The term apsis refers to an extreme point in the orbit of an object. It denotes either the respective distance of the bodies; the word comes via Latin from Greek, there denoting a whole orbit, is cognate with apse. Except for the theoretical possibility of one common circular orbit for two bodies of equal mass at diametral positions, there are two apsides for any elliptic orbit, named with the prefixes peri- and ap-/apo-, added in reference to the body being orbited. All periodic orbits are, according to Newton's Laws of motion, ellipses: either the two individual ellipses of both bodies, with the center of mass of this two-body system at the one common focus of the ellipses, or the orbital ellipses, with one body taken as fixed at one focus, the other body orbiting this focus. All these ellipses share a straight line, the line of apsides, that contains their major axes, the foci, the vertices, thus the periapsis and the apoapsis; the major axis of the orbital ellipse is the distance of the apsides, when taken as points on the orbit, or their sum, when taken as distances.
The major axes of the individual ellipses around the barycenter the contributions to the major axis of the orbital ellipses are inverse proportional to the masses of the bodies, i.e. a bigger mass implies a smaller axis/contribution. Only when one mass is sufficiently larger than the other, the individual ellipse of the smaller body around the barycenter comprises the individual ellipse of the larger body as shown in the second figure. For remarkable asymmetry, the barycenter of the two bodies may lie well within the bigger body, e.g. the Earth–Moon barycenter is about 75% of the way from Earth's center to its surface. If the smaller mass is negligible compared to the larger the orbital parameters are independent of the smaller mass. For general orbits, the terms periapsis and apoapsis are used. Pericenter and apocenter are equivalent alternatives, referring explicitly to the respective points on the orbits, whereas periapsis and apoapsis may refer to the smallest and largest distances of the orbiter and its host.
For a body orbiting the Sun, the point of least distance is the perihelion, the point of greatest distance is the aphelion. The terms become apastron when discussing orbits around other stars. For any satellite of Earth, including the Moon, the point of least distance is the perigee and greatest distance the apogee, from Ancient Greek Γῆ, "land" or "earth". For objects in lunar orbit, the point of least distance is sometimes called the pericynthion and the greatest distance the apocynthion. Perilune and apolune are used. In orbital mechanics, the apsides technically refer to the distance measured between the barycenters of the central body and orbiting body. However, in the case of a spacecraft, the terms are used to refer to the orbital altitude of the spacecraft above the surface of the central body; these formulae characterize the pericenter and apocenter of an orbit: Pericenter Maximum speed, v per = μ a, at minimum distance, r per = a. Apocenter Minimum speed, v ap = μ a, at maximum distance, r ap = a.
While, in accordance with Kepler's laws of planetary motion and the conservation of energy, these two quantities are constant for a given orbit: Specific relative angular momentum h = μ a Specific orbital energy ε = − μ 2 a where: a is the semi-major axis: a = r per + r ap 2 μ is the standard gravitational parameter e is the eccentricity, defined as e = r ap − r per r ap + r per = 1 − 2 r ap r per + 1 Note t
University of Pisa
The University of Pisa is an Italian public research university located in Pisa, Italy. It was founded in 1343 by an edict of Pope Clement VI, it is the 10th oldest in Italy. The university is ranked within the top 10 nationally and the top 400 in the world according to the ARWU and the QS, it houses the Orto botanico di Pisa, Europe's oldest academic botanical garden, founded in 1544. The University of Pisa is part of the Pisa University System, which includes the Scuola Normale Superiore and the Sant'Anna School of Advanced Studies; the university has about 50,000 students. In the fields of philology and cultural studies, the University of Pisa is a leading member of ICoN, an inter-university consortium of 21 Italian universities supported by the Ministry of Education and Research, as well as a member of the European University Association, the Partnership of a European Group of Aeronautics and Space Universities network and the Cineca consortium. It's the only university in Italy which has become a member of the Universities Research Association.
Among its notable graduates there are several national and foreign political leaders including two Italian presidents, five Popes, five Italian prime ministers and three Nobel Laureates as students, faculty or staff affiliates. Pisa has an intense athletic rivalry with the University of Pavia, which traditionally culminates in the Pisa-Pavia Regatta, the oldest competition of this kind in Italy, second in Europe only to the Oxford Cambridge boat race. In 2013, the University of Pisa finished with La Sapienza University of Rome in first place among the Italian universities, according to the Academic Ranking of World Universities; the University of Pisa was established on 3 September 1343. However, a number of scholars claim its origin dates back to the 11th century; the first reliable data on the presence of secular and monastic schools of law in Pisa is from the 11th century and the second half of the 12th century, a time when Pisa had achieved a remarkable economic development. The following century formed the first documents to prove the presence of doctors of medicine and surgery.
