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Kepler's laws of planetary motion

In astronomy, Kepler's laws of planetary motion are three scientific laws describing the motion of planets around the Sun, published by Johannes Kepler between 1609 and 1619. These improved the heliocentric theory of Nicolaus Copernicus, replacing its circular orbits with epicycles with elliptical trajectories, explaining how planetary velocities vary; the laws state that: The orbit of a planet is an ellipse with the Sun at one of the two foci. A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time; the square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit. The elliptical orbits of planets were indicated by calculations of the orbit of Mars. From this, Kepler inferred that other bodies in the Solar System, including those farther away from the Sun have elliptical orbits; the second law helps to establish. The third law expresses that the farther a planet is from the Sun, the longer its orbit, vice versa.

Isaac Newton showed in 1687 that relationships like Kepler's would apply in the Solar System to a good approximation, as a consequence of his own laws of motion and law of universal gravitation. Kepler's laws improved the model of Copernicus. If the eccentricities of the planetary orbits are taken as zero Kepler agreed with Copernicus: The planetary orbit is a circle; the Sun is at the center of the orbit. The speed of the planet in the orbit is constant; the eccentricities of the orbits of those planets known to Copernicus and Kepler are small, so the foregoing rules give fair approximations of planetary motion, but Kepler's laws fit the observations better than does the model proposed by Copernicus. Kepler's corrections are not at all obvious: The planetary orbit is not a circle, but an ellipse; the Sun is not at a focal point of the elliptical orbit. Neither the linear speed nor the angular speed of the planet in the orbit is constant, but the area speed is constant; the eccentricity of the orbit of the Earth makes the time from the March equinox to the September equinox, around 186 days, unequal to the time from the September equinox to the March equinox, around 179 days.

A diameter would cut the orbit into equal parts, but the plane through the Sun parallel to the equator of the Earth cuts the orbit into two parts with areas in a 186 to 179 ratio, so the eccentricity of the orbit of the Earth is e ≈ π 4 186 − 179 186 + 179 ≈ 0.015, close to the correct value. The calculation is correct when perihelion, the date the Earth is closest to the Sun, falls on a solstice; the current perihelion, near January 4, is close to the solstice of December 21 or 22. It took nearly two centuries for current formulation of Kepler's work to take on its settled form. Voltaire's Eléments de la philosophie de Newton of 1738 was the first publication to use the terminology of "laws"; the Biographical Encyclopedia of Astronomers in its article on Kepler states that the terminology of scientific laws for these discoveries was current at least from the time of Joseph de Lalande. It was the exposition of Robert Small, in An account of the astronomical discoveries of Kepler that made up the set of three laws, by adding in the third.

Small claimed, against the history, that these were empirical laws, based on inductive reasoning. Further, the current usage of "Kepler's Second Law" is something of a misnomer. Kepler had two versions, related in a qualitative sense: the "distance law" and the "area law"; the "area law" is. Johannes Kepler published his first two laws about planetary motion in 1609, having found them by analyzing the astronomical observations of Tycho Brahe. Kepler's third law was published in 1619. Kepler had believed in the Copernican model of the solar system, which called for circular orbits, but he could not reconcile Brahe's precise observations with a circular fit to Mars' orbit – Mars coincidentally having the highest eccentricity of all planets except Mercury, his first law reflected this discovery. Kepler in 1621 and Godefroy Wendelin in 1643 noted that Kepler's third law applies to the four brightest moons of Jupiter; the second law, in the "area law" form, was contested by Nicolaus Mercator in a book from 1664, but by 1670 his Philosophical Transactions were in its favour.

As the century proceeded it became more accepted. The reception in Germany changed noticeably between 1688, the year in which Newton's Principia was published and was taken to be Copernican, 1690, by which time work of Gottfried Leibniz on Kepler had been published. Newton was credited with understanding that the second law is not special to the inverse square law of gravitation, being a consequence just of the radial nature of that law. Carl Runge and Wilhelm Lenz much identified a symmetry principle in the phase space of planetary motion which accounts for the first and third laws in the case of Newtonian gravitation, as conservation of angular momentum does via rotational symmetry for the second law; the mathematical model of the kinematics of a planet subject to the laws allows a large range of further calculations. The orbit of every planet is an ellipse

