title: Two-Face

text: In "Batman" #700, which establishes Terry McGinnis as part of the DC Universe canon, it is revealed that Two-Face-Two kidnapped the infant Terry, along with an 80-year-old Carter Nichols, and tried to disfigure them in the style of the Joker. His plans were foiled by Damian Wayne, the fourth Robin and Batman's biological son. Unlike the original Two-Face, this version of the character was born deformed with a second face rather than being scarred by acid or fire and flips two coins instead of one. He is then killed when a machine falls on him. Another Two-Face-Two is briefly mentioned during the course of the "DC One Million" storyline, when the Batman of the 853rd century comments how this villain was defeated when the second Batman convinced him that the law of averages proved his coin-tossing would ultimately cause him to make more "good" decisions than "bad" ones.


title: Two-Face

text: A number of alternate universes in DC Comics publications allow writers to introduce variations on Two-Face, in which the character's origins, behavior, and morality differ from the mainstream setting.


title: Two-Face

text: In the alternate future setting of "The Dark Knight Returns", plastic surgery returns Dent's face to normal, but at the unforeseen cost of permanently destroying the good-hearted Harvey Dent personality. The monstrous Two-Face is left in permanent control—to the extent that one of his henchmen now refers to him only as "Face". Now with his face swathed in bandages, he attempts to blow up the Gotham Twin Towers in exchange for ransom, but is stopped by Batman. He now sees both sides of his face as scarred, or as he says to Batman when he captures him, "At least both sides match". Later in the series, his psychiatrist (who is characterized as completely inept) describes Dent's condition as "recovering steadily".


title: Two-Face

text: Two-Face has a brief short story in the first issue of "Batman Black and White", in the comic titled "Two of a Kind" featuring him receiving plastic surgery to regain his original identity as Harvey Dent, only to suffer a relapse when his fiancée - his former psychiatrist - is revealed to have a psychotic twin sister, who kills her sister and forces him to become Two-Face again in order to take his revenge.


title: Two-Face

text: In the "" universe, there are two versions of Two-Face. One is Detective Duell, a corrupt officer on the Gotham City Police Department, whose face is scarred in a manner similar to the version of Two-Face in the mainstream continuity. Duell is arrested at the end of "Batgirl and Robin: Thrillkiller" #1-3. In the sequel, "Batgirl and Batman: Thrillkiller '62", Harvey Dent is the new District Attorney. He appears at the end as the new Mayor of Gotham.


title: Two-Face

text: The new Earth-Three features a heroic female counterpart to Two-Face: Evelyn "Eve" Dent—"Three-Face"—the mother of Duela Dent (a nod to the classic film, "The Three Faces of Eve"). Her original affiliation is to the heroic Riddler Family (like the similar Batman Family); it included herself, Quizmaster, Jokester, and Riddler's/Joker's Daughter (her daughter Duela). They were later part of Alexander Luthor's Justice Underground, opposing Ultraman's Crime Syndicate.


title: Two-Face

text: Evelyn has three personalities (Irrational, Practical, and Hedonistic). To portray this, she wears a costume that is divided in three parts. Her right side favors loud fabrics like polka-dots, stripes, or plaids; her left side favors animal prints like tiger or leopard; and the center is a wide stripe of green. Over her leotard she wears a leather jacket that is a brown bomber jacket on the right and a black biker jacket on the left. Her face is not scarred but is instead usually painted all white with a vertical green center stripe and dark green or black lipstick; sometimes she is shown with her face parted into light green on the right, white in the middle, and mauve on the left. Her black hair is divided into cropped short on the right (sometimes dyed pink or red), worn shoulder-length on the left, and a mohawk in the center. She carries a revolver in a holster slung on her right hip.


title: Two-Face

text: On the Tangent Earth, Harvey Dent is an African-American man with psionic powers and is that world's Superman, although he has no other similarities to the Two-Face character.


title: Two-Face

text: In the "Flashpoint" alternate timeline, Harvey Dent is a judge. When Joker kidnaps Dent's children, Dent asks Batman for help in their search, agreeing to do anything asked. Dent warns Batman that he will shut down everything Batman owns, including Wayne Casinos, unless his children are saved.


title: Two-Face

text: In "The Batman Adventures", which is set in the continuity of "", Two-Face is on the verge of being cured when the Joker convinces him that his fiancée, Grace Lamont, is cheating on him with Bruce Wayne. His evil personality takes hold once again, and he kidnaps Grace. Batman and Robin foil his plan and send him back to Arkham. Grace, meanwhile, realizes that Dent will never be cured and leaves him.


title: Two-Face

text: In another issue, Two-Face's life is thrown into chaos when he loses his coin during an unplanned breakout from Arkham and replaces it with a quarter. Little Jonni Infantino, the mastermind behind the breakout, threatens to hurt Grace if Two-Face doesn't provide information on one of Rupert Thorne's thugs: Weird Tony Hendra, one of Harvey Dent's last cases as District Attorney. Two-Face runs into a pay phone and warns Grace to get out of her apartment before Infantino can get to her. Later on, Grace is seen crying at a Chinese restaurant, calling Bruce Wayne to tell him that Dent saved her life; it is implied that Grace still loves him. Batman and Robin overpower Infantino and his gang, but Two-Face tries to kill him anyway.


title: Two-Face

text: In the story "Lucky Day", Two-Face and his gang take a game show hostage to get revenge on one of the contestants - Lester Dent, his father; Two-Face indicates Lester is a gambling addict who brutalized him and Harvey's mother whenever he lost.


title: Two-Face

text: According to Ty Templeton, series writer Dan Slott had many ideas for Two-Face's stories for the series, but the series was canceled before many of these ideas could be made.


title: Two-Face

text: In the graphic novel "", Harvey Dent has a twin sister named Jessica, who was a friend of Bruce Wayne from preparatory school. Harvey Dent occasionally would bully Bruce, as his maternal family (Arkhams rather than Kanes) had a reputation of eventually going insane. This led to the two boys having a fight at least once. After the twins reach adulthood, Harvey becomes Gotham City's District Attorney, and Jessica was the president of the city's board of supervisors. They are also political enemies of Gotham's corrupt mayor Oswald Cobblepot. Jessica takes over Cobblepot's term as mayor following his confrontation with Batman, which resulted in Cobblepot's death and most of his crimes being posthumously outed.


title: Two-Face

text: In Volume Two, Jessica discovers that Bruce is Batman, and they each reciprocate the romantic affection they had for each other since childhood. However, after Sal Maroni kills Harvey, Jessica is disfigured following the incident when she presses her face against Harvey's burning, her final exchange with Bruce suggesting that she has developed a split personality with her brother as the other identity.


title: Two-Face

text: In Volume Three, Jessica's new split-personality manifests as a hallucination of Harvey as the 'traditional' Two-Face, driving her to trigger a gang war.


title: Two-Face

text: In the "Batman Beyond" universe, Two-Face is revealed to be reformed into Harvey Dent again. Though not a district attorney again due to his terms being already ended, he helped the city set up a law preventing deceased villains to have public graves in order to prevent martyrdom, including hiding their corpses from the public eye.


title: Two-Face

text: In the "" prequel comic, Two-Face crashes a live broadcast on a Gotham news channel, having murdered a guest speaker and taken his place. His obsession with duality appealed to by the recent actions of Superman due to the destruction of Metropolis and with half the nation in favor of his recent actions and the other not, Two-Face himself admits, "I couldn't stay away. I tried. But the coin...". Two-Face flips his signature coin to decide which of the anchors he will kill when the coin is vaporized by a blast of Superman's heat vision before it has a chance to land in his hand. Shocked, infuriated and at a loss, Two-Face brandishes his gun at the Man of Steel but the weapon is easily destroyed. Two-Face is then subdued by the news station's security guards and he is last seen back in Arkham Asylum in a straitjacket when Batman and Nightwing confront Superman, Wonder Woman, Cyborg and Robin. While still bound and restrained, Two-Face witnesses the heroes arguing and attempts to attack Robin during Harley Quinn's riot, but is knocked out by one of Green Arrow's boxing arrows.


title: Two-Face

text: In an alternate history set in 1941, issue 13 of the "DC Comics Bombshells" comic depicts Harvey Dent as the newly elected mayor of Gotham City. Despite having been elected on a platform of supporting World War II refugees from Europe, he becomes an anti-immigrant isolationist in office, who vows to crack down on vigilantes under the slogan "Make Gotham Golden Once More". Tim Drake acknowledges this as a "heavy-handed-but-uncomfortably-timely political allegory" of Donald Trump, whom Dent is drawn to resemble. During the issue, it is revealed that Dent's change is due to him being mind controlled by Hugo Strange, and Dent is freed from the professor's influence at the end. After Dent was saved, he dedicated himself to aiding the Batgirls in their cause. During a battle between Killer Frost and the Reaper, Harvey saves Alyssa Yeoh and Nell Little from one of Killer Frost's blasts, causing half of his face to get frozen and blackened from severe frostbite. Harvey's facial damage doesn't drive him insane, as the Batgirls remind him that since he got it from risking his life to save them, it shows that he's more whole than two-faced. He is seen in their lair serving as their butler similar to Alfred Pennyworth.


title: Two-Face

text: In "Batman/Teenage Mutant Ninja Turtles" crossover, Two-Face is mutated into a mutant baboon as one of the various other Arkham inmates by Shredder and Foot Clan to attack Batman and Robin. Batman is captured, but Robin manages to escape. The Ninja Turtles and Splinter then arrive, where Splinter defeats the mutated villains, while Batman uses his new Intimidator Armor to defeat Shredder and the Turtles defeat Ra's al Ghul. Later, Gordon tells Batman that the police scientists have managed to turn Two-Face and the rest of the mutated inmates at Arkham back to normal and are currently in A.R.G.U.S. custody.


title: Two-Face

text: In the "Emperor Joker" storyline, when the Joker stole the reality warping power of Mister Mxyzptlk, he warped reality in his own image. Here, Two-Face was a small plushie-like creature that was a servant of Harley Quinn. He had a penchant for double entendres, such as quipping to the reader "If you think I'm small, you should see my silver dollar!"


title: Two-Face

text: In "Thy Kingdom Come" storyline, when Power Girl was briefly transferred to another version of the pre-"Crisis" Earth-2 by Gog, she learned that the Joker of this world once attempted to deal with the aging and 'retirement' of Batman's old Rogue's Gallery by repeating the events of Two-Face's creation, attacking new District Attorney Harvey Sims to create a new Two-Face just as he was proposing to Helena Wayne, only for the Joker's attack to leave Sims disfigured and confined to the hospital rather than driving him insane.


