Orbital elements are the parameters required to uniquely identify a specific orbit. In celestial mechanics these elements are considered in two-body systems using a Kepler orbit. There are many different ways to mathematically describe the same orbit, but certain schemes, each consisting of a set of six parameters, are used in astronomy and orbital mechanics. A real orbit and its elements change over time due to gravitational perturbations by other objects and the effects of general relativity. A Kepler orbit is an mathematical approximation of the orbit at a particular time; the traditional orbital elements are the six Keplerian elements, after Johannes Kepler and his laws of planetary motion. When viewed from an inertial frame, two orbiting bodies trace out distinct trajectories; each of these trajectories has its focus at the common center of mass. When viewed from a non-inertial frame centred on one of the bodies, only the trajectory of the opposite body is apparent. An orbit has two sets of Keplerian elements depending on which body is used as the point of reference.

The reference body is called the primary, the other body is called the secondary. The primary does not possess more mass than the secondary, when the bodies are of equal mass, the orbital elements depend on the choice of the primary. Two elements define the shape and size of the ellipse: Eccentricity —shape of the ellipse, describing how much it is elongated compared to a circle. Semimajor axis —the sum of the periapsis and apoapsis distances divided by two. For classic two-body orbits, the semimajor axis is the distance between the centers of the bodies, not the distance of the bodies from the center of mass. Two elements define the orientation of the orbital plane in which the ellipse is embedded: Inclination —vertical tilt of the ellipse with respect to the reference plane, measured at the ascending node. Tilt angle is measured perpendicular to line of intersection between orbital plane and reference plane. Any three points on an ellipse will define the ellipse orbital plane; the plane and the ellipse are both two-dimensional objects defined in three-dimensional space.

Longitude of the ascending node —horizontally orients the ascending node of the ellipse with respect to the reference frame's vernal point. This is measured in the reference plane, is shown as the green angle Ω in the diagram; the remaining two elements are as follows: Argument of periapsis defines the orientation of the ellipse in the orbital plane, as an angle measured from the ascending node to the periapsis. True anomaly at epoch defines the position of the orbiting body along the ellipse at a specific time; the mean anomaly M is a mathematically convenient fictitious "angle" which varies linearly with time, but which does not correspond to a real geometric angle. It can be converted into the true anomaly ν, which does represent the real geometric angle in the plane of the ellipse, between periapsis and the position of the orbiting object at any given time. Thus, the true anomaly is shown as the red angle ν in the diagram, the mean anomaly is not shown; the angles of inclination, longitude of the ascending node, argument of periapsis can be described as the Euler angles defining the orientation of the orbit relative to the reference coordinate system.

Note that non-elliptic trajectories exist, but are not closed, are thus not orbits. If the eccentricity is greater than one, the trajectory is a hyperbola. If the eccentricity is equal to one and the angular momentum is zero, the trajectory is radial. If the eccentricity is one and there is angular momentum, the trajectory is a parabola. Given an inertial frame of reference and an arbitrary epoch six parameters are necessary to unambiguously define an arbitrary and unperturbed orbit; this is. These correspond to the three spatial dimensions which define position, plus the velocity in each of these dimensions; these can be described as orbital state vectors, but this is an inconvenient way to represent an orbit, why Keplerian elements are used instead. Sometimes the epoch is considered a "seventh" orbital parameter, rather than part of the reference frame. If the epoch is defined to be at the moment when one of the elements is zero, the number of unspecified elements is reduced to five. Keplerian elements can be obtained from orbital state vectors by manual transformations or with computer software.

Other orbital parameters can be computed from the Keplerian elements such as the period and periapsis. It is common to specify the period instead of the semi-major axis in Keplerian element sets, as each can be computed from the other provided the standard gravitational parameter, GM, is given for the central body. Instead of the mean anomaly at epoch, the mean anomaly M, mean longitude, true anomaly ν0, or the eccentric anomaly might be used. Usi

The fortifications of the town of Rhodes are shaped like a defensive crescent around the medieval town and consist in a modern fortification composed of a huge wall made of an embankment encased in stone, equipped with scarp, moat and glacis. The portion of fortifications facing the harbour is instead composed of a crenellated wall. On the moles towers and defensive forts are found, they were built by the Knights Hospitaller of Saint John by enhancing the existing Byzantine walls starting from 1309, the year in which they took possession of the island after a three-year struggle. Like most of the defensive walls they were built with a technique called rubble masonry which allows for a great mass capable of withstanding the gunshots with smooth external stone faces to avoid climbing; the defence of different portions of fortifications was assigned to different Langue of Knights. The North face was under the rule of the Grand Master moving West and South the posts were held by the Langue of France and Alvernia, the Langue of Spain, the Langue of Germany, the Langue of Italy.

