and for having a compelling story.

Legacy.

GameSpot described "StarCraft" as "The defining game of its genre. It is the standard by which all real-time strategy games are judged." IGN stated that "StarCraft" "is hands down one of the best, if not the best, real-time strategy games ever created." "StarCraft" is frequently included in the industry's best games rankings, for example it ranked 37 in "Edge"s top 100 games of all time. "StarCraft" has even been taken into space, as Daniel Barry took a copy of the game with him on the Space Shuttle mission STS-96 in 1999. "StarCraft"s popularity resulted in "Guinness World Records" awarding the game four world records, including "Best Selling PC Strategy Game," "Largest Income in Professional Gaming," and "Largest Audience for a Game Competition" when 120,000 fans turned out to watch the final of the SKY proleague season 2005 in Busan, South Korea. Researchers have shown that the audience for watching "StarCraft" games is diverse and that "StarCraft" uses instances of information asymmetry to make the game more entertaining for spectators. In addition, "StarCraft" has been the subject of an academic course; the University of California, Berkeley offered a student-run introductory course on theory and strategy in spring 2009.  After its release, "StarCraft" rapidly grew in popularity in South Korea, eventually making its way to become the country's national e-sport after establishing a successful pro-gaming scene. Professional gamers in South Korea are media celebrities, and "StarCraft" games are broadcast over three television channels dedicated to the professional gaming scene. Professional gamers in South Korea have gained television contracts, sponsorships, and tournament prizes, allowing one of the most famous players, Lim "BoxeR" Yo-hwan, to gain a fan club of over half a million people. One player, Lee Yun-yeol, reported earnings in 2005 of.  "StarCraft" was part of the United States Air Force's Air and Space Basic Course, used to teach newly active officers about crisis planning under stress and joint service teamwork. Other efforts to make more'realistic' current-day battle software led to distractions when simulated hardware didn't align with the real hardware active duty officers knew about. The science fiction setting allowed students to focus on the battle tactics.  The annual Conference on Artificial Intelligence and Interactive Digital Entertainment hosts a competition for AIs playing the game. As of 2015, humans still win.  In 2014, an unofficial version for the Pandora handheld and the ARM architecture became available by static recompilation and reverse engineering of the original x86 version.  The original game, along with the expansion, was released for free in April 2017.

Merchandise.

The storyline of "StarCraft" has been adapted into several novels. The first novel, "Uprising", which was written by Blizzard employee Micky Neilson and published in December 2000, acts as a prequel to the events of "StarCraft". Other novels—"Liberty's Crusade" by Jeff Grubb and Aaron Rosenberg's "Queen of Blades"—retell the story of the game from different perspectives. At BlizzCon 2007, "StarCraft" creator Chris Metzen stated that he hoped to novelize the entirety of "StarCraft" and its expansion "Brood War" into a definitive text-based story. Later novels, such as Gabriel Mesta's "Shadow of the Xel'Naga" and Christie Golden's "The Dark Templar Saga", further expand the storyline, creating the setting for "".  A number of action figures and collectable statues based upon the characters and units in "StarCraft" have been produced by ToyCom. A number of model kits, made by Academy Hobby Model Kits, were also produced, displaying 1/30 scale versions of the marine and the hydralisk. In addition, Blizzard Entertainment teamed up with Fantasy Flight Games to create a board game with detailed sculptures of game characters. Blizzard Entertainment also licensed Wizards of the Coast to produce an Alternity based game entitled "StarCraft Adventures".

StarCraft is a 1998 military science fiction real-time strategy game developed and published by Blizzard Entertainment for Microsoft Windows. The game spawned the StarCraft franchise, and became the first game of the video game series. A Classic Mac OS version was released in 1999, and a Nintendo 64 adaptation, co-developed with Mass Media, was released in 2000.

En novembre 1998, la sortie de l’extension "" également développée par précède les sorties des versions Macintosh et qui ont lieu respectivement en et en juin 2000. Une suite est publiée le sous le nom de "", et rencontre également un grand succès commercial avec plus de de copies vendues six mois après sa sortie. Une édition remastérisée intitulée "", comprenant le jeu original et son extension, est sortie le.