title: Two-Face

text: Two-Face has a minor appearance in the 2017 series "". Dent, along with several other Batman villains, is tricked by Jack Napier (who in this reality was a Joker who had been force fed an overdose of pills by Batman which temporarily cured him of his insanity) into drinking drinks that had been laced with particles from Clayface's body. This was done so that Napier, who was using Mad Hatter’s technology to control Clayface, could control them by way of Clayface's ability to control parts of his body that had been separated from him. Dent and the other villains are then used to attack a library which Napier himself was instrumental in building in one of Gotham City’s poorer districts. Later on in the story, the control hat is stolen by Neo-Joker (the second Harley Quinn, who felt that Jack Napier was a pathetic abnormality while Joker was the true, beautiful personality), in an effort to get Napier into releasing the Joker persona. Two-Face also appears in the sequel storyline "Batman: Curse of the White Knight", being among the villains murdered by Azrael.


title: Grand Duchy of Lithuania

text: The Grand Duchy of Lithuania was a European state that existed from the 13th century to 1795, when the territory was partitioned among the Russian Empire, the Kingdom of Prussia, and the Habsburg Empire of Austria. The state was founded by Lithuanians, who were at the time a polytheistic nation born from several united Baltic tribes from Aukštaitija.


title: Grand Duchy of Lithuania

text: The Grand Duchy expanded to include large portions of the former Kievan Rus' and other neighbouring states, including what is now Lithuania, Belarus and parts of Ukraine, Latvia, Poland, Russia and Moldova. At its greatest extent, in the 15th century, it was the largest state in Europe. It was a multi-ethnic and multiconfessional state, with great diversity in languages, religion, and cultural heritage.


title: Grand Duchy of Lithuania

text: The consolidation of the Lithuanian lands began in the late 13th century. Mindaugas, the first ruler of the Grand Duchy, was crowned as Catholic King of Lithuania in 1253. The pagan state was targeted in a religious crusade by the Teutonic Knights and the Livonian Order, but survived. Its rapid territorial expansion started late in the reign of Gediminas, and continued under the diarchy and co-leadership of his sons Algirdas and Kęstutis. Algirdas's son Jogaila signed the Union of Krewo in 1386, bringing two major changes in the history of the Grand Duchy of Lithuania: conversion to Christianity of Europe's last pagan state, and establishment of a dynastic union between the Grand Duchy of Lithuania and the Crown of the Kingdom of Poland.


title: Grand Duchy of Lithuania

text: The reign of Vytautas the Great, son of Kęstutis, marked both the greatest territorial expansion of the Grand Duchy and the defeat of the Teutonic Knights in the Battle of Grunwald in 1410. It also marked the rise of the Lithuanian nobility. After Vytautas's death, Lithuania's relationship with the Kingdom of Poland greatly deteriorated. Lithuanian noblemen, including the Radvila family, attempted to break the personal union with Poland. However, unsuccessful wars with the Grand Duchy of Moscow forced the union to remain intact.


title: Grand Duchy of Lithuania

text: Eventually, the Union of Lublin of 1569 created a new state, the Polish–Lithuanian Commonwealth. In the Federation, the Grand Duchy of Lithuania maintained its political distinctiveness and had separate ministries, laws, army, and treasury. The federation was terminated by the passing of the Constitution of 3 May 1791, when it was supposed to become a single country, the Commonwealth, under one monarch, one parliament and no Lithuanian autonomy. Shortly afterward, the unitary character of the state was confirmed by adopting the Reciprocal Guarantee of Two Nations.


title: Grand Duchy of Lithuania

text: However, the newly reformed Commonwealth was invaded by Russia in 1792 and partitioned between neighbouring states. A truncated state (whose principal cities were Kraków, Warsaw and Vilnius) remained that was nominally independent. After the Kościuszko Uprising, the territory was completely partitioned among the Russian Empire, the Kingdom of Prussia and Austria in 1795.


title: Grand Duchy of Lithuania

text: The name of Lithuania ("Litua") was first mentioned in 1009 in Annals of Quedlinburg. Some older etymological theories relate the name to a small river not far from Kernavė, the core area of the early Lithuanian state and a possible first capital of the would-be Grand Duchy of Lithuania, is usually credited as the source of the name. This river's original name is Lietava. As time passed, the suffix -"ava" could have changed into -"uva", as the two are from the same suffix branch. The river flows in the lowlands and easily spills over its banks, therefore the traditional Lithuanian form "liet"- could be directly translated as "lietis" (to spill), of the root derived from the Proto-Indo-European "leyǝ-". However, the river is very small and some find it improbable that such a small and local object could have lent its name to an entire nation. On the other hand, such a fact is not unprecedented in world history. The most credible modern theory of etymology of the name of Lithuania (Lithuanian: "Lietuva") is Artūras Dubonis's hypothesis, that Lietuva relates to the word "leičiai" (plural of "leitis", a social group of warriors-knights in the early Grand Duchy of Lithuania). The title of the "Grand Duchy" was consistently applied to Lithuania from the 14th century onward.


title: Grand Duchy of Lithuania

text: Naming convention of both title of ruler (hospodar) and the state changed as it expanded its territory. Following the decline of the Kingdom of Ruthenia and incorporation of its lands into the Grand Duchy of Lithuania, Gediminas started to title himself as "King of Lithuanians and many Ruthenians", while the name of the state became the Grand Duchy of Lithuania and Ruthenia. Similarly the title changed to "King of Lithuanians and Ruthenians, ruler and duke of Semigallia" when Semigallia became part of the state. The 1529 edition of the Statute of Lithuania described the titles of Sigismund I the Old as "King of Poland, the Grand Duke of Lithuania, Ruthenia, Prussia, Samogitia, Mazovia, and other [ lands ]". When southern and western Ruthenian lands were transferred to the Crown after the Union of Lublin, the titles of the Grand Duke of Lithuania were transferred to the titles of the rulers of the Polish–Lithuanian Commonwealth.


title: Grand Duchy of Lithuania

text: The country was also called the Republic of Lithuania () since at least the mid-16th century, already before the Union of Lublin in 1569.


title: Grand Duchy of Lithuania

text: The first written reference to Lithuania is found in the Quedlinburg Chronicle, which dates from 1009. In the 12th century, Slavic chronicles refer to Lithuania as one of the areas attacked by the Rus'. Pagan Lithuanians initially paid tribute to Polotsk, but they soon grew in strength and organized their own small-scale raids. At some point between 1180 and 1183 the situation began to change, and the Lithuanians started to organize sustainable military raids on the Slavic provinces, raiding the Principality of Polotsk as well as Pskov, and even threatening Novgorod. The sudden spark of military raids marked consolidation of the Lithuanian lands in Aukštaitija. The Lithuanians are the only branch within the Baltic group that managed to create a state entity in premodern times.


title: Grand Duchy of Lithuania

text: The Lithuanian Crusade began after the Livonian Order and Teutonic Knights, crusading military orders, were established in Riga and in Prussia in 1202 and 1226 respectively. The Christian orders posed a significant threat to pagan Baltic tribes, and further galvanized the formation of the Lithuanian state. The peace treaty with Galicia–Volhynia of 1219 provides evidence of cooperation between Lithuanians and Samogitians. This treaty lists 21 Lithuanian dukes, including five senior Lithuanian dukes from Aukštaitija (Živinbudas, Daujotas, Vilikaila, Dausprungas and Mindaugas) and several dukes from Žemaitija. Although they had battled in the past, the Lithuanians and the Žemaičiai now faced a common enemy. Likely Živinbudas had the most authority and at least several dukes were from the same families. The formal acknowledgement of common interests and the establishment of a hierarchy among the signatories of the treaty foreshadowed the emergence of the state.


title: Grand Duchy of Lithuania

text: Mindaugas, the duke of southern Lithuania, was among the five senior dukes mentioned in the treaty with Galicia–Volhynia. The Livonian Rhymed Chronicle, reports that by the mid-1230s, Mindaugas had acquired supreme power in the whole of Lithuania. In 1236, the Samogitians, led by Vykintas, defeated the Livonian Order in the Battle of Saule. The Order was forced to become a branch of the Teutonic Knights in Prussia, making Samogitia, a strip of land that separated Livonia from Prussia, the main target of both orders. The battle provided a break in the wars with the Knights, and Lithuania exploited this situation, arranging attacks on the Ruthenian provinces and annexing Navahrudak and Hrodna.


title: Grand Duchy of Lithuania

text: In 1248, a civil war broke out between Mindaugas and his nephews Tautvilas and Edivydas. The powerful coalition against Mindaugas included Vykintas, the Livonian Order, Daniel of Galicia and Vasilko of Volhynia. Taking advantage of internal conflicts, Mindaugas allied with the Livonian Order. He promised to convert to Christianity and exchange some lands in western Lithuania in return for military assistance against his nephews and the royal crown. In 1251, Mindaugas was baptized and Pope Innocent IV issued a papal bull proclaiming the creation of the Kingdom of Lithuania. After the civil war ended, Mindaugas was crowned as King of Lithuania on 6 July 1253, starting a decade of relative peace. Mindaugas later renounced Christianity and converted back to paganism. Mindaugas tried to expand his influence in Polatsk, a major centre of commerce in the Daugava River basin, and Pinsk. The Teutonic Knights used this period to strengthen their position in parts of Samogitia and Livonia, but they lost the Battle of Skuodas in 1259 and the Battle of Durbe in 1260. This encouraged the conquered Semigallians and Old Prussians to rebel against the Knights.


title: Grand Duchy of Lithuania

text: Encouraged by Treniota, Mindaugas broke the peace with the Order, possibly reverted to pagan beliefs. He hoped to unite all Baltic tribes under the Lithuanian leadership. As military campaigns were not successful, the relationships between Mindaugas and Treniota deteriorated. Treniota, together with Daumantas of Pskov, assassinated Mindaugas and his two sons, Ruklys and Rupeikis, in 1263. The state lapsed into years of internal fighting.


title: Grand Duchy of Lithuania

text: From 1263 to 1269, Lithuania had three grand dukes – Treniota, Vaišvilkas, and Švarnas. The state did not disintegrate, however, and Traidenis came to power in 1269. He strengthened Lithuanian control in Black Ruthenia and fought with the Livonian Order, winning the Battle of Karuse in 1270 and the Battle of Aizkraukle in 1279. There is considerable uncertainty about the identities of the grand dukes of Lithuania between his death in 1282 and the assumption of power by Vytenis in 1295. During this time the Orders finalized their conquests. In 1274, the Great Prussian Rebellion ended, and the Teutonic Knights proceeded to conquer other Baltic tribes: the Nadruvians and Skalvians in 1274–1277, and the Yotvingians in 1283; the Livonian Order completed its conquest of Semigalia, the last Baltic ally of Lithuania, in 1291. The Orders could now turn their full attention to Lithuania. The "buffer zone" composed of other Baltic tribes had disappeared, and Grand Duchy of Lithuania was left to battle the Orders on its own.