The earliest evidence of a Pisan Studium dates to 1338, when jurist Ranieri Arsendi transferred to Pisa from Bologna. He, along with Bartolo da Sassoferrato, a lecturer in civil law, were paid by the municipality to teach public lessons; the papal bull In supremae dignitatis, granted by Pope Clement VI on 3 September 1343, recognized the Studium of Pisa as a Studium Generale. Pisa was one of the first European universities to boast this papal attestation, which guaranteed the universal and legal value of its educational qualifications; the first taught subjects were civil law, canon law and medicine. In 1355, Francesco da Buti, the well-known commentator of Dante's Divine Comedy, began teaching at the Studium. Pisa and its Studium underwent a period of crisis around the turn of the 15th century: the Florentines' conquest of the town led to the university's closure in 1403. In 1473, thanks to Lorenzo de Medici, the Pisan Studium resumed its systematic development, the construction of a building for holding lessons was provided for in 1486.
The building — known as Palazzo della Sapienza — was located in the 14th-century Piazza del Grano. The image of a cherub was placed above the gate Dell'Abbondanza, leading to the piazza, today is still the symbol of the university. Following the rebellion and the war against Florence in 1494, the Pisan Studium suffered a period of decline and was transferred to Pistoia and Florence; the ceremonial reopening of the university on 1 November 1543, under the rule of Duke Cosimo I de Medici, was considered as a second inauguration. The quality of the university was furthered by the statute of 1545 and the Pisan Athenaeum became one of the most significant in Europe for teaching and research; the chair of Semplici was held by founder of the world's first botanical gardens. He was succeeded by Andrea Cesalpino, who pioneered the first scientific methodology for the classification of plants, is considered a forerunner in the discovery of blood circulation. Gabriele Falloppio and Marcello Malpighi lectured in medicine.
Galileo Galilei, born and studied in Pisa, became professor of mathematics at the Pisan Studium in 1589. The university's role as a state institution became more accentuated during the Medici Grand Duchy period. A protectionist policy ensured a consistent nucleus of teachers. Laws issued by Cosimo I, Ferdinando I and Ferdinando II obliged those who intended to obtain a degree to attend the Studium of Pisa. Many notable figures lectured at Pisa in the fields of law and medicine; the university's development continued under the Lorenas. They completed the construction of the astronomic observatory, enriched the university library with important publications, they helped develop the botanical gardens, natural science museum, established new chairs including experimental Physics and Chemistry. The annexation of Tuscany to the Napoleonic Empire resulted in the transformation of the Studium into an Imperial Academy; the Athenaeum became a branch of the University of Paris, the courses and study programs were structured following the French public education model.
Five new faculties were established:, along with
787 Moskva is a minor planet orbiting the Sun. The object 1914 UQ discovered 20 April 1914 by Grigory Neujmin was named 787 Moskva for the capital of Russia Moscow; the object 1934 FD discovered on 19 March 1934 by C. Jackson was given the sequence number 1317. In 1938, G. N. Neujmin found that asteroid 1317 and 787 Moskva were the same object; the sequence number 1317 was reused for the object 1935 RC discovered on 1 September 1935 by Karl Reinmuth. Photometric observations at the Palmer Divide Observatory in Colorado Springs, Colorado, in 1999 were used to build a light curve for this object; the asteroid displayed a rotation period of 6.056 ± 0.001 hours and a brightness variation of 0.62 ± 0.01 in magnitude. Lightcurve plot of 787 Moskva, Palmer Divide Observatory, B. D. Warner Asteroid Lightcurve Database, query form Dictionary of Minor Planet Names, Google books Asteroids and comets rotation curves, CdR – Observatoire de Genève, Raoul Behrend Discovery Circumstances: Numbered Minor Planets - – Minor Planet Center 787 Moskva at the JPL Small-Body Database Close approach · Discovery · Ephemeris · Orbit diagram · Orbital elements · Physical parameters
Orders of magnitude (length)
The following are examples of orders of magnitude for different lengths. To help compare different orders of magnitude, the following list describes various lengths between 1.6 × 10 − 35 metres and 10 10 10 122 metres. To help compare different orders of magnitude, this section lists lengths shorter than 10−23 m. 1.6 × 10−11 yoctometres – the Planck length. 1 ym – 1 yoctometre, the smallest named subdivision of the metre in the SI base unit of length, one septillionth of a metre 1 ym – length of a neutrino. 2 ym – the effective cross-section radius of 1 MeV neutrinos as measured by Clyde Cowan and Frederick Reines To help compare different orders of magnitude, this section lists lengths between 10−23 metres and 10−22 metres. To help compare different orders of magnitude, this section lists lengths between 10−22 m and 10−21 m. 100 ym – length of a top quark, one of the smallest known quarks To help compare different orders of magnitude, this section lists lengths between 10−21 m and 10−20 m. 2 zm – length of a preon, hypothetical particles proposed as subcomponents of quarks and leptons.
