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Celestial mechanics

Celestial mechanics is the branch of astronomy that deals with the motions of objects in outer space. Celestial mechanics applies principles of physics to astronomical objects, such as stars and planets, to produce ephemeris data. Modern analytic celestial mechanics started with Isaac Newton's Principia of 1687; the name "celestial mechanics" is more recent than that. Newton wrote that the field should be called "rational mechanics." The term "dynamics" came in a little with Gottfried Leibniz, over a century after Newton, Pierre-Simon Laplace introduced the term "celestial mechanics." Prior to Kepler there was little connection between exact, quantitative prediction of planetary positions, using geometrical or arithmetical techniques, contemporary discussions of the physical causes of the planets' motion. Johannes Kepler was the first to integrate the predictive geometrical astronomy, dominant from Ptolemy in the 2nd century to Copernicus, with physical concepts to produce a New Astronomy, Based upon Causes, or Celestial Physics in 1609.

His work led to the modern laws of planetary orbits, which he developed using his physical principles and the planetary observations made by Tycho Brahe. Kepler's model improved the accuracy of predictions of planetary motion, years before Isaac Newton developed his law of gravitation in 1686. Isaac Newton is credited with introducing the idea that the motion of objects in the heavens, such as planets, the Sun, the Moon, the motion of objects on the ground, like cannon balls and falling apples, could be described by the same set of physical laws. In this sense he unified terrestrial dynamics. Using Newton's law of universal gravitation, proving Kepler's Laws for the case of a circular orbit is simple. Elliptical orbits involve more complex calculations. After Newton, Lagrange attempted to solve the three-body problem, analyzed the stability of planetary orbits, discovered the existence of the Lagrangian points. Lagrange reformulated the principles of classical mechanics, emphasizing energy more than force and developing a method to use a single polar coordinate equation to describe any orbit those that are parabolic and hyperbolic.

This is useful for calculating the behaviour of such. More it has become useful to calculate spacecraft trajectories. Simon Newcomb was a Canadian-American astronomer who revised Peter Andreas Hansen's table of lunar positions. In 1877, assisted by George William Hill, he recalculated all the major astronomical constants. After 1884, he conceived with A. M. W. Downing a plan to resolve much international confusion on the subject. By the time he attended a standardisation conference in Paris, France in May 1886, the international consensus was that all ephemerides should be based on Newcomb's calculations. A further conference as late as 1950 confirmed Newcomb's constants as the international standard. Albert Einstein explained the anomalous precession of Mercury's perihelion in his 1916 paper The Foundation of the General Theory of Relativity; this led astronomers to recognize. Binary pulsars have been observed, the first in 1974, whose orbits not only require the use of General Relativity for their explanation, but whose evolution proves the existence of gravitational radiation, a discovery that led to the 1993 Nobel Physics Prize.

Celestial motion, without additional forces such as thrust of a rocket, is governed by gravitational acceleration of masses due to other masses. A simplification is the n-body problem, where the problem assumes some number n of spherically symmetric masses. In that case, the integration of the accelerations can be well approximated by simple summations. Examples: 4-body problem: spaceflight to Mars 3-body problem: Quasi-satellite Spaceflight to, stay at a Lagrangian pointIn the case that n=2, the situation is much simpler than for larger n. Various explicit formulas apply, where in the more general case only numerical solutions are possible, it is a useful simplification, approximately valid. Examples: A binary star, e.g. Alpha Centauri A binary asteroid, e.g. 90 Antiope A further simplification is based on the "standard assumptions in astrodynamics", which include that one body, the orbiting body, is much smaller than the other, the central body. This is often valid. Examples: Solar system orbiting the center of the Milky Way A planet orbiting the Sun A moon orbiting a planet A spacecraft orbiting Earth, a moon, or a planet Perturbation theory comprises mathematical methods that are used to find an approximate solution to a problem which cannot be solved exactly.