Name.

The script is either called Latin script or Roman script, in reference to its origin in ancient Rome. In the context of transliteration, the term "romanization" (British English: "romanisation") is often found. Unicode uses the term "Latin" as does the International Organization for Standardization (ISO).  The numeral system is called the Roman numeral system and the collection of the elements, Roman numerals. The numbers 1, 2, 3... are Latin/Roman script numbers for the Hindu–Arabic numeral system.

History.

Archaic Latin alphabet.

The letter was the western form of the Greek gamma, but it was used for the sounds and alike, possibly under the influence of Etruscan, which might have lacked any voiced plosives. Later, probably during the 3rd century BC, the letter – unneeded to write Latin properly – was replaced with the new letter, a modified with a small horizontal stroke, which took its place in the alphabet. From then on, represented the voiced plosive, while was generally reserved for the voiceless plosive. The letter was used only rarely, in a small number of words such as "Kalendae", often interchangeably with.

Classical Latin alphabet.

After the Roman conquest of Greece in the 1st century BC, Latin adopted the Greek letters and (or readopted, in the latter case) to write Greek loanwords, placing them at the end of the alphabet. An attempt by the emperor Claudius to introduce three additional letters did not last. Thus it was during the classical Latin period that the Latin alphabet contained 23 letters:

ISO basic Latin alphabet.

The use of the letters I and V for both consonants and vowels proved inconvenient as the Latin alphabet was adapted to Germanic and Romance languages. W originated as a doubled V (VV) used to represent the found in Old English as early as the 7th century. It came into common use in the later 11th century, replacing the letter wynn, which had been used for the same sound. In the Romance languages, the minuscule form of V was a rounded "u"; from this was derived a rounded capital U for the vowel in the 16th century, while a new, pointed minuscule "v" was derived from V for the consonant. In the case of I, a word-final swash form, "j", came to be used for the consonant, with the un-swashed form restricted to vowel use. Such conventions were erratic for centuries. J was introduced into English for the consonant in the 17th century (it had been rare as a vowel), but it was not universally considered a distinct letter in the alphabetic order until the 19th century.  By the 1960s, it became apparent to the computer and telecommunications industries in the First World that a non-proprietary method of encoding characters was needed. The International Organization for Standardization (ISO) encapsulated the Latin alphabet in their (ISO/IEC 646) standard. To achieve widespread acceptance, this encapsulation was based on popular usage. As the United States held a preeminent position in both industries during the 1960s, the standard was based on the already published "American Standard Code for Information Interchange", better known as ASCII, which included in the character set the 26 × 2 (uppercase and lowercase) letters of the English alphabet. Later standards issued by the ISO, for example ISO/IEC 10646 (Unicode Latin), have continued to define the 26 × 2 letters of the English alphabet as the basic Latin alphabet with extensions to handle other letters in other languages.

Spread.

The Latin alphabet spread, along with Latin, from the Italian Peninsula to the lands surrounding the Mediterranean Sea with the expansion of the Roman Empire. The eastern half of the Empire, including Greece, Turkey, the Levant, and Egypt, continued to use Greek as a lingua franca, but Latin was widely spoken in the western half, and as the western Romance languages evolved out of Latin, they continued to use and adapt the Latin alphabet.

Middle Ages.

With the spread of Western Christianity during the Middle Ages, the Latin alphabet was gradually adopted by the peoples of Northern Europe who spoke Celtic languages (displacing the Ogham alphabet) or Germanic languages (displacing earlier Runic alphabets) or Baltic languages, as well as by the speakers of several Uralic languages, most notably Hungarian, Finnish and Estonian.  The Latin script also came into use for writing the West Slavic languages and several South Slavic languages, as the people who spoke them adopted Roman Catholicism. The speakers of East Slavic languages generally adopted Cyrillic along with Orthodox Christianity. The Serbian language uses both scripts, with Cyrillic predominating in official communication and Latin elsewhere, as determined by the Law on Official Use of the Language and Alphabet.