title: Grand Duchy of Lithuania

text: The Gediminid dynasty ruled the grand duchy for over a century, and Vytenis was the first ruler of the dynasty. During his reign Lithuania was in constant war with the Order, the Kingdom of Poland, and Ruthenia. Vytenis was involved in succession disputes in Poland, supporting Boleslaus II of Masovia, who was married to a Lithuanian duchess, Gaudemunda. In Ruthenia, Vytenis managed to recapture lands lost after the assassination of Mindaugas and to capture the principalities of and Turov. In the struggle against the Order, Vytenis allied with Riga's citizens; securing positions in Riga strengthened trade routes and provided a base for further military campaigns. Around 1307, Polotsk, an important trading centre, was annexed by military force. Vytenis also began constructing a defensive castle network along Nemunas. Gradually this network developed into the main defensive line against the Teutonic Order.


title: Grand Duchy of Lithuania

text: The expansion of the state reached its height under Grand Duke Gediminas, also titled by some contemporaneous German sources as "Rex de Owsteiten" (), who created a strong central government and established an empire that later spread from the Black Sea to the Baltic Sea. In 1320, most of the principalities of western Rus' were either vassalized or annexed by Lithuania. In 1321, Gediminas captured Kiev, sending Stanislav, the last Rurikid to rule Kiev, into exile. Gediminas also re-established the permanent capital of the Grand Duchy in Vilnius, presumably moving it from Old Trakai in 1323. The state continued to expand its territory under the reign of Grand Duke Algirdas and his brother Kęstutis, who both ruled the state harmonically.


title: Grand Duchy of Lithuania

text: Lithuania was in a good position to conquer the western and the southern parts of former Kievan Rus'. While almost every other state around it had been plundered or defeated by the Mongols, the hordes stopped at the modern borders of Belarus, and the core territory of the Grand Duchy was left mostly untouched. The weak control of the Mongols over the areas they had conquered allowed the expansion of Lithuania to accelerate. Rus' principalities were never incorporated directly into the Golden Horde, maintaining vassal relationships with a fair degree of independence. Lithuania annexed some of these areas as vassals through diplomacy, as they exchanged rule by the Mongols or the Grand Prince of Moscow with rule by the Grand Duchy. An example is Novgorod, which was often in the Lithuanian sphere of influence and became an occasional dependency of the Grand Duchy. Lithuanian control resulted from internal frictions within the city, which attempted to escape submission to Moscow. Such relationships could be tenuous, however, as changes in a city's internal politics could disrupt Lithuanian control, as happened on a number of occasions with Novgorod and other East-Slavic cities.


title: Grand Duchy of Lithuania

text: The Grand Duchy of Lithuania managed to hold off Mongol incursions and eventually secured gains. In 1333 and 1339, Lithuanians defeated large Mongol forces attempting to regain Smolensk from the Lithuanian sphere of influence. By about 1355, the State of Moldavia had formed, and the Golden Horde did little to re-vassalize the area. In 1362, regiments of the Grand Duchy army defeated the Golden Horde at the Battle at Blue Waters. In 1380, a Lithuanian army allied with Russian forces to defeat the Golden Horde in the Battle of Kulikovo, and though the rule of the Mongols did not end, their influence in the region waned thereafter. In 1387, Moldavia became a vassal of Poland and, in a broader sense, of Lithuania. By this time, Lithuania had conquered the territory of the Golden Horde all the way to the Dnieper River. In a crusade against the Golden Horde in 1398 (in an alliance with Tokhtamysh), Lithuania invaded northern Crimea and won a decisive victory. In an attempt to place Tokhtamish on the Golden Horde throne in 1399, Lithuania moved against the Horde but was defeated in the Battle of the Vorskla River, losing the steppe region.


title: Grand Duchy of Lithuania

text: Lithuania was Christianized in 1387, led by Jogaila, who personally translated Christian prayers into the Lithuanian language and his cousin Vytautas the Great who founded many Catholic churches and allocated lands for parishes in Lithuania. The state reached a peak under Vytautas the Great, who reigned from 1392 to 1430. Vytautas was one of the most famous rulers of the Grand Duchy of Lithuania, serving as the Grand Duke from 1401 to 1430, and as the Prince of Hrodna (1370–1382) and the Prince of Lutsk (1387–1389). Vytautas was the son of Kęstutis, uncle of Jogaila, who became King of Poland in 1386, and he was the grandfather of Vasili II of Moscow.


title: Grand Duchy of Lithuania

text: In 1410, Vytautas commanded the forces of the Grand Duchy in the Battle of Grunwald. The battle ended in a decisive Polish-Lithuanian victory against the Teutonic Order. The war of Lithuania against military Orders, which lasted for more than 200 years, and was one of the longest wars in the history of Europe, was finally ended. Vytautas backed the economic development of the state and introduced many reforms. Under his rule, the Grand Duchy of Lithuania slowly became more centralized, as the governours loyal to Vytautas replaced local princes with dynastic ties to the throne. The governours were rich landowners who formed the basis for the nobility of the Grand Duchy. During Vytautas' rule, the Radziwiłł and Goštautas families started to gain influence.


title: Grand Duchy of Lithuania

text: The rapid expansion of the influence of Moscow soon put it into a comparable position to the Grand Duchy of Lithuania, and after the annexation of Novgorod in 1478, Muscovy was among the preeminent states in northeastern Europe. Between 1492 and 1508, Ivan III further consolidated Muscovy, winning the key Battle of Vedrosha and regaining such ancient lands of Kievan Rus' as Chernihiv and Bryansk.


title: Grand Duchy of Lithuania

text: On 8 September 1514, the allied forces of the Grand Duchy of Lithuania and the Kingdom of Poland, under the command of Hetman Konstanty Ostrogski, fought the Battle of Orsha against the army of the Grand Duchy of Moscow, under Konyushy Ivan Chelyadnin and Kniaz Mikhail Golitsin. The battle was part of a long series of Muscovite–Lithuanian Wars conducted by Russian rulers striving to gather all the former lands of Kievan Rus' under their rule. According to "Rerum Moscoviticarum Commentarii" by Sigismund von Herberstein, the primary source for the information on the battle, the much smaller army of Poland–Lithuania (under 30,000 men) defeated the 80,000 Muscovite soldiers, capturing their camp and commander. The Muscovites lost about 30,000 men, while the losses of the Poland–Lithuania army totalled only 500. While the battle is remembered as one of the greatest Lithuanian victories, Muscovy ultimately prevailed in the war. Under the 1522 peace treaty, the Grand Duchy of Lithuania made large territorial concessions.


title: Grand Duchy of Lithuania

text: The wars with the Teutonic Order, the loss of land to Moscow, and the continued pressure threatened the survival of the state of Lithuania, so it was forced to ally more closely with Poland, uniting with its western neighbour as the Polish–Lithuanian Commonwealth (Commonwealth of Two Nations) in the Union of Lublin of 1569. During the period of the Union, many of the territories formerly controlled by the Grand Duchy of Lithuania were transferred to the Crown of the Polish Kingdom, while the gradual process of Polonization slowly drew Lithuania itself under Polish domination. The Grand Duchy retained many rights in the federation (including separate ministries, laws, army, and treasury) until the May Constitution of Poland and Reciprocal Guarantee of Two Nations were passed in 1791.


title: Grand Duchy of Lithuania

text: Following the partitions of the Polish–Lithuanian Commonwealth, most of the lands of the former Grand Duchy were directly annexed by the Russian Empire, the rest by Prussia. In 1812, just prior to the French invasion of Russia, the former Grand Duchy revolted against the Russians. Soon after his arrival in Vilnius, Napoleon proclaimed the creation of a Commissary Provisional Government of the Grand Duchy of Lithuania which, in turn, renewed the Polish-Lithuanian Union. The union was never formalized, however, as only half a year later Napoleon's "Grande Armée" was pushed out of Russia and forced to retreat further westwards. In December 1812, Vilnius was recaptured by Russian forces, bringing all plans of recreation of the Grand Duchy to an end. Most of the lands of the former Grand Duchy were re-annexed by Russia. The Augustów Voivodeship (later Augustów Governorate), including the counties of Marijampolė and Kalvarija, was attached to the Kingdom of Poland, a rump state in personal union with Russia.


title: Grand Duchy of Lithuania

text: After the baptism in 1252 and coronation of King Mindaugas in 1253, Lithuania was recognized as a Christian state until 1260, when Mindaugas supported an uprising in Courland and (according to the German order) renounced Christianity. Up until 1387, Lithuanian nobles professed their own religion, which was polytheistic. Ethnic Lithuanians were very dedicated to their faith. The pagan beliefs needed to be deeply entrenched to survive strong pressure from missionaries and foreign powers. Until the 17th century, there were relics of old faith reported by counter-reformation active Jesuit priests, like feeding žaltys with milk or bringing food to graves of ancestors. The lands of modern-day Belarus and Ukraine, as well as local dukes (princes) in these regions, were firmly Orthodox Christian (Greek Catholic after the Union of Brest), though. While pagan beliefs in Lithuania were strong enough to survive centuries of pressure from military orders and missionaries, they did eventually succumb. A separate Eastern Orthodox metropolitan eparchy was created sometime between 1315 and 1317 by the Constantinople Patriarch John XIII. Following the Galicia–Volhynia Wars which divided the Kingdom of Galicia–Volhynia between the Grand Duchy of Lithuania and the Kingdom of Poland, in 1355 the Halych metropoly was liquidated and its eparchies transferred to the metropoles of Lithuania and Volhynia.


title: Grand Duchy of Lithuania

text: In 1387, Lithuania converted to Catholicism, while most of the Ruthenian lands stayed Orthodox, however, on 22 February 1387, Supreme Duke Jogaila banned Catholics marriages with Orthodox, and demanded those Orthodox who previously married with the Catholics to convert to Catholicism. At one point, though, Pope Alexander VI reprimanded the Grand Duke for keeping non-Catholics as advisers. Consequently, only in 1563 did Grand Duke Sigismund II Augustus issue a privilege that equalized the rights of Orthodox and Catholics in Lithuania and abolished all previous restrictions on Orthodox. There was an effort to polarise Orthodox Christians after the Union of Brest in 1596, by which some Orthodox Christians acknowledged papal authority and Catholic catechism, but preserved their liturgy. The country also became one of the major centres of the Reformation.