The earliest use of modern perturbation theory was to deal with the otherwise unsolvable mathematical problems of celestial mechanics: Newton's solution for the orbit of the Moon, which moves noticeably differently from a simple Keplerian ellipse because of the competing gravitation of the Earth and the Sun. Perturbation methods start with a simplified form of the original problem, chosen to be solvable. In celestial mechanics, this is a Keplerian ellipse, which is

Nieuport-Delage NiD 940

The Nieuport-Delage NiD 940 was a French, pusher configuration touring aircraft first flown in 1934. It suffered from longitudinal instabilities and despite modifications and a more powerful engine, it did not receive its Certificate of Airworthiness; the NiD 940 was a low cantilever wing aircraft. Its wing had a thick section and a chrome-steel tube structure and in plan was swept with straight-taper. Elevons, hinged at right angles to the line of flight, controlled both roll. Triangular wing tip fins, externally braced from tip to wing, provided yaw stability and carried generous, five-sided, angular rudders which could operate together for directional control but be opened at right angles as air brakes; the wings could be folded for transport. The fuselage of the NiD 940 was a steel tube structure, flat-sided and short, not reaching the wing trailing edge, it was covered with tulipwood plywood overlain with fabric. A well glazed cabin provided two side-by-side seats, with room for a third seat and baggage space behind them.

The steel structure mounted an 89 kW Lorraine 5Pc five-cylinder radial engine in uncowled pusher configuration. The NiD 940 had tricycle landing gear, with its mainwheels on V-struts hinged from the lower fuselage and with vertical shock absorber legs to the wings. Wingtips were protected by skids mounted on the bottom of the fins; the nosewheel was large and well forward. In its initial form the prototype was known as the NiD 941. Though this was on display in November 1932 at the 13th Paris Salon de l'Aviation, it did not fly until February 1934, piloted by Nieuport's test pilot Joseph Sadi-Lecointe; the early trials showed a lack of longitudinal stability. Despite modifications and a new 101 kW Salmson 9Nc nine-cylinder radial engine, after which it became the NiD 942, an airworthiness certificate was not granted. NiD 941 original aircraft with Lorraine 5Ps engine. NiD 942 modified aircraft with Salmson 9Nc engine. Data from Nieuport 1909-1950, p.216General characteristics Crew: One Capacity: one or two passengers Length: 5.05 m Wingspan: 13.30 m Height: 2.35 m Wing area: 27 m2 Empty weight: 615 kg Gross weight: 1,039 kg Fuel capacity: fuel and oil, 90 kg Powerplant: 1 × Lorraine 5Pc 5-cylinder radial, 89 kW Propellers: 2-bladedPerformance Maximum speed: 220 km/h at ground level Range: 600 km Service ceiling: 6,800 m service Time to altitude: 9 min 50 sec to 2,000 m Landing speed: 70 km/h

Andrew Pixley

Andrew Pixley was a convicted murderer from Dallas, Oregon. He was executed December 10, 1965, in Wyoming for the murder of two young girls in August 1964. Born Andrew Armandoz Benavidez in Las Cruces, New Mexico, Pixley joined the U. S. Army after being charged with passing bad checks, his father Columbus Pixley had never held a job. He served two years overseas, he was described as "slightly built" and "nervous" and dishwasher. There was a previous warrant out for his arrest in his home town on a charge of larceny, he was accused and cleared of being in possession of a stolen car in Davenport, two weeks before the murders. He had been living in a trailer with two employees of the hotel where the murders took place, David Starling and Orval Edwards. Starling was described as having had prior knowledge of Pixley's violent tendencies. On the night of August 5/6, 1964, Pixley broke into a room of the Wort Motor Hotel in Jackson, occupied by the family of Illinois Circuit Court Judge Robert McAuliffe, who were on vacation.

McAuliffe and his wife were elsewhere in the hotel taking in a show. When they returned to their room, they found Pixley lying on the floor, he may have been feigning. McAuliffe pinned him to the floor. Police officer James Jensen heard Mrs. McAuliffe screaming and rushed to the scene, where McAuliffe shouted "My God, this man has killed my babies."Their older daughters, Debbie, 12, Cindy, 8 lay dead in their beds. The girls had been sexually assaulted, Debbie had been bludgeoned with a rock, Cindy beaten and strangled; the youngest child, six-year-old Susan, was unharmed. Described as asleep during the crime, she may have witnessed the assault on her sisters. Pixley had climbed a stack of wood and scaled the rear wall of the hotel, removing a screen to get in at the window; as Pixley was taken by police from the hotel, a crowd outside called. He was taken to a jail in another town and to the Wyoming State Penitentiary for better security; the McAuliffe sisters were buried together in a single casket.

Their parents filed suit against the hotel in order to pay for the surviving child's psychiatric treatment. Pixley only told police "I didn't do it." Hotel employee Richard Southern testified that Pixley cited his Native American heritage in explaining why he "couldn't" have done such a thing. Pixley asked to make a statement, was examined using sodium pentothal interviews, he said he remembered drinking earlier in the evening, but could not remember entering the hotel or killing the girls. His court-appointed attorney, Robert Hufsmith, added that Pixley remembered being in the company of another person earlier that evening, but that his mind was "blank since he left that person."Pixley was examined by Dr. William Karn, Jr. of the Wyoming State Hospital, who pronounced him sane, but an "incurable sociopath" at the trial, adding that "it meant a lot more to Pixley to kill the girls while they were awake." At this, Judge McAuliffe got up from his seat and attempted to assault Pixley before being restrained.