Since the 16th century.

As late as 1500, the Latin script was limited primarily to the languages spoken in Western, Northern, and Central Europe. The Orthodox Christian Slavs of Eastern and Southeastern Europe mostly used Cyrillic, and the Greek alphabet was in use by Greek-speakers around the eastern Mediterranean. The Arabic script was widespread within Islam, both among Arabs and non-Arab nations like the Iranians, Indonesians, Malays, and Turkic peoples. Most of the rest of Asia used a variety of Brahmic alphabets or the Chinese script.  Through European colonization the Latin script has spread to the Americas, Oceania, parts of Asia, Africa, and the Pacific, in forms based on the Spanish, Portuguese, English, French, German and Dutch alphabets.  It is used for many Austronesian languages, including the languages of the Philippines and the Malaysian and Indonesian languages, replacing earlier Arabic and indigenous Brahmic alphabets. Latin letters served as the basis for the forms of the Cherokee syllabary developed by Sequoyah; however, the sound values are completely different.

Since 19th century.

In the late 19th century, the Romanians returned to the Latin alphabet, which they had used until the Council of Florence in 1439, primarily because Romanian is a Romance language. The Romanians were predominantly Orthodox Christians, and their Church, increasingly influenced by Russia after the fall of Byzantine Greek Constantinople in 1453 and capture of the Greek Orthodox Patriarch, had begun promoting the Slavic Cyrillic.  Under French rule and Portuguese missionary influence, a Latin alphabet was devised for the Vietnamese language, which had previously used Chinese characters.

Since 20th century.

In 1928, as part of Mustafa Kemal Atatürk's reforms, the new Republic of Turkey adopted a Latin alphabet for the Turkish language, replacing a modified Arabic alphabet. Most of the Turkic-speaking peoples of the former USSR, including Tatars, Bashkirs, Azeri, Kazakh, Kyrgyz and others, used the Latin-based Uniform Turkic alphabet in the 1930s; but, in the 1940s, all were replaced by Cyrillic. In 2017 Kazakhstan adopted the Latin script as their second official script replacing Cyrillic by 2025.  After the collapse of the Soviet Union in 1991, three of the newly independent Turkic-speaking republics, Azerbaijan, Uzbekistan, Turkmenistan, and Kazakhstan as well as Romanian-speaking Moldova, officially adopted Latin alphabets for their languages. Kyrgyzstan, Iranian-speaking Tajikistan, and the breakaway region of Transnistria kept the Cyrillic alphabet, chiefly due to their close ties with Russia.  In the 1930s and 1940s, the majority of Kurds replaced the Arabic script with two Latin alphabets. Although the only official Kurdish government uses an Arabic alphabet for public documents, the Latin Kurdish alphabet remains widely used throughout the region by the majority of Kurdish-speakers.

21st century.

In 2015, the government of Kazakhstan announced that a Kazakh Latin alphabet would replace the Kazakh Cyrillic alphabet as the official writing system for the Kazakh language by 2025. There are also talks about switching from the Cyrillic script to Latin in Ukraine, Kyrgyzstan, and Mongolia.  In October 2019, the organization National Representational Organization for Inuit in Canada (ITK) announced that they will introduce a unified writing system for the Inuit languages in the country. The writing system is based on the Latin alphabet and is modeled after the one used in the Greenlandic language.

International standards.

As used by various languages.

In the course of its use, the Latin alphabet was adapted for use in new languages, sometimes representing phonemes not found in languages that were already written with the Roman characters. To represent these new sounds, extensions were therefore created, be it by adding diacritics to existing letters, by joining multiple letters together to make ligatures, by creating completely new forms, or by assigning a special function to pairs or triplets of letters. These new forms are given a place in the alphabet by defining an alphabetical order or collation sequence, which can vary with the particular language.

Letters.