title: Grand Duchy of Lithuania

text: In the second half of the 16th century, Calvinism spread in Lithuania, supported by the families of Radziwiłł, Chodkiewicz, Sapieha, Dorohostajski and others. By the 1580s the majority of the senators from Lithuania were Calvinist or Socinian Unitarians (Jan Kiszka).


title: Grand Duchy of Lithuania

text: In 1579, Stephen Báthory, King of Poland and Grand Duke of Lithuania, founded Vilnius University, one of the oldest universities in Northern Europe. Due to the work of the Jesuits during the Counter-Reformation the university soon developed into one of the most important scientific and cultural centres of the region and the most notable scientific centre of the Grand Duchy of Lithuania. The work of the Jesuits as well as conversions from among the Lithuanian senatorial families turned the tide and by the 1670s Calvinism lost its former importance though it still retained some influence among the ethnically Lithuanian peasants and some middle nobility.


title: Grand Duchy of Lithuania

text: Islam in Lithuania, unlike many other northern and western European countries, has a long history starting from 14th century. Small groups of Muslim Lipka Tatars migrated to ethnically Lithuanian lands, mainly under the rule of Grand Duke Vytautas (early 15th century). In Lithuania, unlike many other European societies at the time, there was religious freedom. Lithuanian Tatars were allowed to settle in certain places, such as Trakai and Kaunas. Keturiasdešimt Totorių is one of the oldest Tatar settlements in the Grand Duchy of Lithuania. After a successful military campaign of the Crimean Peninsula in 1397, Vytautas brought the first Crimean Tatar prisoners of war to Trakai and various places in the Duchy of Trakai, including localities near Vokė river just south of Vilnius. The first mosque in this village was mentioned for the first time in 1558. There were 42 Tatar families in the village in 1630.


title: Grand Duchy of Lithuania

text: In the 13th century, the centre of the Grand Duchy of Lithuania was inhabited by a majority that spoke Lithuanian, though it was not a written language until the 16th century. In the other parts of the duchy, the majority of the population, including Ruthenian nobles and ordinary people, used both spoken and written Ruthenian. Nobles who migrated from one place to another would adapt to a new locality and adopt the local religion and culture and those Lithuanian noble families that moved to Slavic areas often took up the local culture quickly over subsequent generations. Ruthenians were native to the east-central and south-eastern parts of the Grand Duchy of Lithuania.


title: Grand Duchy of Lithuania

text: Ruthenian, also called Chancery Slavonic in its written form, was used to write laws alongside Polish, Latin and German, but its use varied between regions. From the time of Vytautas, there are fewer remaining documents written in Ruthenian than there are in Latin and German, but later Ruthenian became the main language of documentation and writings, especially in eastern and southern parts of the Duchy. In the 16th century at the time of the Polish–Lithuanian Commonwealth, Lithuanian lands became partially polonized over time and started to use Polish for writing much more often than the Lithuanian and Ruthenian languages. Polish finally became the official chancellery language of the Commonwealth in 1697.


title: Grand Duchy of Lithuania

text: The voivodeships with a predominantly ethnic Lithuanian population, Vilnius, Trakai, and Samogitian voivodeships, remained almost wholly Lithuanian-speaking, both colloquially and by ruling nobility. Ruthenian communities were also present in the extreme southern parts of Trakai voivodeship and south-eastern parts of Vilnius Voivodeship. In addition to Lithuanians and Ruthenians, other important ethnic groups throughout the Grand Duchy of Lithuania were Jews and Tatars.


title: Grand Duchy of Lithuania

text: Numerous languages were used in state documents depending on which period in history and for what purpose. These languages included Lithuanian, Ruthenian, Polish and, to a lesser extent (mostly in early diplomatic communication), Latin and German.


title: Grand Duchy of Lithuania

text: The Court used Ruthenian to correspond with Eastern countries while Latin and German were used in foreign affairs with Western countries. During the latter part of the history of the Grand Duchy, Polish was increasingly used in State documents, especially after the Union of Lublin. By 1697, Polish had largely replaced Ruthenian as the "official" language at Court, although Ruthenian continued to be used on a few official documents until the second half of the 18th century.


title: Grand Duchy of Lithuania

text: It is known that Jogaila, being ethnic Lithuanian by the man's line, himself knew and spoke in the Lithuanian language with Vytautas the Great, his cousin from the Gediminids dynasty. Also, during the Christianization of Samogitia, none of the clergy, who came to Samogitia with Jogaila, were able to communicate with the natives, therefore Jogaila himself taught the Samogitians about the Catholicism, thus he was able to communicate in the Samogitian dialect of the Lithuanian language. Use of Lithuanian still continued at the Court after the death of Vytautas and Jogaila. Since the young Grand Duke Casimir IV Jagiellon was underage, the supreme control over the Grand Duchy of Lithuania was in the hands of the Lithuanian Council of Lords, presided by Jonas Goštautas, while Casimir was taught Lithuanian language and the customs of Lithuania by appointed court officials. Grand Duke Alexander Jagiellon also could understand and speak Lithuanian. While Grand Duke Sigismund II Augustus maintained both Polish-speaking and Lithuanian-speaking courts.


title: Grand Duchy of Lithuania

text: From the beginning of the 16th century, and especially after a rebellion led by Michael Glinski in 1508, there were attempts by the Court to replace the usage of Ruthenian with Latin. The use of Ruthenian by academics in areas formerly part of Rus' and even in Lithuania proper was widespread. Court Chancellor of the Grand Duchy of Lithuania Lew Sapieha noted in the preface of the Third Statute of Lithuania (1588) that all state documents to be written exclusively in Ruthenian. The same was stated in part 4 of the Statute: Despite that, Polish-language editions stated the same in Polish. Statutes of the Grand Duchy were translated into Latin and Polish. One of the main reasons for translations into Latin was that Ruthenian had no well defined and codified law concepts and definitions, which caused many disputes in courts. Another reason to use Latin was a popular idea that Lithuanians were descendants of Romans – the mythical house of Palemonids. Augustinus Rotundus translated the Second Statute into Latin.


title: Grand Duchy of Lithuania

text: According to scientist Rita Regina Trimonienė, the Lithuanians surnames are not slavified and are written as they were pronounced by parishioners in the registers of baptism of Šiauliai Church (dated in the 17th century).


title: Grand Duchy of Lithuania

text: In 1552, Grand Duke Sigismund II Augustus ordered that orders of the Magistrate of Vilnius be announced in Lithuanian, Polish, and Ruthenian. The same requirement was valid for the Magistrate of Kaunas.


title: Grand Duchy of Lithuania

text: Mikalojus Daukša, writing in the introduction to his "Postil" (1599) (which was written in Lithuanian) in Polish, advocated the promotion of Lithuanian in the Grand Duchy, noting in the introduction that many people, especially szlachta, preferred to speak Polish rather than Lithuanian, but spoke Polish poorly. Such were the linguistic trends in the Grand Duchy that, by the political reforms of 1564–1566, parliaments, local land courts, appellate courts and other State functions were recorded in Polish, and Polish became increasingly spoken across all social classes.


title: Grand Duchy of Lithuania

text: Ruthenian and Polish were used as state languages of the Grand Duchy of Lithuania, besides Latin and German in diplomatic correspondence. However, Lithuanian was dominant in parts of the Grand Duchy of Lithuania like Samogitia, where the local nobility's reliance on Lithuanian resulted in Stanislovas Radvila remarking in a letter to his brother Mikalojus Kristupas Radvila Našlaitėlis immediately after becoming the Elder of Samogitia that: "While learning various languages, I forgot Lithuanian, and now I see, I have to go to school again, because that language, as I see, God willing, will be needed." Vilnius, Trakai and Samogitia were the core voivodeships of the state, being part of Lithuania Proper, as evidenced by the privileged position of their governors in state authorities, such as the Council of Lords. Peasants in ethnic Lithuanian territories spoke exclusively Lithuanian, except in transitional border regions, but the Statutes of Lithuania and other laws and documentation were written in Ruthenian, Latin and Polish. Following the example of the royal court, there was a tendency to replace Lithuanian with Polish in the ethnic Lithuanian areas, whereas Ruthenian was stronger in ethnic Belarusian and Ukrainian territories. A note written by Sigismund von Herberstein's states that, in an ocean of Ruthenian in this part of Europe, there were two non-Ruthenian regions: Lithuania and Samogitia.


title: Grand Duchy of Lithuania

text: Since the founding of the Grand Duchy of Lithuania, the higher strata of Lithuanian society from ethnic Lithuania spoke Lithuanian, although from the later 16th century gradually began using Polish, and those from Ruthenia – Ruthenian. Samogitia was unique because of its economic situation – it lay near sea ports and there were fewer people under corvee, instead of that, many commoners were taxpayers. As a result, the stratification of society was not as sharp as in other areas. Being more similar to a commoner population, the local szlachta spoke Lithuanian to a bigger extent than in the areas close to the capital Vilnius, which itself had become the starting point of intensive linguistic Polonization of the surrounding areas since the 18th century.


title: Grand Duchy of Lithuania

text: In Vilnius University, there are preserved texts written in the Lithuanian language of the Vilnius area, a dialect of Eastern Aukštaitian, which was spoken in a territory located south-eastwards from Vilnius. The sources are preserved in works of graduates from Stanislovas Rapolionis-based Lithuanian language schools, graduate Martynas Mažvydas and Rapalionis relative Abraomas Kulvietis.


title: Grand Duchy of Lithuania

text: One of the main sources of Lithuanian written in the Eastern Aukštaitian dialect (Vilnius dialect) was preserved by Konstantinas Sirvydas in a trilingual (Polish-Latin-Lithuanian) 17th-century dictionary, "Dictionarium trium linguarum in usum studiosæ juventutis", which was the main Lithuanian dictionary used until the late 19th century.


title: Grand Duchy of Lithuania

text: "Universitas lingvarum Litvaniæ", published in Vilnius, 1737, is the oldest surviving grammar of the Lithuanian language published in the territory of the Grand Duchy of Lithuania.


title: Grand Duchy of Lithuania

text: In 1260, the Grand Duchy of Lithuania was the land of Lithuania, and ethnic Lithuanians formed the majority (67.5%) of its 400,000 people. With the acquisition of new Ruthenian territories, in 1340 this portion decreased to 30%. By the time of the largest expansion towards Rus' lands, which came at the end of the 13th and during the 14th century, the territory of the Grand Duchy of Lithuania was 800 to 930 thousand km, just 10% to 14% of which was ethnically Lithuanian.


title: Grand Duchy of Lithuania

text: On 6 May 1434, Grand Duke Sigismund Kęstutaitis released his privilege which tied the Orthodox and Catholic Lithuanian nobles rights in order to attract the Slavic nobles of the eastern regions of the Grand Duchy of Lithuania who supported the former Grand Duke Švitrigaila.