2 zm – radius of effective cross section for a 20 GeV neutrino scattering off a nucleon 7 zm – radius of effective cross section for a 250 GeV neutrino scattering off a nucleon To help compare different orders of magnitude, this section lists lengths between 10−20 m and 10−19 m. 15 zm – length of a high energy neutrino 30 zm – length of a bottom quark To help compare different orders of magnitude, this section lists lengths between 10−19 m and 10−18 m. 177 zm – de Broglie wavelength of protons at the Large Hadron Collider To help compare different orders of magnitude, this section lists lengths between 10−18 m and 10−17 m. 1 am – sensitivity of the LIGO detector for gravitational waves 1 am – upper limit for the size of quarks and electrons 1 am – upper bound of the typical size range for "fundamental strings" 1 am – length of an electron 1 am – length of an up quark 1 am – length of a down quark To help compare different orders of magnitude, this section lists lengths between 10−17 m and 10−16 m. 10 am – range of the weak force To help compare different orders of magnitude, this section lists lengths between 10−16 m and 10−15 m. 100 am – all lengths shorter than this distance are not confirmed in terms of size 850 am – approximate proton radius The femtometre is a unit of length in the metric system, equal to 10−15 metres.
In particle physics, this unit is more called a fermi with abbreviation "fm". To help compare different orders of magnitude, this section lists lengths between 10−15 metres and 10−14 metres. 1 fm – length of a neutron 1.5 fm – diameter of the scattering cross section of an 11 MeV proton with a target proton 1.75 fm – the effective charge diameter of a proton 2.81794 fm – classical electron radius 7 fm – the radius of the effective scattering cross section for a gold nucleus scattering a 6 MeV alpha particle over 140 degrees To help compare different orders of magnitude, this section lists lengths between 10−14 m and 10−13 m. 1.75 to 15 fm – Diameter range of the atomic nucleus To help compare different orders of magnitude, this section lists lengths between 10−13 m and 10−12 m. 570 fm – typical distance from the atomic nucleus of the two innermost electrons in the uranium atom, the heaviest naturally-occurring atom To help compare different orders of magnitude this section lists lengths between 10−12 and 10−11 m. 1 pm – distance between atomic nuclei in a white dwarf 2.4 pm – The Compton wavelength of the electron 5 pm – shorter X-ray wavelengths To help compare different orders of magnitude this section lists lengths between 10−11 and 10−10 m. 25 pm – approximate radius of a helium atom, the smallest neutral atom 50 pm – radius of a hydrogen atom 50 pm – bohr radius: approximate radius of a hydrogen atom ~50 pm – best resolution of a high-resolution transmission electron microscope 60 pm – radius of a carbon atom 93 pm – length of a diatomic carbon molecule To help compare different orders of magnitude this section lists lengths between 10−10 and 10−9 m. 100 pm – 1 ångström 100 pm – covalent radius of sulfur atom 120 pm – van der Waals radius of a neutral hydrogen atom 120 pm – radius of a gold atom 126 pm – covalent radius of ruthenium atom 135 pm – covalent radius of technetium atom 150 pm – Length of a typical covalent bond 153 pm – covalent radius of silver atom 155 pm – covalent radius of zirconium atom 175 pm – covalent radius of thulium atom 200 pm – highest resolution of a typical electron microscope 225 pm – covalent radius of caesium atom 280 pm – Average size of the water molecule 298 pm – radius of a caesium atom, calculated to be the largest atomic radius 340 pm – thickness of single layer graphene 356.68 pm – width of diamond unit cell 403 pm – width of lithium fluoride unit cell 500 pm – Width of protein α helix 543 pm – silicon lattice spacing 560 pm – width of sodium chloride unit cell 700 pm – width of glucose molecule 780 pm – mean width of quartz unit cell 820 pm – mean width of ice unit cell 900 pm – mean width of coesite unit cell To help compare different orders
The National Aeronautics and Space Administration is an independent agency of the United States Federal Government responsible for the civilian space program, as well as aeronautics and aerospace research. NASA was established in 1958; the new agency was to have a distinctly civilian orientation, encouraging peaceful applications in space science. Since its establishment, most US space exploration efforts have been led by NASA, including the Apollo Moon landing missions, the Skylab space station, the Space Shuttle. NASA is supporting the International Space Station and is overseeing the development of the Orion Multi-Purpose Crew Vehicle, the Space Launch System and Commercial Crew vehicles; the agency is responsible for the Launch Services Program which provides oversight of launch operations and countdown management for unmanned NASA launches. NASA science is focused on better understanding Earth through the Earth Observing System. From 1946, the National Advisory Committee for Aeronautics had been experimenting with rocket planes such as the supersonic Bell X-1.