Some examples of new letters to the standard Latin alphabet are the Runic letters wynn and thorn, and the letter eth, which were added to the alphabet of Old English. Another Irish letter, the insular "g", developed into yogh, used in Middle English. Wynn was later replaced with the new letter, eth and thorn with, and yogh with. Although the four are no longer part of the English or Irish alphabets, eth and thorn are still used in the modern Icelandic and Faroese alphabets.  Some West, Central and Southern African languages use a few additional letters that have a similar sound value to their equivalents in the IPA. For example, Adangme uses the letters and, and Ga uses, and. Hausa uses and for implosives, and for an ejective. Africanists have standardized these into the African reference alphabet.  The Azerbaijani language also has, which represents the near-open front unrounded vowel.

Multigraphs.

A digraph is a pair of letters used to write one sound or a combination of sounds that does not correspond to the written letters in sequence. Examples are,,, in English, and in Dutch. In Dutch the is capitalized as or the ligature, but never as, and it often takes the appearance of a ligature very similar to the letter in handwriting.  A trigraph is made up of three letters, like the German, the Breton or the Milanese. In the orthographies of some languages, digraphs and trigraphs are regarded as independent letters of the alphabet in their own right. The capitalization of digraphs and trigraphs is language-dependent, as only the first letter may be capitalized, or all component letters simultaneously (even for words written in titlecase, where letters after the digraph or trigraph are left in lowercase).

Ligatures.

A ligature is a fusion of two or more ordinary letters into a new glyph or character. Examples are (from, called "ash"), (from, sometimes called "oethel"), the abbreviation (from, called "ampersand"), and (from or, the archaic medial form of, followed by an or, called "sharp S" or "eszett").

Diacritics.

A diacritic, in some cases also called an accent, is a small symbol that can appear above or below a letter, or in some other position, such as the umlaut sign used in the German characters,, or the Romanian characters ă, â, î, ș, ț. Its main function is to change the phonetic value of the letter to which it is added, but it may also modify the pronunciation of a whole syllable or word, or distinguish between homographs (such as the Dutch words "een" meaning "a" or "an", and "één", meaning "one"). As with letters, the value of diacritics is language-dependent.  English is the only major modern European language requiring no diacritics for native words (although a diaeresis may be used in words such as "coöperation").

Collation.

Some modified letters, such as the symbols,, and, may be regarded as new individual letters in themselves, and assigned a specific place in the alphabet for collation purposes, separate from that of the letter on which they are based, as is done in Swedish. In other cases, such as with,, in German, this is not done; letter-diacritic combinations being identified with their base letter. The same applies to digraphs and trigraphs. Different diacritics may be treated differently in collation within a single language. For example, in Spanish, the character is considered a letter, and sorted between and in dictionaries, but the accented vowels,,,, are not separated from the unaccented vowels,,,,.

Capitalization.

The languages that use the Latin script today generally use capital letters to begin paragraphs and sentences and proper nouns. The rules for capitalization have changed over time, and different languages have varied in their rules for capitalization. Old English, for example, was rarely written with even proper nouns capitalized; whereas Modern English of the 18th century had frequently all nouns capitalized, in the same way that Modern German is written today, e.g..

Romanization.

Words from languages natively written with other scripts, such as Arabic or Chinese, are usually transliterated or transcribed when embedded in Latin-script text or in multilingual international communication, a process termed Romanization.  Whilst the Romanization of such languages is used mostly at unofficial levels, it has been especially prominent in computer messaging where only the limited 7-bit ASCII code is available on older systems. However, with the introduction of Unicode, Romanization is now becoming less necessary. Note that keyboards used to enter such text may still restrict users to Romanized text, as only ASCII or Latin-alphabet characters may be available.

Latin script, also known as Roman script, is a set of graphic signs (script) based on the letters of the classical Latin alphabet. This is derived from a form of the Cumaean Greek version of the Greek alphabet used by the Etruscans. Several Latin-script alphabets exist, which differ in graphemes, collation and phonetic values from the classical Latin alphabet.