title: Grand Duchy of Lithuania

text: An estimate of the population in the territory of Poland and Grand Duchy of Lithuania together gives a population at 7.5 million for 1493, breaking them down by ethnicity at 3.75 million Ruthenians (ethnic Ukrainians, Belarusians), 3.25 million Poles and 0.5 million Lithuanians. With the Union of Lublin, 1569, Lithuanian Grand Duchy lost large part of lands to the Polish Crown.


title: Grand Duchy of Lithuania

text: According to an analysis of the tax registers in 1572, Lithuania proper had 850,000 residents of which 680,000 were Lithuanians.


title: Grand Duchy of Lithuania

text: In the mid and late 17th century, due to Russian and Swedish invasions, there was much devastation and population loss on throughout the Grand Duchy of Lithuania, including ethnic Lithuanian population in Vilnius surroundings. Besides devastation, the Ruthenian population declined proportionally after the territorial losses to Russian Empire. By 1770 there were about 4.84 million inhabitants in the territory of 320 thousand km, the biggest part of whom were inhabitants of Ruthenia and about 1.39 million or 29% – of ethnic Lithuania. During the following decades, the population decreased in a result of partitions.


title: Grand Duchy of Lithuania

text: Prussian tribes (of Baltic origin) were the subject of Polish expansion, which was largely unsuccessful, so Duke Konrad of Masovia invited the Teutonic Knights to settle near the Prussian area of settlement. The fighting between Prussians and the Teutonic Knights gave the more distant Lithuanian tribes time to unite. Because of strong enemies in the south and north, the newly formed Lithuanian state concentrated most of its military and diplomatic efforts on expansion eastward.


title: Grand Duchy of Lithuania

text: The rest of the former Ruthenian lands were conquered by the Grand Duchy of Lithuania. Some other lands in Ukraine were vassalized by Lithuania later. The subjugation of Eastern Slavs by two powers created substantial differences between them that persist to this day. While there were certainly substantial regional differences in Kievan Rus', it was the Lithuanian annexation of much of southern and western Ruthenia that led to the permanent division between Ukrainians, Belarusians, and Russians. And even four Grand Dukes of Lithuania are appeared on the Millennium of Russia monument.


title: Grand Duchy of Lithuania

text: In the 19th century, the romantic references to the times of the Grand Duchy of Lithuania were an inspiration and a substantial part of both the Lithuanian and Belarusian national revival movements and Romanticism in Poland.


title: Grand Duchy of Lithuania

text: Notwithstanding the above, Lithuania was a kingdom under Mindaugas, who was crowned by the authority of Pope Innocent IV in 1253. Vytenis, Gediminas and Vytautas the Great also assumed the title of King, although uncrowned by the Pope. A failed attempt was made in 1918 to revive the Kingdom under a German Prince, Wilhelm Karl, Duke of Urach, who would have reigned as Mindaugas II of Lithuania.


title: Grand Duchy of Lithuania

text: In the first half of the 20th century, the memory of the multiethnic history of the Grand Duchy was revived by the Krajowcy movement, which included Ludwik Abramowicz (Liudvikas Abramovičius), Konstancja Skirmuntt, Mykolas Römeris (Michał Pius Römer), Józef Albin Herbaczewski (Juozapas Albinas Herbačiauskas), Józef Mackiewicz and Stanisław Mackiewicz. This feeling was expressed in poetry by Czesław Miłosz.


title: Grand Duchy of Lithuania

text: According to the 10th article of the "Law on the State Flag and Other Flags of the Republic of Lithuania" (), adopted by the Seimas, the historical Lithuanian state flag (with horseback knight on a red field, which initial design dates back to the reign of Grand Duke Vytautas the Great) must be constantly raised over the most important governmental buildings (e.g. Seimas Palace, Government of Lithuania and its ministries, Lithuanian courts, municipal council buildings) and significant historical buildings (e.g. Palace of the Grand Dukes of Lithuania, Trakai Island Castle), also in Kernavė and in the site of the Senieji Trakai Castle.


title: Coriolis force

text: In physics, the Coriolis force is an inertial or fictitious force that acts on objects in motion within a frame of reference that rotates with respect to an inertial frame. In a reference frame with clockwise rotation, the force acts to the left of the motion of the object. In one with anticlockwise (or counterclockwise) rotation, the force acts to the right. Deflection of an object due to the Coriolis force is called the Coriolis effect. Though recognized previously by others, the mathematical expression for the Coriolis force appeared in an 1835 paper by French scientist Gaspard-Gustave de Coriolis, in connection with the theory of water wheels. Early in the 20th century, the term "Coriolis force" began to be used in connection with meteorology.


title: Coriolis force

text: Newton's laws of motion describe the motion of an object in an inertial (non-accelerating) frame of reference. When Newton's laws are transformed to a rotating frame of reference, the Coriolis and centrifugal accelerations appear. When applied to objects with masses, the respective forces are proportional to their masses. The magnitude of the Coriolis force is proportional to the rotation rate, and the magnitude of the centrifugal force is proportional to the square of the rotation rate. The Coriolis force acts in a direction perpendicular to two quantities: the angular velocity of the rotating frame relative to the inertial frame and the velocity of the body relative to the rotating frame, and its magnitude is proportional to the object's speed in the rotating frame (more precisely, to the component of its velocity that is perpendicular to the axis of rotation). The centrifugal force acts outwards in the radial direction and is proportional to the distance of the body from the axis of the rotating frame. These additional forces are termed inertial forces, fictitious forces, or "pseudo forces". By introducing these fictitious forces to a rotating frame of reference, Newton's laws of motion can be applied to the rotating system as though it were an inertial system; these forces are correction factors that are not required in a non-rotating system.


title: Coriolis force

text: In popular (non-technical) usage of the term "Coriolis effect", the rotating reference frame implied is almost always the Earth. Because the Earth spins, Earth-bound observers need to account for the Coriolis force to correctly analyze the motion of objects. The Earth completes one rotation for each day/night cycle, so for motions of everyday objects the Coriolis force is usually quite small compared with other forces; its effects generally become noticeable only for motions occurring over large distances and long periods of time, such as large-scale movement of air in the atmosphere or water in the ocean; or where high precision is important, such as long-range artillery or missile trajectories. Such motions are constrained by the surface of the Earth, so only the horizontal component of the Coriolis force is generally important. This force causes moving objects on the surface of the Earth to be deflected to the right (with respect to the direction of travel) in the Northern Hemisphere and to the left in the Southern Hemisphere. The horizontal deflection effect is greater near the poles, since the effective rotation rate about a local vertical axis is largest there, and decreases to zero at the equator. Rather than flowing directly from areas of high pressure to low pressure, as they would in a non-rotating system, winds and currents tend to flow to the right of this direction north of the equator (anticlockwise) and to the left of this direction south of it (clockwise). This effect is responsible for the rotation and thus formation of cyclones (see Coriolis effects in meteorology).


title: Coriolis force

text: For an intuitive explanation of the origin of the Coriolis force, consider an object, constrained to follow the Earth's surface and moving northward in the Northern Hemisphere. Viewed from outer space, the object does not appear to go due north, but has an eastward motion (it rotates around toward the right along with the surface of the Earth). The further north it travels, the smaller the "radius of its parallel (latitude)" (the minimum distance from the surface point to the axis of rotation, which is in a plane orthogonal to the axis), and so the slower the eastward motion of its surface. As the object moves north, to higher latitudes, it has a tendency to maintain the eastward speed it started with (rather than slowing down to match the reduced eastward speed of local objects on the Earth's surface), so it veers east (i.e. to the right of its initial motion).


title: Coriolis force

text: Though not obvious from this example, which considers northward motion, the horizontal deflection occurs equally for objects moving eastward or westward (or in any other direction). However, the theory that the effect determines the rotation of draining water in a typical size household bathtub, sink or toilet has been repeatedly disproven by modern-day scientists; the force is negligibly small compared to the many other influences on the rotation.


title: Coriolis force

text: Italian scientist Giovanni Battista Riccioli and his assistant Francesco Maria Grimaldi described the effect in connection with artillery in the 1651 "Almagestum Novum", writing that rotation of the Earth should cause a cannonball fired to the north to deflect to the east. In 1674, Claude François Milliet Dechales described in his "Cursus seu Mundus Mathematicus" how the rotation of the Earth should cause a deflection in the trajectories of both falling bodies and projectiles aimed toward one of the planet's poles. Riccioli, Grimaldi, and Dechales all described the effect as part of an argument against the heliocentric system of Copernicus. In other words, they argued that the Earth's rotation should create the effect, and so failure to detect the effect was evidence for an immobile Earth. The Coriolis acceleration equation was derived by Euler in 1749, and the effect was described in the tidal equations of Pierre-Simon Laplace in 1778.


title: Coriolis force

text: Gaspard-Gustave Coriolis published a paper in 1835 on the energy yield of machines with rotating parts, such as waterwheels. That paper considered the supplementary forces that are detected in a rotating frame of reference. Coriolis divided these supplementary forces into two categories. The second category contained a force that arises from the cross product of the angular velocity of a coordinate system and the projection of a particle's velocity into a plane perpendicular to the system's axis of rotation. Coriolis referred to this force as the "compound centrifugal force" due to its analogies with the centrifugal force already considered in category one. The effect was known in the early 20th century as the "acceleration of Coriolis", and by 1920 as "Coriolis force".


title: Coriolis force

text: In 1856, William Ferrel proposed the existence of a circulation cell in the mid-latitudes with air being deflected by the Coriolis force to create the prevailing westerly winds.


title: Coriolis force

text: The understanding of the kinematics of how exactly the rotation of the Earth affects airflow was partial at first. Late in the 19th century, the full extent of the large scale interaction of pressure-gradient force and deflecting force that in the end causes air masses to move along isobars was understood.


title: Coriolis force

text: where formula_2 is the vector sum of the physical forces acting on the object, formula_3 is the mass of the object, and formula_4 is the acceleration of the object relative to the inertial reference frame.


title: Coriolis force

text: Transforming this equation to a reference frame rotating about a fixed axis through the origin with angular velocity formula_5 having variable rotation rate, the equation takes the form


title: Coriolis force

text: The fictitious forces as they are perceived in the rotating frame act as additional forces that contribute to the apparent acceleration just like the real external forces. The fictitious force terms of the equation are, reading from left to right:


title: Coriolis force

text: Notice the Euler and centrifugal forces depend on the position vector formula_15 of the object, while the Coriolis force depends on the object's velocity formula_16 as measured in the rotating reference frame. As expected, for a non-rotating inertial frame of reference formula_17 the Coriolis force and all other fictitious forces disappear. The forces also disappear for zero mass formula_18.