Enxet language

Enxet known as "Lengua Ser," "Lengua," "Vowak," and "Enhlit" is one of twenty languages spoken by the Gran Chaco people of South America. Enxet belongs to the Mascoian language family. Once a dialect of the broader language lengua and Enhlet diverged as extensive differences between the two were realized. Enxet belongs to the Mascoian language family, spoken by Native Americans in the Paraguayan region of the South American Gran Chaco; the South Amerindians living in this region are referred to as Guaycuru. Enxet and Enhlet were once considered dialects of Lengua, they were dubbed "Southern Lengua" and "Northern Lengua," respectively. The Enxet language was first documented in the late 19th century by explorers from Spain. Enxet contains only three phonemic vowel qualities /e,a,o/, each requiring a certain length such to maximize distinction. Bilingual speakers of Spanish and Enxet purportedly utilize shorter spacing between vowels when speaking the latter compared to the former; the region occupied by the Enxet people is the subject of an ongoing legal dispute with the state of Paraguay.

The Enxet language and people are of interest to Anglican missionaries. Campbell, Lyle. "Language Contact and Linguistic Change in the Chaco". Revista Brasileira de Linguística Antropológica. 5: 259–292. Doi:10.26512/rbla.v5i2.16268. Messineo, Cristina. "Ethnobiological Classification in Two Indigenous Languages of the Gran Chaco Region: Toba and Maká". Anthropological Linguistics. 53: 132–169. Doi:10.1353/anl.2011.0010. Hammarström, H.. Basic vocabulary comparison in South American languages; the Native Languages of South America: Origins, Typology, 56. Kidd, Stephen W.. "Land and Benevolent Shamanism: The Enxet Indians in a Democratic Paraguay". Journal of Latin American Studies. 27: 43–75. Doi:10.1017/S0022216X00010166. Klein, Harriet Manelis. "Indian Languages of the Paraguayan Chaco". Anthropological Linguistics. 19: 378–401. JSTOR 30027605. Langer, Erick D.. "Peoples of the Gran Chaco". American Ethnologist. 28: 249–251. Doi:10.1525/ae.2001.28.1.249. ELAR collection: The Enxet documentation project deposited by John Elliott Latvian

Sanctuary of Fátima

The Sanctuary of Fátima known as Sanctuary of Our Lady of Fátima, is a group of Catholic religious buildings and structures in Cova da Iria, in the civil parish of Fátima, in the municipality of Ourém, in Portugal. In addition to the Basilica of Our Lady of the Rosary, the shrine comprises the Chapel of the Lausperene, a great oak tree, a monument to the Sacred Heart of Jesus and the Chapel of the Apparitions, where three children Lúcia Santos and her cousins and Francisco Marto, said they were first visited by the Virgin Mary. In addition, several other structures and monuments were built in the intervening years to commemorate the events. Across from the main sanctuary is the much larger Basilica of the Holy Trinity constructed after 1953, owing to the limited scale of the Sanctuary for large-scale pilgrimages and religious services. In 1916, on three separate occasions, Lúcia Santos and her two cousins and Jacinta Marto, began reporting witnessing apparitions of an angel in the region of Valinhos.

These alleged visitations persisted until the 13 May 1917 when, while tending their family's sheep in Cova da Iria, they said they witnessed the apparition of what they assumed was the Virgin Mary, began doing penance and self-sacrifice to atone for sinners. Many flocked to Fátima and Aljustrel to witness these alleged apparitions along with the children, but not before the children were jailed for being politically disruptive; these visitations culminated in the 13 October 1917 public Miracle of the Sun event as the apparition of Virgin Mary divulged three secrets to the children. Although the Miracle of the Sun marked the children's last claimed apparition, the region of Fátima continued to be a destination of pilgrims. Victims of the 1918 flu pandemic epidemic, both cousins died on 4 April 1919 and 20 February 1920, respectively. Along with the Three Secrets of Fátima, their stories, would be linked to religious construction that followed in Fátima. A small chapel, the Capelinha das Aparições was begun on 28 April 1919 by local people: its construction was neither hindered or encouraged by church authorities.

On 13 May 1920, pilgrims defied government troops to install a statue of the Virgin Mary in the chapel, while the first celebrated mass occurred on 13 October 1921. A hostel for the sick was begun in the same year, but the original chapel was destroyed on 6 March 1922; the first investigations by the Roman Catholic Church in regards to the events at Fátima began on 3 May 1922. Meanwhile, the small Chapel of the Appariations was rebuilt and functioning by 1923, it would take the next four years to see a change in attitude from the Roman Catholic church. On 13 May 1928, the first foundation stone was laid in the construction of the basilica and colonnade of Fátima, a process that continued until 1954; the construction of the colonnade, by architect António Lino began in 1949 and extended to 1954. Meanwhile, on 13 October 1930, the Roman Catholic Church permitted the existence of the first cult of Nossa Senhora de Fátima. Before the completion of the complex, the mortal remains of Jacinta Marto was moved from her modest grave in Vila Nova de Ourém to Fátima, to the completed basilica sanctuary.