Lalphabet latin est un alphabet bicaméral comportant vingt-six lettres de base, principalement utilisé pour écrire les langues d’Europe de l'Ouest, d'Europe du Nord et d'Europe centrale, ainsi que les langues de nombreux pays qui ont été exposés à une forte influence européenne, notamment à travers la colonisation européenne des Amériques, de l'Afrique et de l'Océanie.


Newtonian.

Momentum is a vector quantity: it has both magnitude and direction. Since momentum has a direction, it can be used to predict the resulting direction and speed of motion of objects after they collide. Below, the basic properties of momentum are described in one dimension. The vector equations are almost identical to the scalar equations (see multiple dimensions).

Single particle.

The momentum of a particle is conventionally represented by the letter. It is the product of two quantities, the particle's mass (represented by the letter ) and its velocity ():  The unit of momentum is the product of the units of mass and velocity. In SI units, if the mass is in kilograms and

Many particles.

The momentum of a system of particles is the vector sum of their momenta. If two particles have respective masses and, and velocities and, the total momentum is The momenta of more than two particles can be added more generally with the following:  A system of particles has a

Relation to force.

If the net force applied to a particle is constant, and is applied for a time interval, the momentum of the particle changes by an amount  In differential form, this is Newton's second law; the rate of change of the momentum of a particle is equal to the instantaneous force acting on it,  If the net force experienced by a particle changes as a function of time,, the change in momentum (or impulse ) between

Conservation.

In a closed system (one that does not exchange any matter with its surroundings and is not acted on by external forces) the total momentum is constant. This fact, known as the "law of conservation of momentum", is implied by Newton's laws of motion. Suppose, for example, that two particles interact. Because of the third law, the forces between them are equal and opposite. If the particles are numbered 1 and 2, the second

Dependence on reference frame.

Momentum is a measurable quantity, and the measurement depends on the motion of the observer. For example: if an apple is sitting in a glass elevator that is descending, an outside observer, looking into the elevator, sees the apple moving, so, to that observer, the apple has a non-zero momentum. To someone inside the elevator, the apple does not move, so, it has zero momentum. The two observers each have a frame of reference, in which, they observe motions, and, if the elevator is descending steadily, they will see behavior that is consistent with those same physical laws.  Suppose a particle has position in a stationary frame of reference. From the point of view of

Application to collisions.

By itself, the law of conservation of momentum is not enough to determine the motion of particles after a collision. Another property of the motion, kinetic energy, must be known. This is not necessarily conserved. If it is conserved, the collision is called an "elastic collision"; if not, it is an "inelastic collision".

Elastic collisions.

An elastic collision is one in which no kinetic energy is absorbed in the collision. Perfectly elastic "collisions" can occur when the objects do not touch each other, as for example in atomic or nuclear scattering where electric repulsion keeps them apart. A slingshot maneuver of a satellite around a planet can also be viewed as a perfectly elastic collision. A collision between two pool balls is a good example of an "almost" totally elastic collision, due to their high rigidity, but when bodies come in contact there is always some dissipation.  A head-on elastic collision between two bodies can be represented by velocities in one dimension, along a line passing through the bodies. If the velocities are and before the collision and and after, the equations

Inelastic collisions.

In an inelastic collision, some of the kinetic energy of the colliding bodies is converted into other forms of energy (such as heat or sound). Examples include traffic collisions, in which the effect of loss of kinetic energy can be seen in the damage to the vehicles; electrons losing some of their energy to atoms (as in the Franck–Hertz experiment); and particle accelerators in which the kinetic energy is converted into mass in the form of new particles.  In a perfectly inelastic collision (such as a bug hitting a windshield), both bodies have the same motion afterwards. A head-on inelastic collision between two bodies can be represented by velocities in one dimension, along a line passing through the bodies. If the velocities are and before the collision then in a perfectly inelastic collision both bodies will be travelling with velocity after the

Multiple dimensions.

Real motion has both direction and velocity and must be represented by a vector. In a coordinate system with axes, velocity has components in the -direction, in the -direction, in the -direction. The vector is represented by a boldface symbol: Similarly, the momentum is a vector quantity and is represented by a boldface symbol:  The equations in the previous sections, work in vector form if the scalars and are replaced by vectors and. Each vector equation

Objects of variable mass.