Pixley was sentenced to death, laughing when the execution date was announced. Although an appeal was filed to change his sentence to life imprisonment, he said he did not want an appeal, he was executed in the Wyoming gas chamber on December 10, 1965. He took the longest time to die of any person executed in the Wyoming gas chamber; until the execution of Mark Hopkinson in 1992, Pixley was the last person to be put to death in Wyoming. According to genealogical research and Betty McAuliffe divorced sometime after the murders. McAuliffe remarried Charlotte Olivia Moon Branch and had a son, Jon David McAuliffe, born on 1/21/1974 in Chicago, he died April 1998, of a heart attack. Betty McAuliffe died November 28, 2010. Susan McAuliffe had five children. Capital punishment in Wyoming List of people executed in Wyoming


Ordona is a small town and comune of the province of Foggia in the region of Apulia in southern Italy. Ascoli Satriano, Foggia, Orta Nova, Cerignola are nearby towns. Ordona lies near the ancient site of Herdonia or Herdoniae, a Roman town where Hannibal fought a major battle against the Roman Army; the ruins of Herdonia were discovered in the years after the Second World War, remain only excavated. The ancient centre, founded by the Daunians enjoyed a noteworthy development and saw its maximum splendour, its economic decline began during the 4th Century BC. The construction of defensive walls during this period suggests a period of battles with other centres in the region comprising clashes with the Greek hegemonic cities in the territory, among them neighbouring Taranto, it passed over to the Romans, with the rest of Apulia, after the wars of the Greek-Messapian League, commanded by King Pyrrhus of Epirus. Herdonia was a protagonist during the Second Punic War and in particular, during the events linked to the war's most famous battle at Cannae on 2 August 216 BC.

According to the Roman historian Livy, after the Battle of Cannae the City passed to Hannibal, but was soon recovered by the Romans, in 214 BC. From this moment on, the city did not recover until its insertion along the Via Traiana route, a coastal alternative of the Via Appia, at the beginning of the 2nd Century AD. Today’s central habitation began in the 9th Century, but had difficulties in developing due to terrible conditions in the territory. In fact, during the Medieval era, the Tavoliere delle Puglie lost its agricultural vocation and became a main transhumance for sheep arriving from all of central Italy; the Jesuits took over the centre and tried to push Ordona’s economy by reclaiming part of its territory and allowing families to settle here. In 1774, Ordona became part of Royal Bourbon property, allowing important new reclamation work to take place throughout the entire 19th Century. Remains from the Roman Erdonia are situated in the following areas: the Forum, the Augustea Basilica, a part of the Via Traiana route where one can visit the remains of shops and the Market, the remains of a temple from the Imperial era, the Amphitheatre and thermal baths with mosaic flooring.

Below this level, in the area of the Basilica, finds uncovered tombs and houses from the Daunian city. The diffusion of Christianity is testified by the remains of a Paleochristian Basilica from the 6th Century AD. Today’s digs have still not touched all the various levels and the Herdonia site could still reserve many surprises for archaeologists and enthusiastic visitors. Ordona's economy is agricultural


Uberlândia is a municipality in the state of Minas Gerais, southeastern Brazil. It is the second largest municipality in the state of Minas Gerais after the state capital Belo Horizonte, its population in 2018 was 683,247, making it the fourth largest city of the interior region of Brazil. The city is located on the Brazilian Highlands 2,802 feet above sea level, it is an important logistic hub between São Brasília. The city sits within the Brazilian cerrado and has eight protected zones of tropical savanna vegetation. Uberlândia is served by Uberlândia–Ten. Cel. Av. César Bombonato Airport. Uberlândia is located in the western part of the state of Minas Gerais, in the region called Triângulo Mineiro, one of the richest agricultural regions of Brazil, between the Paranaíba and Grande rivers, it is connected to major cities by the following federal highways: BR-050, BR-365, BR-455, BR-452, BR-497. Uberlândia is about 580 km away from São Paulo, connected by a safe double trace highway; the capital of the state of Minas Gerais, Belo Horizonte, is 560 km away and Brasília, the capital of the country, lies just 440 kilometres to the north.