title: Coriolis force

text: As the Coriolis force is proportional to a cross product of two vectors, it is perpendicular to both vectors, in this case the object's velocity and the frame's rotation vector. It therefore follows that:


title: Coriolis force

text: The time, space, and velocity scales are important in determining the importance of the Coriolis force. Whether rotation is important in a system can be determined by its Rossby number, which is the ratio of the velocity, "U", of a system to the product of the Coriolis parameter, formula_19, and the length scale, "L", of the motion:


title: Coriolis force

text: The Rossby number is the ratio of inertial to Coriolis forces. A small Rossby number indicates a system is strongly affected by Coriolis forces, and a large Rossby number indicates a system in which inertial forces dominate. For example, in tornadoes, the Rossby number is large, in low-pressure systems it is low, and in oceanic systems it is around 1. As a result, in tornadoes the Coriolis force is negligible, and balance is between pressure and centrifugal forces. In low-pressure systems, centrifugal force is negligible and balance is between Coriolis and pressure forces. In the oceans all three forces are comparable.


title: Coriolis force

text: An atmospheric system moving at "U" =  occupying a spatial distance of "L" = , has a Rossby number of approximately 0.1.


title: Coriolis force

text: A baseball pitcher may throw the ball at "U" =  for a distance of "L" = . The Rossby number in this case would be 32,000 "(at latitude 31°47'46.382")".


title: Coriolis force

text: Baseball players don't care about which hemisphere they're playing in. However, an unguided missile obeys exactly the same physics as a baseball, but can travel far enough and be in the air long enough to experience the effect of Coriolis force. Long-range shells in the Northern Hemisphere landed close to, but to the right of, where they were aimed until this was noted. (Those fired in the Southern Hemisphere landed to the left.) In fact, it was this effect that first got the attention of Coriolis himself.


title: Coriolis force

text: The figure illustrates a ball tossed from 12:00 o'clock toward the center of a counter-clockwise rotating carousel. On the left, the ball is seen by a stationary observer above the carousel, and the ball travels in a straight line to the center, while the ball-thrower rotates counter-clockwise with the carousel. On the right, the ball is seen by an observer rotating with the carousel, so the ball-thrower appears to stay at 12:00 o'clock. The figure shows how the trajectory of the ball as seen by the rotating observer can be constructed.


title: Coriolis force

text: On the left, two arrows locate the ball relative to the ball-thrower. One of these arrows is from the thrower to the center of the carousel (providing the ball-thrower's line of sight), and the other points from the center of the carousel to the ball. (This arrow gets shorter as the ball approaches the center.) A shifted version of the two arrows is shown dotted.


title: Coriolis force

text: On the right is shown this same dotted pair of arrows, but now the pair are rigidly rotated so the arrow corresponding to the line of sight of the ball-thrower toward the center of the carousel is aligned with 12:00 o'clock. The other arrow of the pair locates the ball relative to the center of the carousel, providing the position of the ball as seen by the rotating observer. By following this procedure for several positions, the trajectory in the rotating frame of reference is established as shown by the curved path in the right-hand panel.


title: Coriolis force

text: The ball travels in the air, and there is no net force upon it. To the stationary observer, the ball follows a straight-line path, so there is no problem squaring this trajectory with zero net force. However, the rotating observer sees a "curved" path. Kinematics insists that a force (pushing to the "right" of the instantaneous direction of travel for a "counter-clockwise" rotation) must be present to cause this curvature, so the rotating observer is forced to invoke a combination of centrifugal and Coriolis forces to provide the net force required to cause the curved trajectory.


title: Coriolis force

text: The figure describes a more complex situation where the tossed ball on a turntable bounces off the edge of the carousel and then returns to the tosser, who catches the ball. The effect of Coriolis force on its trajectory is shown again as seen by two observers: an observer (referred to as the "camera") that rotates with the carousel, and an inertial observer. The figure shows a bird's-eye view based upon the same ball speed on forward and return paths. Within each circle, plotted dots show the same time points. In the left panel, from the camera's viewpoint at the center of rotation, the tosser (smiley face) and the rail both are at fixed locations, and the ball makes a very considerable arc on its travel toward the rail, and takes a more direct route on the way back. From the ball tosser's viewpoint, the ball seems to return more quickly than it went (because the tosser is rotating toward the ball on the return flight).


title: Coriolis force

text: On the carousel, instead of tossing the ball straight at a rail to bounce back, the tosser must throw the ball toward the right of the target and the ball then seems to the camera to bear continuously to the left of its direction of travel to hit the rail ("left" because the carousel is turning "clockwise"). The ball appears to bear to the left from direction of travel on both inward and return trajectories. The curved path demands this observer to recognize a leftward net force on the ball. (This force is "fictitious" because it disappears for a stationary observer, as is discussed shortly.) For some angles of launch, a path has portions where the trajectory is approximately radial, and Coriolis force is primarily responsible for the apparent deflection of the ball (centrifugal force is radial from the center of rotation, and causes little deflection on these segments). When a path curves away from radial, however, centrifugal force contributes significantly to deflection.


title: Coriolis force

text: The ball's path through the air is straight when viewed by observers standing on the ground (right panel). In the right panel (stationary observer), the ball tosser (smiley face) is at 12 o'clock and the rail the ball bounces from is at position 1. From the inertial viewer's standpoint, positions 1, 2, and 3 are occupied in sequence. At position 2, the ball strikes the rail, and at position 3, the ball returns to the tosser. Straight-line paths are followed because the ball is in free flight, so this observer requires that no net force is applied.


title: Coriolis force

text: The acceleration affecting the motion of air "sliding" over the Earth's surface is the horizontal component of the Coriolis term


title: Coriolis force

text: In the Northern Hemisphere where the sign is positive this force/acceleration, as viewed from above, is to the right of the direction of motion, in the Southern Hemisphere where the sign is negative this force/acceleration is to the left of the direction of motion


title: Coriolis force

text: Consider a location with latitude "φ" on a sphere that is rotating around the north–south axis. A local coordinate system is set up with the "x" axis horizontally due east, the "y" axis horizontally due north and the "z" axis vertically upwards. The rotation vector, velocity of movement and Coriolis acceleration expressed in this local coordinate system (listing components in the order east ("e"), north ("n") and upward ("u")) are:


title: Coriolis force

text: When considering atmospheric or oceanic dynamics, the vertical velocity is small, and the vertical component of the Coriolis acceleration (formula_28) is small compared with the acceleration due to gravity (g, approximately near Earth's surface). For such cases, only the horizontal (east and north) components matter. The restriction of the above to the horizontal plane is (setting "v" = 0):


title: Coriolis force

text: By setting "v" = 0, it can be seen immediately that (for positive φ and ω) a movement due east results in an acceleration due south. Similarly, setting "v" = 0, it is seen that a movement due north results in an acceleration due east.


title: Coriolis force

text: In general, observed horizontally, looking along the direction of the movement causing the acceleration, the acceleration always is turned 90° to the right (for positive φ) and of the same size regardless of the horizontal orientation.


title: Coriolis force

text: As a different case, consider equatorial motion setting φ = 0°. In this case, Ω is parallel to the north or "n"-axis, and:


title: Coriolis force

text: Accordingly, an eastward motion (that is, in the same direction as the rotation of the sphere) provides an upward acceleration known as the Eötvös effect, and an upward motion produces an acceleration due west.


title: Coriolis force

text: Perhaps the most important impact of the Coriolis effect is in the large-scale dynamics of the oceans and the atmosphere. In meteorology and oceanography, it is convenient to postulate a rotating frame of reference wherein the Earth is stationary. In accommodation of that provisional postulation, the centrifugal and Coriolis forces are introduced. Their relative importance is determined by the applicable Rossby numbers. Tornadoes have high Rossby numbers, so, while tornado-associated centrifugal forces are quite substantial, Coriolis forces associated with tornadoes are for practical purposes negligible.


title: Coriolis force

text: Because surface ocean currents are driven by the movement of wind over the water's surface, the Coriolis force also affects the movement of ocean currents and cyclones as well. Many of the ocean's largest currents circulate around warm, high-pressure areas called gyres. Though the circulation is not as significant as that in the air, the deflection caused by the Coriolis effect is what creates the spiralling pattern in these gyres. The spiralling wind pattern helps the hurricane form. The stronger the force from the Coriolis effect, the faster the wind spins and picks up additional energy, increasing the strength of the hurricane.


title: Coriolis force

text: Air within high-pressure systems rotates in a direction such that the Coriolis force is directed radially inwards, and nearly balanced by the outwardly radial pressure gradient. As a result, air travels clockwise around high pressure in the Northern Hemisphere and anticlockwise in the Southern Hemisphere. Air around low-pressure rotates in the opposite direction, so that the Coriolis force is directed radially outward and nearly balances an inwardly radial pressure gradient.


title: Coriolis force

text: If a low-pressure area forms in the atmosphere, air tends to flow in towards it, but is deflected perpendicular to its velocity by the Coriolis force. A system of equilibrium can then establish itself creating circular movement, or a cyclonic flow. Because the Rossby number is low, the force balance is largely between the pressure-gradient force acting towards the low-pressure area and the Coriolis force acting away from the center of the low pressure.


title: Coriolis force

text: Instead of flowing down the gradient, large scale motions in the atmosphere and ocean tend to occur perpendicular to the pressure gradient. This is known as geostrophic flow. On a non-rotating planet, fluid would flow along the straightest possible line, quickly eliminating pressure gradients. The geostrophic balance is thus very different from the case of "inertial motions" (see below), which explains why mid-latitude cyclones are larger by an order of magnitude than inertial circle flow would be.


title: Coriolis force

text: This pattern of deflection, and the direction of movement, is called Buys-Ballot's law. In the atmosphere, the pattern of flow is called a cyclone. In the Northern Hemisphere the direction of movement around a low-pressure area is anticlockwise. In the Southern Hemisphere, the direction of movement is clockwise because the rotational dynamics is a mirror image there. At high altitudes, outward-spreading air rotates in the opposite direction. Cyclones rarely form along the equator due to the weak Coriolis effect present in this region.


title: Coriolis force

text: An air or water mass moving with speed formula_35 subject only to the Coriolis force travels in a circular trajectory called an "inertial circle". Since the force is directed at right angles to the motion of the particle, it moves with a constant speed around a circle whose radius formula_36 is given by:


title: Coriolis force

text: where formula_38 is the Coriolis parameter formula_39, introduced above (where formula_40 is the latitude). The time taken for the mass to complete a full circle is therefore formula_41. The Coriolis parameter typically has a mid-latitude value of about 10 s; hence for a typical atmospheric speed of , the radius is with a period of about 17 hours. For an ocean current with a typical speed of , the radius of an inertial circle is . These inertial circles are clockwise in the northern hemisphere (where trajectories are bent to the right) and anticlockwise in the southern hemisphere.