The concept of momentum plays a fundamental role in explaining the behavior of variable-mass objects such as a rocket ejecting fuel or a star accreting gas. In analyzing such an object, one treats the object's mass as a function that varies with time:. The momentum of the object at time is therefore. One might then try to invoke Newton's second law of motion by saying that the external force on the object is related to

Relativistic.

Lorentz invariance.

Newtonian physics assumes that absolute time and space exist outside of any observer; this gives rise to Galilean invariance. It also results in a prediction that the speed of light can vary from one reference frame to another. This is contrary to observation. In the special theory of relativity, Einstein keeps the postulate that the equations of motion do not depend on the reference frame, but assumes that the speed of light is invariant. As a result, position and

Four-vector formulation.

In the theory of special relativity, physical quantities are expressed in terms of four-vectors that include time as a fourth coordinate along with the three space coordinates. These vectors are generally represented by capital letters, for example for position. The expression for the "four-momentum" depends on how the coordinates are expressed. Time may be given in its normal units or multiplied by the speed of light so that all the components of the four-vector have dimensions of length. If the latter scaling is used, an interval of proper time,, defined by is invariant under Lorentz transformations (in this expression and in what follows the metric signature has been used, different authors use different conventions). Mathematically this invariance can be ensured in one of two ways: by treating the four-vectors as Euclidean vectors and multiplying time

Generalized.

Newton's laws can be difficult to apply to many kinds of motion because the motion is limited by "constraints". For example, a bead on an abacus is constrained to move along its wire and a pendulum bob is constrained to swing at a fixed distance from the pivot. Many such constraints can be incorporated by changing the normal Cartesian coordinates to a set of "generalized coordinates" that may be fewer in number. Refined mathematical methods have been developed for solving mechanics problems in generalized coordinates. They introduce a "generalized momentum", also known as the "canonical" or "conjugate momentum", that extends the concepts of both linear momentum and angular momentum. To distinguish it from generalized momentum, the product of mass and velocity is also referred to as "mechanical", "kinetic" or "kinematic momentum". The two main methods are described below.

Lagrangian mechanics.

In Lagrangian mechanics, a Lagrangian is defined as the difference between the kinetic energy and the potential energy :  If the generalized coordinates are represented as a vector and time differentiation is represented by a dot over the variable, then the equations of motion (known as the Lagrange or Euler–Lagrange equations) are a set of equations: If a coordinate is not a Cartesian coordinate, the associated generalized momentum component does not necessarily have the dimensions of linear momentum. Even

Hamiltonian mechanics.

In Hamiltonian mechanics, the Lagrangian (a function of generalized coordinates and their derivatives) is replaced by a Hamiltonian that is a function of generalized coordinates and momentum. The

Symmetry and conservation.

Conservation of momentum is a mathematical consequence of the homogeneity (shift symmetry) of space (position in space is the canonical conjugate

Electromagnetic.

Particle in a field.

In Maxwell's equations, the forces between particles are mediated by electric and magnetic fields. The electromagnetic force ("Lorentz force") on a particle with charge due to a combination of electric field and magnetic field is (in SI units). It has an electric potential and magnetic vector potential. In the non-relativistic regime, its generalized momentum is

Conservation.

In Newtonian mechanics, the law of conservation of momentum can be derived from the law of action and reaction, which states that every force has a reciprocating equal and opposite force. Under some circumstances, moving charged particles can exert forces on each other in non-opposite directions. Nevertheless, the combined momentum of the particles and the electromagnetic field is conserved.

Vacuum.

The Lorentz force imparts a momentum to the particle, so by Newton's second law the particle must impart a momentum to the electromagnetic fields.  In a vacuum, the momentum per unit volume is where is the vacuum permeability and is the speed of light. The momentum density is proportional to the Poynting vector which gives the directional rate of energy transfer per unit area:  If momentum is to be conserved over the volume

Media.