Bastions and terrepleins still hold the name of the langue involved. Due to its geographical position as a gate to the Aegean Sea, Rhodes has always had a vantage position on the trade routes between the West and the East and has been an important stop thanks to its well protected harbours. During the Hellenistic period in the late 4th century BC, the town of Rhodes was enclosed in defensive walls which allowed to withstand the siege of Demetrius Poliorketes king of Macedonia, in 305 BC; the famous Colossus of Rhodes was built to thank gods for the victory against Demetrius. Philo of Byzantium author of the treatise "Paraskeuastica" on defensive works, stayed in Rhodes in the 3rd century BC and expressed his admiration for its walls; the earthquake of 226 BC damaged the fortifications, but they were soon rebuilt. The Byzantines built a fortress on the highest part of the town; when the Knight Hospitallers conquered the island, the town was still wealthy but in decline. Rhodes underwent an economical growth thanks to the richness that the knights brought in from the Holy Land and to the inheritance of the Templars' assets given to the Hospitallers after the Templar Order was suppressed in 1312 by decree of the king of France Philip IV.

The richness of the island attracted the Ottomans from the nearby coast. The knights started continuous works on the fortifications, both to include the new villages in the South of the historical Byzantine town and to update the fortification to the new military defensive techniques after the artillery started to be used as a siege means; the Knights of Saint John had had a long experience in building fortresses and fortifications during the three centuries of their stay in the Holy Land the reference model for the construction of the fortification were the Theodosian Walls of Constantinople which, during the centuries, had shown a great capacity to withstand sieges. The expansion of the walls was undertaken by Grand Master Antonio Fluvian de Riviere who allowed the town of Rhodes to reach the current area of about 42 hectares; the wall curtain was finished between 1457 and 1465. The Byzantine fortifications were demolished leaving just a portion of those of the old fort known at the time of Knights as Collachium.

In 1440 the Mameluke sultan of Egypt tried without success to conquer the town sieging it for 40 days. In 1480 Rhodes was besieged by the troops of Mehmed II but the powerful army of the conqueror of Constantinople manned with 100,000 troops and 170 ships was repelled by the courage of the Knights and the strong fortifications, notwithstanding the outnumbering assailants. In 1481 a destructive earthquake struck the island causing severe damages to the houses and the fortification and about 30,000 casualties. A new Ottoman siege could not be withstood, so the Knights made available their great financial resources and in a short time the most important palaces of the town and the fortifications were rebuilt. In the following years Grand Masters Pierre d'Aubusson, Emery d'Amboise, Fabrizio del Carretto and Philippe Villiers de l’Isle Adam ordered the fortifications to be rebuilt to withstand the cannons. For the purpose they called to Rhodes the best Italian military architects. Among them Matteo Gioeni, Basilio della Scuola, Gerolamo Bartolucci and Gabriele Tadino da Martinengo.

The latter two were present in Rhodes during the final siege in 1522. The Bastion of Italy in which the Ottomans had opened a breach in 1480 was rebuilt with a powerful chemin de ronde for the reverse fire of cannons on the nearby spans of wall; this bastion was named "Bastion Del Carretto" after the Grand Master. The gate of Saint John was closed and a pentagonal bastion with the same name was built on the western side of the walls to guard Gate d'Amboise. After The Ottoman conquered Rhodes in 1522 they did not demolish the walls but repaired them and kept them under maintenance during the four centuries of their rule; the fortifications of Rhodes were frozen at 1522 so that Rhodes is one of the few European walled towns that still shows the transition between the classical medieval fortification and the modern ones. The fortifications that still today make a belt around the medieval town, so that it is a separate neighbour from the new town, were restored during the Italian administration of the island and are, at present, being studied and maintained.

After their expulsion from Rhodes, the Hospitallers moved to the central Mediterranean island of Malta in 1530. They settled

Leanne M Williams is a Professor in Psychiatry and Behavioral Sciences at Stanford University. She is the founding director of the Stanford Center for Precision Mental Health and Wellness and of the Precision Psychiatry and Translational Neuroscience Laboratory in the Stanford Medical School She received a B. A. Clinical Psychology 1987 from the University of Queensland, a Class I honours B. A. in Psychology in 1990 from the University of New England, Australia She received a Ph. D. from the University of New England, Australia PhD in 1996 for research conducted on a British Council scholarship at Oxford University. In 1999 she was appointed Senior Lecturer at the University of Sydney, promoted to Associate Professor there in 2002, in 2008 to foundation Professor of Cognitive Neuropsychiatry at the Sydney Medical School and Director of the interdisciplinary Sydney Brain Dynamics Center. CV at Stanford She came to Stanford in 2013, her research focusses on the use of human neuroimaging and computational approaches to find methods for diagnosing and treating mental disorders.