title: Coriolis force

text: If the rotating system is a parabolic turntable, then formula_38 is constant and the trajectories are exact circles. On a rotating planet, formula_38 varies with latitude and the paths of particles do not form exact circles. Since the parameter formula_38 varies as the sine of the latitude, the radius of the oscillations associated with a given speed are smallest at the poles (latitude of ±90°), and increase toward the equator.


title: Coriolis force

text: The Coriolis effect strongly affects the large-scale oceanic and atmospheric circulation, leading to the formation of robust features like jet streams and western boundary currents. Such features are in geostrophic balance, meaning that the Coriolis and "pressure gradient" forces balance each other. Coriolis acceleration is also responsible for the propagation of many types of waves in the ocean and atmosphere, including Rossby waves and Kelvin waves. It is also instrumental in the so-called Ekman dynamics in the ocean, and in the establishment of the large-scale ocean flow pattern called the Sverdrup balance.


title: Coriolis force

text: The practical impact of the "Coriolis effect" is mostly caused by the horizontal acceleration component produced by horizontal motion.


title: Coriolis force

text: There are other components of the Coriolis effect. Westward-traveling objects are deflected downwards, while eastward-traveling objects are deflected upwards. This is known as the Eötvös effect. This aspect of the Coriolis effect is greatest near the equator. The force produced by the Eötvös effect is similar to the horizontal component, but the much larger vertical forces due to gravity and pressure suggest that it is unimportant in the hydrostatic equilibrium. However, in the atmosphere, winds are associated with small deviations of pressure from the hydrostatic equilibrium. In the tropical atmosphere, the order of magnitude of the pressure deviations is so small that the contribution of the Eötvös effect to the pressure deviations is considerable.


title: Coriolis force

text: In addition, objects traveling upwards (i.e. "out") or downwards (i.e. "in") are deflected to the west or east respectively. This effect is also the greatest near the equator. Since vertical movement is usually of limited extent and duration, the size of the effect is smaller and requires precise instruments to detect. For example, idealized numerical modeling studies suggest that this effect can directly affect tropical large-scale wind field by roughly 10% given long-duration (2 weeks or more) heating or cooling in the atmosphere. Moreover, in the case of large changes of momentum, such as a spacecraft being launched into orbit, the effect becomes significant. The fastest and most fuel-efficient path to orbit is a launch from the equator that curves to a directly eastward heading.


title: Coriolis force

text: Imagine a train that travels through a frictionless railway line along the equator. Assume that, when in motion, it moves at the necessary speed to complete a trip around the world in one day (465 m/s). The Coriolis effect can be considered in three cases: when the train travels west, when it is at rest, and when it travels east. In each case, the Coriolis effect can be calculated from the rotating frame of reference on Earth first, and then checked against a fixed inertial frame. The image below illustrates the three cases as viewed by an observer at rest in a (near) inertial frame from a fixed point above the North Pole along the Earth's axis of rotation; the train is denoted by a few red pixels, fixed at the left side in the leftmost picture, moving in the others formula_45


title: Coriolis force

text: This also explains why high-speed projectiles that travel west are deflected down, and those that travel east are deflected up. This vertical component of the Coriolis effect is called the Eötvös effect.


title: Coriolis force

text: The above example can be used to explain why the Eötvös effect starts diminishing when an object is traveling westward as its tangential speed increases above Earth's rotation (465 m/s). If the westward train in the above example increases speed, part of the force of gravity that pushes against the track accounts for the centripetal force needed to keep it in circular motion on the inertial frame. Once the train doubles its westward speed at that centripetal force becomes equal to the force the train experiences when it stops. From the inertial frame, in both cases it rotates at the same speed but in the opposite directions. Thus, the force is the same cancelling completely the Eötvös effect. Any object that moves westward at a speed above experiences an upward force instead. In the figure, the Eötvös effect is illustrated for a object on the train at different speeds. The parabolic shape is because the centripetal force is proportional to the square of the tangential speed. On the inertial frame, the bottom of the parabola is centered at the origin. The offset is because this argument uses the Earth's rotating frame of reference. The graph shows that the Eötvös effect is not symmetrical, and that the resulting downward force experienced by an object that travels west at high velocity is less than the resulting upward force when it travels east at the same speed.


title: Coriolis force

text: Contrary to popular misconception, bathtubs, toilets, and other water receptacles do not drain in opposite directions in the Northern and Southern Hemispheres. This is because the magnitude of the Coriolis force is negligible at this scale. Forces determined by the initial conditions of the water (e.g. the geometry of the drain, the geometry of the receptacle, preexisting momentum of the water, etc.) are likely to be orders of magnitude greater than the Coriolis force and hence will determine the direction of water rotation, if any. For example, identical toilets flushed in both hemispheres drain in the same direction, and this direction is determined mostly by the shape of the toilet bowl.


title: Coriolis force

text: Under real-world conditions, the Coriolis force does not influence the direction of water flow perceptibly. Only if the water is so still that the effective rotation rate of the Earth is faster than that of the water relative to its container, and if externally applied torques (such as might be caused by flow over an uneven bottom surface) are small enough, the Coriolis effect may indeed determine the direction of the vortex. Without such careful preparation, the Coriolis effect will be much smaller than various other influences on drain direction such as any residual rotation of the water and the geometry of the container.


title: Coriolis force

text: In 1962, Ascher Shapiro performed an experiment at MIT to test the Coriolis force on a large basin of water, across, with a small wooden cross above the plug hole to display the direction of rotation, covering it and waiting for at least 24 hours for the water to settle. Under these precise laboratory conditions, he demonstrated the effect and consistent counterclockwise rotation.


title: Coriolis force

text: Lloyd Trefethen reported clockwise rotation in the Southern Hemisphere at the University of Sydney in five tests with settling times of 18 h or more.


title: Coriolis force

text: The Coriolis force is important in external ballistics for calculating the trajectories of very long-range artillery shells. The most famous historical example was the Paris gun, used by the Germans during World War I to bombard Paris from a range of about . The Coriolis force minutely changes the trajectory of a bullet, affecting accuracy at extremely long distances. It is adjusted for by accurate long-distance shooters, such as snipers. At the latitude of Sacramento, California, a northward shot would be deflected to the right. There is also a vertical component, explained in the Eötvös effect section above, which causes westward shots to hit low, and eastward shots to hit high.


title: Coriolis force

text: The effects of the Coriolis force on ballistic trajectories should not be confused with the curvature of the paths of missiles, satellites, and similar objects when the paths are plotted on two-dimensional (flat) maps, such as the Mercator projection. The projections of the three-dimensional curved surface of the Earth to a two-dimensional surface (the map) necessarily results in distorted features. The apparent curvature of the path is a consequence of the sphericity of the Earth and would occur even in a non-rotating frame.


title: Coriolis force

text: The Coriolis force on a moving projectile depends on velocity components in all three directions, latitude, and azimuth. The directions are typically downrange (the direction that the gun is initially pointing), vertical, and cross-range.


title: Coriolis force

text: On a flat turntable, the inertia of a co-rotating object forces it off the edge. However, if the turntable surface has the correct paraboloid (parabolic bowl) shape (see the figure) and rotates at the corresponding rate, the force components shown in the figure make the component of gravity tangential to the bowl surface exactly equal to the centripetal force necessary to keep the object rotating at its velocity and radius of curvature (assuming no friction). (See .) This carefully contoured surface allows the Coriolis force to be displayed in isolation.


title: Coriolis force

text: Discs cut from cylinders of dry ice can be used as pucks, moving around almost frictionlessly over the surface of the parabolic turntable, allowing effects of Coriolis on dynamic phenomena to show themselves. To get a view of the motions as seen from the reference frame rotating with the turntable, a video camera is attached to the turntable so as to co-rotate with the turntable, with results as shown in the figure. In the left panel of the figure, which is the viewpoint of a stationary observer, the gravitational force in the inertial frame pulling the object toward the center (bottom ) of the dish is proportional to the distance of the object from the center. A centripetal force of this form causes the elliptical motion. In the right panel, which shows the viewpoint of the rotating frame, the inward gravitational force in the rotating frame (the same force as in the inertial frame) is balanced by the outward centrifugal force (present only in the rotating frame). With these two forces balanced, in the rotating frame the only unbalanced force is Coriolis (also present only in the rotating frame), and the motion is an "inertial circle". Analysis and observation of circular motion in the rotating frame is a simplification compared with analysis and observation of elliptical motion in the inertial frame.


title: Coriolis force

text: Because this reference frame rotates several times a minute rather than only once a day like the Earth, the Coriolis acceleration produced is many times larger and so easier to observe on small time and spatial scales than is the Coriolis acceleration caused by the rotation of the Earth.


title: Coriolis force

text: In a manner of speaking, the Earth is analogous to such a turntable. The rotation has caused the planet to settle on a spheroid shape, such that the normal force, the gravitational force and the centrifugal force exactly balance each other on a "horizontal" surface. (See equatorial bulge.)


title: Coriolis force

text: The Coriolis effect caused by the rotation of the Earth can be seen indirectly through the motion of a Foucault pendulum.


title: Coriolis force

text: A practical application of the Coriolis effect is the mass flow meter, an instrument that measures the mass flow rate and density of a fluid flowing through a tube. The operating principle involves inducing a vibration of the tube through which the fluid passes. The vibration, though not completely circular, provides the rotating reference frame that gives rise to the Coriolis effect. While specific methods vary according to the design of the flow meter, sensors monitor and analyze changes in frequency, phase shift, and amplitude of the vibrating flow tubes. The changes observed represent the mass flow rate and density of the fluid.


title: Coriolis force

text: In polyatomic molecules, the molecule motion can be described by a rigid body rotation and internal vibration of atoms about their equilibrium position. As a result of the vibrations of the atoms, the atoms are in motion relative to the rotating coordinate system of the molecule. Coriolis effects are therefore present, and make the atoms move in a direction perpendicular to the original oscillations. This leads to a mixing in molecular spectra between the rotational and vibrational levels, from which Coriolis coupling constants can be determined.


title: Coriolis force

text: When an external torque is applied to a spinning gyroscope along an axis that is at right angles to the spin axis, the rim velocity that is associated with the spin becomes radially directed in relation to the external torque axis. This causes a "torque-induced" force to act on the rim in such a way as to tilt the gyroscope at right angles to the direction that the external torque would have tilted it. This tendency has the effect of keeping spinning bodies in their rotational frame.