The above results are for the "microscopic" Maxwell equations, applicable to electromagnetic forces in a vacuum (or on a very small scale in media). It is more difficult to define momentum density in media because the division into electromagnetic and mechanical is arbitrary. The definition of electromagnetic momentum density is modified to where the H-field is related to the B-field and the magnetization by The electromagnetic stress tensor depends on the properties of the media.

Quantum mechanical.

In quantum mechanics, momentum is defined as a self-adjoint operator on the wave function. The Heisenberg uncertainty principle defines limits on how accurately the momentum and position of a single observable system can be known at once. In quantum mechanics, position and momentum are conjugate variables.  For a single particle described in the position basis the momentum operator can be written as  where is the gradient operator, is the reduced Planck constant, and is the imaginary unit. This is a commonly encountered form of the momentum operator, though

In deformable bodies and fluids.

Conservation in a continuum.

In fields such as fluid dynamics and solid mechanics, it is not feasible to follow the motion of individual atoms or molecules. Instead, the materials must be approximated by a continuum in which there is a particle or fluid parcel at each point that is assigned the average of the properties of atoms in a small region nearby. In particular, it has a density and velocity that depend on time and position. The momentum per unit volume is.  Consider a column of water

Acoustic waves.

A disturbance in a medium gives rise to oscillations, or waves, that propagate away from their source. In a fluid, small changes in pressure can often be described by the acoustic wave equation: where is the speed of sound. In a solid, similar equations can be obtained for propagation

History of the concept.

In about 530 AD, working in Alexandria, Byzantine philosopher John Philoponus developed a concept of momentum in his commentary to Aristotle's "Physics". Aristotle claimed that everything that is moving must be kept moving by something. For example, a thrown ball must be kept moving by motions of the air. Most writers continued to accept Aristotle's theory until the time of Galileo, but a few were skeptical. Philoponus pointed out the absurdity in Aristotle's claim that motion of an object is promoted by the same air that is resisting its passage. He proposed instead that an impetus was imparted to the object in the act of throwing it. Ibn Sīnā (also known by his Latinized name Avicenna) read Philoponus and published his own theory of motion in "The Book of Healing" in 1020. He agreed that an impetus is imparted to a projectile by the thrower; but unlike Philoponus, who believed that it was a temporary virtue that would decline even in a vacuum, he viewed it as a persistent, requiring external forces such as air resistance to dissipate it. The work of Philoponus, and possibly that of Ibn Sīnā, was read and refined by the European philosophers Peter Olivi and Jean Buridan. Buridan, who in about 1350 was made rector of the University of Paris, referred to impetus being proportional to the weight times the speed. Moreover, Buridan's theory was different from his predecessor's in that he did not consider impetus to be self-dissipating, asserting that a body would be arrested by the forces of air resistance and gravity which might be opposing its impetus.  René Descartes believed that the total "quantity of motion" () in the universe is conserved, where the quantity of motion is understood as the product of size and speed. This should not be read as a statement of the modern law of momentum, since he had no concept of mass as distinct from weight and size, and more important, he believed that it is speed rather than velocity that is conserved. So for Descartes if a moving object were to bounce off a surface, changing its direction but not its speed, there would be no change in its quantity of motion. Galileo, in his "Two New Sciences", used the Italian word "impeto" to similarly describe Descartes' quantity of motion.  Leibniz, in his "Discourse on Metaphysics", gave an argument against Descartes' construction of the conservation of the "quantity of motion" using an example of dropping blocks of different sizes different distances. He points out that force is conserved but quantity of motion, construed as the product of size and speed of an object, is not conserved.  Christiaan Huygens concluded quite early that Descartes's laws for the elastic collision of two bodies must be wrong, and he formulated the correct laws. An important step was his recognition of the Galilean invariance of the problems. His views then took many years to be circulated. He passed them on in person to William Brouncker and Christopher Wren in London, in 1661. What Spinoza wrote to Henry Oldenburg about them, in 1666 which was during the Second Anglo-Dutch War, was guarded. Huygens had actually worked them out in a manuscript "De motu corporum ex percussione" in the period 1652–6. The war ended in 1667, and Huygens announced his results to the Royal Society in 1668. He published them in the "Journal des sçavans" in 1669.  The first correct statement of the law of conservation of momentum was by English mathematician John Wallis in his 1670 work, "Mechanica sive De Motu, Tractatus Geometricus": "the initial state of the body, either of rest or of motion, will persist" and "If the force is greater than the resistance, motion will result". Wallis used "momentum" for quantity of motion, and "vis" for force. Newton's "Philosophiæ Naturalis Principia Mathematica", when it was first published in 1687, showed a similar casting around for words to use for the mathematical momentum. His Definition II defines "quantitas motus", "quantity of motion", as "arising from the velocity and quantity of matter conjointly", which identifies it as momentum. Thus when in Law II he refers to "mutatio motus", "change of motion", being proportional to the force impressed, he is generally taken to mean momentum and not motion. It remained only to assign a standard term to the quantity of motion. The first use of "momentum" in its proper mathematical sense is not clear but by the time of Jennings's "Miscellanea" in 1721, five years before the final edition of Newton's "Principia Mathematica", momentum or "quantity of motion" was being defined for students as "a rectangle", the product of and, where is "quantity of material" and is "velocity",.