Her brother's remains were moved from the cemetery in Fátima to the basilica on 13 March 1952. An organ was mounted that same year in the completed church, by the firm Fratelli Rufatti of Pádua. Before this period, on 13 May 1942, a large pilgrimage had marked the 25th anniversary of the apparitions. Two years Cardinal Massella, Pontifical Legate, crowned the image of Our Lady of Fátima in the Chapel of the Apparitions, marking a complete reversal in the official posture of the Vatican See towards the events at Fátima. On 7 October 1953 the Church of the Sanctuary of Fátima was consecrated, within a year, Pope Pius XII conceded the church the title of Basilica in his short Luce Superna document. On 13 May 1956, cardinal Angelo Roncalli, patriarch of Venice and future Pope John XXIII, presided over an international pilgrimage anniversary. From this point forward, there would continue to be an active presence and influence of the patriarchy of the Vatican in the events at Fátima. On 1 January 1960, the sacred Lausperene rite was initiated.

The sections of the organ, until this time dispersed throughout the basilica, were united in one unit in 1962, in the high choir. On 13 May 1967, Pope Paul VI visited Fátima to mark the 50th anniversary of the first apparitions. On 19 September 1977, the civil parish was elevated to the status of town. Between 12–13 May 1982, in a pilgrimage to Fátima by Pope John Paul II, the first cornerstone of the Capela do Sagrado Lausperene was laid: the construction would continue until 1987, its completion and consecration on 1 January 1987 was attributed to donations and gifts from the Austrian association Cruzada de Reparação pelo Rosário para a Paz no Mundo. Pope John Paul II would return once more on 12–13 May 1991 to preside ove

Song Hye-rang

Seong Hye-rang is a North Korean defector and author. Her father was a wealthy South Korean landowner who moved to the North for political reasons, while her mother was an editor of the official North Korean newspaper Rodong Shinmun. Seong's younger sister Song Hye-rim, a popular actress, secretly began an affair with Kim Jong-il against his father Kim Il-sung's wishes in the late 1960s or early 1970s, which culminated in Hye-rim's forced divorce from her husband. Five years Hye-rang would become responsible for raising Kim Jong-nam, the son resulting from that pregnancy. Hye-rim moved into the household, their lives were managed by Kim Jong-il to ensure that his father would not find out about his continuing affair. In September 28, 1982, Seong Hye-rang's son defected to South Korea. Seong herself defected in Geneva in February 1996, carrying nothing but her medicines, her diary, a book of short stories by Anton Chekhov. Following her defection, she went into hiding in the European countryside in fear of her life, travelling with an unidentified Japanese woman.

She now lives in an undisclosed location in Europe. Song, Hye-rang. 《등나무집:성혜랑 자서전》. Seoul: Chisiknara. Pp. 528 pages. ISBN 89-8375-538-5. Song, Hye-rang. 北朝鮮はるかなり―金正日官邸で暮らした20年. Translated by Hagiwara Ryō. Bungeishunjū. ISBN 4163571604

Montreal Aquarium

The Montreal Aquarium was a public aquarium on St. Helen's Island, Quebec, Canada, it was built in 1966 for Expo 67 and shut down in 1991. It reopened as the Nintendo Mégadôme from 1995 to 2007; the Expo pavilion was sponsored by Alcan Aluminum Ltd. who built the site as a joint venture with the City of Montreal and the Zoological Society of Montreal. The main aquarium featured exhibits space and a gift shop; the separate dolphin pool had show pool and holding tanks. After a workers' strike in February 1980, two dolphins starved to death; the surviving dolphins were sold to a roadside dolphin attraction in Florida. The failing aquarium received more negative publicity; the city planned in 1988 to move the aquarium to a more popular location at the Old Port, but the plan did not come through when the city was mired in recession in the early 1990s. On September 15, 1991, the aquarium closed. Most of its exhibits were transferred to the Biodome; the site of the former aquarium now belongs to the amusement park La Ronde.