title: Coriolis force

text: Flies (Diptera) and some moths (Lepidoptera) exploit the Coriolis effect in flight with specialized appendages and organs that relay information about the angular velocity of their bodies.


title: Coriolis force

text: Coriolis forces resulting from linear motion of these appendages are detected within the rotating frame of reference of the insects' bodies. In the case of flies, their specialized appendages are dumbbell shaped organs located just behind their wings called "halteres".


title: Coriolis force

text: The fly's halteres oscillate in a plane at the same beat frequency as the main wings so that any body rotation results in lateral deviation of the halteres from their plane of motion.


title: Coriolis force

text: In moths, their antennae are known to be responsible for the "sensing" of Coriolis forces in the similar manner as with the halteres in flies. In both flies and moths, a collection of mechanosensors at the base of the appendage are sensitive to deviations at the beat frequency, correlating to rotation in the pitch and roll planes, and at twice the beat frequency, correlating to rotation in the yaw plane.


title: Coriolis force

text: In astronomy, Lagrangian points are five positions in the orbital plane of two large orbiting bodies where a small object affected only by gravity can maintain a stable position relative to the two large bodies. The first three Lagrangian points (L, L, L) lie along the line connecting the two large bodies, while the last two points (L and L) each form an equilateral triangle with the two large bodies. The L and L points, although they correspond to maxima of the effective potential in the coordinate frame that rotates with the two large bodies, are stable due to the Coriolis effect. The stability can result in orbits around just L or L, known as tadpole orbits, where trojans can be found. It can also result in orbits that encircle L, L, and L, known as horseshoe orbits.


title: Luhansk

text: Luhansk (, ; , ), also known as Lugansk (, ; , ), is a city in what is internationally recognised as Ukraine, although it is administered by Russia as capital of the Luhansk People's Republic (LPR). As of 2021, the population was estimated to be 399,559, making Luhansk the most populous city in the region and the 12th largest in Ukraine. In 2001, nearly half of the population was ethnically Ukrainian, and 47% was ethnically Russian.


title: Luhansk

text: Luhansk has been the capital and administrative center of Luhansk Oblast, although the Ukrainian administration was relocated to Sievierodonetsk when the War in Donbas broke out following the establishment of LPR.


title: Luhansk

text: Luhansk was named after the Luhan River, which flows through the city. According to folk etymology, the name is also derived to the word "Luh" (Ukrainian: Луг), which means "meadow", referring to the floodplains around the river.


title: Luhansk

text: The city traces its history to 1795 when the British industrialist Charles Gascoigne founded a metal factory near the Zaporizhian Cossacks settlement Kamianyi Brid. The settlement around the factory was known as "Luganskiy Zavod". In 1882 the factory settlement Luganskiy Zavod was merged with the town of Kamianyi Brid into the city of Luhansk (also Luhanske, according to the Kharkiv orthography).


title: Luhansk

text: Located in the Donets Basin, Luhansk developed into an important industrial center of Eastern Europe, particularly as a home to the major locomotive-building company Luhanskteplovoz. The city was occupied by Nazi Germany between 14 July 1942 and 14 February 1943.


title: Luhansk

text: On 5 November 1935, the city was renamed Voroshilovgrad (; ) in honour of Soviet military commander and politician Kliment Voroshilov. On 5 March 1958, after Khrushchev's call to not name cities after living people, the old name was reinstated.


title: Luhansk

text: On 5 January 1970, after the death of Voroshilov on 2 December 1969, the name changed again to Voroshilovgrad. On 4 May 1990, a decree of the Supreme Soviet of the Ukrainian SSR gave the city back its original name.


title: Luhansk

text: In 1994 a consultative referendum took place in the Donetsk Oblast and the Luhansk Oblast, with around 90% supporting the Russian language gaining status of an official language alongside Ukrainian, and for the Russian language to be an official language on a regional level.


title: Luhansk

text: During the war in Donbas, separatists seized governmental buildings in the region, proclaiming the Luhansk People's Republic. An independence referendum, unconstitutional under Ukrainian law, was held on 11 May 2014. This referendum was not recognized as legitimate by any government.


title: Luhansk

text: In August 2014, Ukrainian government forces completely surrounded rebel-held Luhansk. Heavy shelling caused civilian casualties in the city. On 17 August, Ukrainian soldiers entered the rebel-controlled Luhansk and for a time had control over a police station.


title: Luhansk

text: After the Ilovaisk counteroffensive, LPR forces regained Lutuhyne and other Luhansk suburbs. Ukrainian forces withdrew from the Luhansk International Airport on 1 September 2014, after heavy fighting.


title: Luhansk

text: Luhansk became the capital and the administrative center of the rebel state of the Luhansk People's Republic. The administration of the Luhansk Oblast was moved to Sievierodonetsk by the government of Ukraine.


title: Luhansk

text: On September 30, 2022, during the Russian invasion of Ukraine, Russian President Vladimir Putin signed a decree declaring the annexation of four regions of Ukraine (Luhansk, Donetsk, Kherson and Zaporizhiya Oblasts) to Russia. The annexation was illegal under international law and was condemned by the General Assembly of the United Nations.


title: Luhansk

text: Some of the more prestigious universities in Ukraine have their home in Luhansk. Luhansk is the location of the main campus of the Taras Shevchenko National University of Luhansk, East Ukrainian Volodymyr Dahl National University and of Luhansk State Medical University.


title: Luhansk

text: In the Ukrainian Census of 2001, 49.6% of the inhabitants declared themselves as ethnically Ukrainians and 47% as Russians. 85.3% of the population spoke Russian as their native language, while 13.7% spoke Ukrainian, 0.2% Armenian and 0.1% Belarusian.


title: Luhansk

text: Luhansk is home to Zorya Luhansk which now plays in the Ukrainian Premier League annual football championship and plays at the Avanhard Stadium. The club won the 1972 Soviet Top League.


title: Luhansk

text: On 7 September 2006, archaeologists in Ukraine announced that an ancient structure had been discovered near Luhansk, which the press reported as a pyramid antedating those in Egypt by at least 300 years. The stone foundations of the structure were said to resemble Aztec and Mayan pyramids in Mesoamerica. It was later concluded that the site in question was not a pyramid but was still of great interest.


title: Luhansk

text: During 2014 and 2015, Luhansk has been the scene of intense fighting and most of these buildings are damaged to some extent. Some may be destroyed.


title: Luhansk

text: Luhansk has a hot summer humid continental climate (Köppen "Dfa"). Luhansk has both the highest and lowest temperature recorded in Ukraine. A record high of was recorded on 12 August 2010, which is the highest temperature to have ever been recorded in Ukraine. A record low of was recorded on 8 January 1935.


title: Ford GT

text: The Ford GT is a mid-engine two-seater sports car manufactured and marketed by American automobile manufacturer Ford for the 2005 model year in conjunction with the company's 2003 centenary. The second generation Ford GT became available for the 2017 model year.


title: Ford GT

text: The GT recalls Ford's historically significant GT40, a consecutive four-time winner of the 24 Hours of Le Mans (1966–1969), including a 1-2-3 finish in 1966.


title: Ford GT

text: The Ford GT began life as a concept car designed in anticipation of the automaker's centennial year and as part of its drive to showcase and revive its "heritage" names such as Mustang and Thunderbird. At the 2002 North American International Auto Show, Ford unveiled a new GT40 Concept car. Camilo Pardo, the then head of Ford's "Living Legends" studio, is credited as the chief designer of the GT and worked under the guidance of J Mays. Carroll Shelby, the original designer of the Shelby GT 500, was brought in by Ford to help develop the GT; which included performance testing of the prototype car. While under development, the project was called "Petunia".


title: Ford GT

text: The GT is similar in outward appearance to the original GT40, but is bigger, wider, and most importantly taller than the original's overall height; as a result, a potential name for the car was the GT44. Although the cars are visually related, structurally, there is no similarity between the modern GT and the 1960s GT40 that inspired it. After six weeks from the unveiling of the GT40 concept, Ford announced a limited production run of the car. Three pre-production cars were shown to the public in 2003 as part of Ford's centenary celebrations, and delivery of the production version called simply the Ford GT began in the fall of 2004.


title: Ford GT

text: As the Ford GT was built as part of the company's 100th anniversary celebration, the left headlight cluster was designed to read "100".


title: Ford GT

text: A British company, Safir Engineering, who built continuation GT40 cars in the 1980s, owned the "GT40" trademark at that time. When production of the continuation cars ended, they sold the excess parts, tooling, design, and trademark to a small Ohio based company called Safir GT40 Spares. This company licensed the use of the "GT40" trademark to Ford for the initial 2002 show car. When Ford decided to put the GT40 concept to production stage, negotiations between the two firms failed as Ford did not pay the US$40 million the owners of the name demanded. Thus, the production cars are simply called the GT.


title: Ford GT

text: The GT was produced for the 2005 and 2006 model years. The car began assembly at Mayflower Vehicle Systems (MVS) in Norwalk, Ohio and was painted and continued assembly at Saleen Special Vehicles (SSV) facility in Troy, Michigan, through contract by Ford. The GT is powered by an engine built at Ford's Romeo Engine Plant in Romeo, Michigan. Installation of the engine and transmission along with seats and interior finishing was handled in the SVT building at Ford's Wixom, Michigan plant.


title: Ford GT

text: Of the 4,500 cars originally planned, approximately 100 were to be exported to Europe, starting in late 2005. An additional 200 cars were destined for sale in Canada. Production ended in September 2006 without reaching the planned production target. Approximately 550 cars were built in 2004, nearly 1,900 in 2005, and just over 1,600 in 2006, for a grand total of 4,038 cars. The final 11 car bodies manufactured by Mayflower Vehicle Systems were disassembled, and the frames and body panels were sold as service parts. The Wixom Assembly Plant has stopped production of all models as of May 31, 2007. Sales of the GT continued into 2007, from cars held in storage and in dealer inventories.


title: Ford GT

text: Ford produced a total of 346 Heritage editions, recognizable by the Gulf Oil-inspired livery. The livery is in honor of the back to back wins of Ford at the 1968 and 1969 24 Hours of Le Mans by the GT40 Mk I.


title: Ford GT

text: When the Ford GT was first announced, the demand outpaced supply, and the cars initially sold for premium prices. The first private sale of Ford's new mid-engine sports car was completed on August 4, 2004, when former Microsoft executive Jon Shirley took delivery of his Midnight Blue 2005 Ford GT. Shirley earned the right to purchase the first production Ford GT (chassis #10) at a charity auction at the Pebble Beach "Concours d'Elegance" Auction after bidding over US$557,000.