In Newtonian mechanics, linear momentum, translational momentum, or simply momentum (pl. momenta) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. If is an object's mass and is its velocity (also a vector quantity), then the object's momentum is:
 formula_1
 In SI units, momentum is measured in kilogram meters per second (kg⋅m/s).

En physique, la quantité de mouvement est le produit de la masse par le vecteur vitesse d'un corps matériel supposé ponctuel. Il s'agit donc d'une grandeur vectorielle, définie par formula_1, qui dépend du référentiel d'étude. Par additivité, il est possible de définir la quantité de mouvement d'un corps non ponctuel (ou système matériel), dont il est possible de démontrer qu'elle est égale à la quantité de mouvement de son centre d'inertie affecté de la masse totale du système, soit formula_2 ("C" étant le centre d'inertie du système). Son unité est le.


History.

United Kingdom of the Netherlands.

After the defeat of Napoleon in 1815, the United Kingdom of the Netherlands was created at the Congress of Vienna, consisting of territories which had been added to France by Napoleon: the former Dutch Republic and the Southern Netherlands. In the newly created kingdom, the former French département Dyle became the new province of South Brabant, distinguishing it from Central Brabant (later Antwerp province); and from North Brabant (now part of the Netherlands), all named after the former Duchy of Brabant. The provincial governors during this time were:

Belgium.

After the Belgian Revolution of 1830, the Southern Netherlands (including South and Central Brabant) became independent as Belgium and later also Luxembourg. The province was then renamed simply Brabant and became the central province of Belgium, with its capital city Brussels. The province contained three arrondissements: Brussels, Leuven and Nivelles.  In 1961–1963 the language border was established, from which the province was divided into a Dutch-speaking region, a French-speaking region and the bilingual Brussels. The Brussels arrondissement was split to this end. In 1989, Brussels-Capital Region was created, but the region was still part of the province of Brabant. In 1995, the province of Brabant was split into the Dutch-speaking Flemish Brabant, the French-speaking Walloon Brabant and the bilingual Brussels-Capital Region. The Brussels-Capital Region exercises the powers of a Province on its own territory.

Demographics.

As comparison, the current two provinces of Brabant, together with Brussels, had 2,621,275 inhabitants in January 2011.  Number of inhabitants x 1000

The Province of Brabant (,, ) was a province in Belgium from 1830 to 1995. It was created in 1815 as South Brabant, part of the United Kingdom of the Netherlands. In 1995, it was split into the Dutch-speaking Flemish Brabant, the French-speaking Walloon Brabant and the bilingual Brussels-Capital Region.

La province de Brabant ou Brabant était l'une des neuf provinces belges définies au début du XIX siècle, centrée autour de sa capitale, Bruxelles. Cette province a été scindée en 1995.