The main aquarium building is now the Pass Building and the dolphin pool is vacant and closed off from the public. The Nintendo Mégadôme opened in 1995. Nintendo Mégadôme Photo and floor plan

Denmark Vesey

Denmark Vesey was a literate, skilled carpenter and leader of African Americans in Charleston, South Carolina. In June 1822 he was accused and convicted of being the leader of "the rising," a major slave revolt, scheduled to take place in the city on July 14, he was executed on July 2. Born into slavery in St. Thomas, Vesey was enslaved to a man in Bermuda for some time before being brought to Charleston, where he gained his freedom. Vesey won a lottery and purchased his freedom around the age of 32, he had a good business and a family, but was unable to buy his first wife Beck and their children out of slavery. Vesey became active in the Second Presbyterian Church. In 1818 he was one of the founders of an independent African Methodist Episcopal Church in the city, which became known as the Emanuel African Methodist Episcopal Church after the Civil War; this first independent black denomination in the US was founded in Philadelphia, Pennsylvania in 1816. His church in Charleston had the support of white clergy in the city.

It attracted 1,848 members, making it the second-largest AME congregation in the nation after Mother Bethel in Philadelphia, Pennsylvania. In 1822, Vesey was alleged to be the leader of a planned slave revolt. Vesey and his followers were said to be planning to kill slaveholders in Charleston, liberate the slaves, sail to the black republic of Haiti for refuge. By some accounts, the revolt would have involved thousands of slaves in the city as well as others who lived on plantations which were located miles away. City officials sent a militia to arrest the plot's leaders and many suspected followers on June 22 before the rising could begin, believed to be planned for July 14. No white people were injured. Vesey and five slaves were among the first group of men to be judged guilty by the secret proceedings of a city-appointed Court and condemned to death, they were executed by hanging on July 2, 1822. Vesey was about 55 years old. In proceedings, some 30 additional followers were executed, his son was judged guilty of conspiracy and deported from the United States, along with many others.

The church was destroyed and its minister was expelled from the city. Manuscript transcripts of testimony at the 1822 Court proceedings in Charleston, South Carolina, its Report after the events constitute the chief source of documentation about Denmark Vesey's life; the Court executed him by hanging. The court reported that he was born into slavery about 1767 in St. Thomas, at the time a colony of Denmark, he was called Telemaque. Biographer David Robertson suggests that Telemaque may have been of Mande origin, but his evidence has not been accepted by historians. Telemaque was purchased around the age of 14 by Joseph Vesey, a Bermudian sea captain and slave merchant. After a time, Vesey sold the youth to a planter in French Saint-Domingue; when the youth was found to suffer epileptic fits, Captain Vesey took him back and returned his purchase price to the former master. Biographer Egerton found no evidence of Denmark Vesey having epilepsy in life, he suggests that Denmark may have faked the seizures in order to escape the brutal conditions on Saint-Domingue.

Telemaque worked as a personal assistant for Joseph Vesey and served Vesey as an interpreter in slave trading, a job which required him to travel to Bermuda for long periods of time, as a result, he was known to be fluent in French and Spanish as well as English. Following the American Revolution, the captain retired from the sea and slave trade, settling in Charleston, South Carolina. Colonists from Bermuda, including the first Governor, had settled here since 1669, there were many ties. Numerous Bermudians, such as Thomas Tudor Tucker, had settled prior to American independence. Telemaque had Vesey settled in Charleston. Charleston was a continental hub, connected to Bermuda's thriving merchant shipping trade; the trading center of the Low country's rice and indigo plantations, the city had a majority-slave population and thriving port. In 1796, Captain Vesey wed Mary Clodner, a wealthy "free East Indian woman", the couple used Telemaque as a domestic at Mary's plantation, "The Grove", just outside Charleston on the Ashley River.

On November 9, 1799, Telemaque won $1500 in a city lottery. At the age of 32, he bought his freedom for $600 from Vesey, he took the surname Vesey and the given name of'Denmark,' after the nation ruling his birthplace of St. Thomas. Denmark Vesey built up his own business. By this time he had married an enslaved woman, their children were born into slavery under the principle of partus sequitur ventrem, by which children of a slave mother took her status. Vesey worked to gain freedom for his family; this meant their future children would be born into slavery. Along with other slaves, Vesey had belonged to the Second Presbyterian church and chafed against its restrictions on black members. In 1818, after becoming a free man of color, he was among founders of a congregation on what was known as the "Bethel circuit" of the African Methodist Episcopal Church; this had been organized in Philadelphia, Pennsylvania in 1816 as the first independent black denomination in the United States. The AME Church in Charleston was supported by leading white clergy.

In 1818 white authorities ordered th