There are railways connecting Uberlândia via the north-south Centro-Atlântica line. Uberlândia is a statistical micro-region including the following municipalities: Araguari, Araporã, Canápolis, Cascalho Rico, Indianópolis, Monte Alegre de Minas, Prata and Uberlândia. In 2007 the population of these cities' agglomeration was 818,395 inhabitants in a total area of 18,864.20 square kilometres. The population density was 43.38 inhabitants/km2. Due to its location and transport links, Uberlândia has been chosen as a point for the Free Economic Zone of Manaus, the first such distribution point. According to the 2010 census its citizens are members of the Roman Catholic Church, while Evangelical Christians comprise the second largest religious affiliation in the city. There are minorities of Spiritists and no religious. There are smaller minorities adhering the Brazilian Catholic Apostolic Church, the Orthodox Church, Jehovah's Witnesses, The Church of Jesus Christ of Latter-day Saints, Buddhism, indigenous beliefs and Candomblé.

The city has architectural and natural values. Here are the main attractions in the city: Municipal Market of Uberlândia: It is located at the centre of the city, it was established in 1923, but only had its construction started in 1944, under the tenure of Mayor Vasconcelos Costa, with modern era architecture. It was a wholesaler centre until 1977, it is situated in Olegario Máciel Road, offers diverse typical products from the state of Minas Gerais. Municipal Museum of Uberlândia: It is located at the centre of the city, on the Clarimundo Carneiro Square; the same building had been used as City Hall. It has been reformed and today is a place where many cultural projects take place. Sabiá Park It is a park/zoo administrated by FUTEL, located in the borough of Tibery, on the East Zone of the city, it is a green complex made up of a Zoo with dozens of animals in captivity. Municipal Park Victoria Siquierolli: It is located on the North Zone of Uberlândia, being where legitimate examples of vegetation of the Brazilian cerrado can be found, with trees with leathery leaves, twisted trunks, colourful flowers and many fruits, as well as a playground for children and a biodiversity museum.

Its total area complies of a total of 232 300 square meters and is located between the boroughs of Jardim América II, Residencial Gramado, Nossa Senhora das Graças e Cruzeiro do Sul. Rondon Pacheco Avenue: It is considered to be the “gastronomic corridor” of Uberlândia. Around it is where the nightlife in Uberlândia can be found, having many bars, cachaçarias, cafes, ice cream parlours and sweet shops. There are more than 60 establishments across the avenue. Furthermore, the avenue has many hotels, convenience stores, gas stations and hypermarkets; the avenue cuts the city from east to west. The Governor Rondon Pacheco Avenue starts with its merge with the Silvio Regain Avenue, on the Tubalina borough, on the southeast region of the city, ends up on the BR-050 highway, on the furthest side of the Custodio Pereira borough, on the west region of the city. List of municipalities in Minas Gerais City Hall of Uberlândia website Government of the State of Minas Gerais website

Hezekiah Woodward

Hezekiah Woodward was an English nonconformist minister and educator, involved in the pamphlet wars of the 1640s. He was a Comenian in educational theory, an associate of Samuel Hartlib, he was one of those articulating the Puritan argument against the celebration of Christmas. In the early 1640s he was a preacher at Aldermanbury in London. At this period he was linked with John Milton, as authors in "the frequent printing of scandalous Books by divers", he was examined about his writings at the end of December 1644, being released after two days, having acknowledged authorship of some work or works, thought to have included the anonymous As You Were. Milton either was not pulled in, or was allowed to go. At St Michael's Church, Bray, he was an Independent minister, but was ejected in 1662, after the English Restoration of 1660. Subsequently he was in one of the founders of the Old Meeting Congregational Church there, he engaged a major writer on the Presbyterian side. Woodward supported Katherine Chidley against Edwards.

As You Were: or a reducing was published anonymously, in support of John Goodwin. It was a reply to Faces About, attributed to George Gillespie. Gillespie hit back from the Presbyterian side. On education, he advanced the argument that the current grammar schools lacked provision for the most elementary schooling, to the detriment of the quality of the latter, his A Light to Grammar makes the case for education based on stimulation. Parents, in his view, delegated too much of a child's upbringing to teachers, he wrote about his own schooling, in A Childes Patrimony, Portion. His daughter Frances married John Oxenbridge, his daughter Sarah married a founder of Worcester, Massachusetts. C. B. Freeman, A Puritan Educator: Hezekiah Woodward and His "Childes Patrimony", British Journal of Educational Studies, Vol. 9, No. 2, pp. 132–142