She has developed a taxonomy for depression and related mood and anxiety disorders that quantifies large-scale human brain circuits for more precise diagnostic subtyping and for personalizing treatment choices Williams' most cited peer=reviewed articles are: Liddell BJ, Brown KJ, Kemp AH, Barton MJ, Das P, Peduto A, Gordon E, Williams LM. A direct brainstem–amygdala–cortical ‘alarm’system for subliminal signals of fear. Neuroimage. 2005 Jan 1. Cited 612 times according to Google Scholar. Lee KH, Williams LM, Breakspear M, Gordon E. Synchronous gamma activity: a review and contribution to an integrative neuroscience model of schizophrenia. Brain Research Reviews. 2003 Jan 1. Cited 492 times according to Google Scholar. Rubinov M, Knock SA, Stam CJ, Micheloyannis S, Harris AW, Williams LM, Breakspear M. Small‐world properties of nonlinear brain activity in schizophrenia. Human brain mapping. 2009 Feb. Cited 362 times according to Google Scholar. Williams LM, Phillips ML, Brammer MJ, Skerrett D, Lagopoulos J, Rennie C, Bahramali H, Olivieri G, David AS, Peduto A, Gordon E. Arousal dissociates amygdala and hippocampal fear responses: evidence from simultaneous fMRI and skin conductance recording.

Neuroimage. 2001 Nov 1. Cited 332 times according to Google Scholar. Williams LM, Das P, Harris AW, Liddell BB, Brammer MJ, Olivieri G, Skerrett D, Phillips ML, David AS, Peduto A, Gordon E. Dysregulation of arousal and amygdala-prefrontal systems in paranoid schizophrenia. American Journal of Psychiatry. 2004 Mar 1. Cited 322 times according to Google Schola. Williams LM, Kemp AH, Felmingham K, Barton M, Olivieri G, Peduto A, Gordon E, Bryant RA. Trauma modulates medial prefrontal responses to consciously attended fear. Neuroimage. 2006 Jan 15. Cited 338 times according to Google Scholar

Ernest Frederic Crosbie Trench CBE, TD was a British civil engineer. Ernest was born on 6 August 1869 to Frances Charlotte Talbot Crosbie. Anne of York, Duchess of Exeter, sister to Edward IV and Richard III was an ancestor of Ernest's mother, he was educated at Monkton Combe School and at Lausanne before studying for a Master of Arts degree from Trinity College, Dublin. He worked as a railway engineer, beginning his railway career as a pupil of E. B. Thornhill on the London and North Western Railway in 1893, after which he worked for the Midland Railway and the North London Railway from January 1903, before returning to the LNWR on 1 March 1906 as assistant engineer. Three years on 1 March 1909, he was promoted to chief assistant engineer, becoming chief engineer on 1 October the same year following the retirement of Thornhill the previous month. At the start of 1923 he was appointed as the chief engineer of the London and Scottish Railway, becoming the LMS consulting engineer from 1 February 1927, retiring on 1 April 1930.

He became involved in the Institution of Civil Engineers as an associate member in 1897, progressing to a full membership in 1904, he was first elected to the council in 1915 and would serve on it for the next seventeen years. He was elected vice president of the institution in 1924 and served as its president from 1927-1928. In 1920 he was appointed a Commander of the Order of the British Empire for "services rendered in connexion with 1914-18 war" and in 1931 received the Territorial Decoration for service as a volunteer Colonel in the Engineer and Railway Staff Corps, he fathered five sons and one daughter. He died in Marlborough, Wiltshire on 15 September 1960

Seasons of a Life was the last album by American vocalist Lena Horne. In early 1999, Lena Horne renewed her recording contract with Blue Note Records following the release of Being Myself; that same year, she recorded a full-length album, entitled Soul. Horne withdrew from the public eye in 2000; the material consists of outtakes and other rarities recorded during the 1990s, when Horne was recording for Blue Note Records. Pianist Herbie Hancock accompanies Horne on "Chelsea Bridge" and "Willow Weep for Me". "Black Is" – 5:20 "Maybe" – 2:42 "I've Got to Have You" – 4:15 "I'll Always Leave the Door a Little Open" – 3:45 "You're the One" – 2:54 "Something to Live For" – 4:33 "Chelsea Bridge" – 4:50 "Singin' in the Rain" – 4:14 "Willow Weep for Me" – 5:05 "Stormy Weather" – 3:47 Tracks 1, 7 & 9: Recorded for the original version of Being Myself, subsequently scrapped. Tracks 2, 5, & 6: Recorded in 1996 and used for Simon Rattle's Classic Ellington album. For this release, Jones appears to have used the pre-recorded versions without the large symphony, thus rendering these tracks small-group performances.

Tracks 3 & 4: Recorded September 19, 1994 live at the Supper Club for the album An Evening with Lena Horne.

Christopher John Chivers is an American journalist and author best known for his work with The New York Times and Esquire magazine. He is assigned to The New York Times Magazine and the newspaper's Investigations Desk as a long-form writer and investigative reporter. In the summer of 2007, he was named the newspaper's Moscow bureau chief. Along with several reporters and photographers based in Pakistan and Afghanistan, he contributed to a New York Times staff entry that received the Pulitzer Prize for International Reporting in 2009, he received the Pulitzer Prize for Feature Writing in 2017. His book, The Gun, a work of history published under the Simon & Schuster imprint, was released in October, 2010. Chivers is considered one of the most important war correspondents of his generation, noted for his expertise on weapons. Chivers attended the College of Sciences at Cornell University. There he played defensive line for Sprint Football for four years, was a member of Alpha Tau Omega fraternity.

After graduating in January 1988, Chivers served as an infantry officer in the U. S. Marine Corps, he graduated from the United States Army's Ranger School, served in the first Gulf War and in peacekeeping operations during the Los Angeles riots in 1992 before being honorably discharged as a captain in 1994. Chivers graduated from the Columbia University Graduate School of Journalism a year later. Chivers reported for the Providence Journal on the Providence city government from 1995 to 1999. From 1999 to 2001 Chivers covered crime and law enforcement in New York City for The New York Times, working out of a three-person bureau co-located inside New York Police Department Headquarters in Lower Manhattan, he was there on the morning of the September 11 attacks, discreetly reported from Ground Zero for the Times for the next twelve days, parlaying his Marine identity and volunteering in order to remain after most of the press was cleared to facilitate rescue and clean-up efforts. Chivers' first publication in Esquire magazine was a September, 2002 retelling of the early days at Ground Zero.

In 2001, Chivers became a foreign correspondent for The New York Times. He has reported from Afghanistan, Israel, Iraq, Uganda and Beslan, he served as Moscow correspondent from 2004 through 2007, was Moscow bureau chief in 2007 and 2008. In Uzbekistan, he covered the Andijan massacre in 2005. Chivers contributed to The Times' "At War" and "Lens" news blogs. In 2013 Chivers published an article in The New York Times about the ordeal of photojournalist Matt Schrier as hostage in the hands of Syrian rebels while his cellmate journalist Peter Theo Curtis still was held captive. Chivers disclosed that Curtis had helped Schrier escape, putting Curtis in jeopardy and delivering him to abuse by his kidnappers; the improvised weapons and munitions of Sunni Islamists were an important focus of his reporting on Libya in 2011 and on Syria in 2012. In 2015 Esquire magazine said Chivers was "the most important war correspondent of his time", saying he developed "a brand of journalism unique in the world for, among other things, its study of the weapons we use to kill one another".

After reporting on a firefight—whether he was in Iraq, South Ossetia, Libya, or Syria—he'd look for shell casings and ordnance fragments. If he was embedded with American soldiers or Marines, he'd ask them if he could look through what they had found for an hour or so—'finger fucking,' he'd call it—and ask his photographer to take pictures of ammunition stamps and serial numbers. Over time and in this way he would reveal a vast world of small-arms trade and secret trafficking that no other journalist had known existed before. Chivers is now assigned to The New York Times Magazine and the newspaper's Investigations Desk as a long-form writer and investigative reporter. In 2010 Chivers published his first book, The Gun on the history of automatic rifles; the scope included the biographies of Hiram Maxim, Richard Gatlin, Paul Mauser, John T. Thompson, their eponymous automatic weapons, their impact on warfare. Reviews were favorable. In August 2018 his second book The Fighters about Americans in conflict in Afghanistan and Iraq will be published.

An advance review in the Kirkus Reviews May 1, 2018, issue the reviewer notes:Given his background, Chivers did not set out to write a book emphasizing the foolishness of American actions in Afghanistan and Iraq. But, the story that emerged from his painstaking, courageous reporting, readers will be thankful for his work. In 1997 Chivers was granted a Pulitzer International Traveling Fellowship to underwrite a series of reports on the collapse of commercial fishing in the North Atlantic entitled "Empty Nets: Atlantic Banks in Peril" for The Providence Journal. In 1997, at age 32, Chivers received the Livingston Award, awarded to a journalist under 35 years of age in the category of Excellence in International Reporting, for the series; the award is sometimes known as the "Pulitzer Prize for the young". Two of Chivers' stories from Afghanistan were included in The New York Times' submission to the 2002 Pulitzer Prize for Public Service, awarded to the team behind A Nation Challenged, "a special section published after the September 11th terrorist attacks."

In 2010 A Nation Challeng