In the early 1950s, there was challenge to launch an artificial satellite for the International Geophysical Year. An effort for this was the American Project Vanguard. After the Soviet launch of the world's first artificial satellite on October 4, 1957, the attention of the United States turned toward its own fledgling space efforts; the US Congress, alarmed by the perceived threat to national security and technological leadership, urged immediate and swift action. On January 12, 1958, NACA organized a "Special Committee on Space Technology", headed by Guyford Stever. On January 14, 1958, NACA Director Hugh Dryden published "A National Research Program for Space Technology" stating: It is of great urgency and importance to our country both from consideration of our prestige as a nation as well as military necessity that this challenge be met by an energetic program of research and development for the conquest of space... It is accordingly proposed that the scientific research be the responsibility of a national civilian agency...
NACA is capable, by rapid extension and expansion of its effort, of providing leadership in space technology. While this new federal agency would conduct all non-military space activity, the Advanced Research Projects Agency was created in February 1958 to develop space technology for military application. On July 29, 1958, Eisenhower signed the National Aeronautics and Space Act, establishing NASA; when it began operations on October 1, 1958, NASA absorbed the 43-year-old NACA intact. A NASA seal was approved by President Eisenhower in 1959. Elements of the Army Ballistic Missile Agency and the United States Naval Research Laboratory were incorporated into NASA. A significant contributor to NASA's entry into the Space Race with the Soviet Union was the technology from the German rocket program led by Wernher von Braun, now working for the Army Ballistic Missile Agency, which in turn incorporated the technology of American scientist Robert Goddard's earlier works. Earlier research efforts within the US Air Force and many of ARPA's early space programs were transferred to NASA.
In December 1958, NASA gained control of the Jet Propulsion Laboratory, a contractor facility operated by the California Institute of Technology. The agency's leader, NASA's administrator, is nominated by the President of the United States subject to approval of the US Senate, reports to him or her and serves as senior space science advisor. Though space exploration is ostensibly non-partisan, the appointee is associated with the President's political party, a new administrator is chosen when the Presidency changes parties; the only exceptions to this have been: Democrat Thomas O. Paine, acting administrator under Democrat Lyndon B. Johnson, stayed on while Republican Richard Nixon tried but failed to get one of his own choices to accept the job. Paine was confirmed by the Senate in March 1969 and served through September 1970. Republican James C. Fletcher, appointed by Nixon and confirmed in April 1971, stayed through May 1977 into the term of Democrat Jimmy Carter. Daniel Goldin was appointed by Republican George H. W. Bush and stayed through the entire administration of Democrat Bill Clinton.
Robert M. Lightfoot, Jr. associate administrator under Democrat Barack Obama, was kept on as acting administrator by Republican Donald Trump until Trump's own choice Jim Bridenstine, was confirmed in April 2018. Though the agency is independent, the survival or discontinuation of projects can depend directly on the will of the President; the first administrator was Dr. T. Keith Glennan appointed by Republican President Dwight D. Eisenhower. During his term he brought together the disparate projects in American space development research; the second administrator, James E. Webb, appointed by President John F. Kennedy, was a Democrat who first publicly served under President Harry S. Truman. In order to implement the Apollo program to achieve Kennedy's Moon la
The Taunus is a mountain range in Hesse, Germany located north of Frankfurt. The tallest peak in the range is Großer Feldberg at 878 m; the Taunus range spans the districts of Hochtaunuskreis, Main-Taunus, Rheingau-Taunus, Limburg-Weilburg, Rhein-Lahn. The range is known for its geothermal springs and mineral waters that attracted members of the European aristocracy to its spa towns; the car line. It is a low range, with smooth, rounded mountains covered with forest; the Taunus is bounded by the valleys of the Rhine and Lahn rivers and it is part of the Rhenish Slate Mountains. On the opposite side of the Rhine, The Taunus range is continued by the Hunsrück. For geographical and geological purposes the Taunus is divided in three parts: Anterior Taunus in the south, next to the cities of Frankfurt am Main and Wiesbaden; this section is made up of old sedimentary rocks with phyllite and muscovite. The rocks are given a greenish hue by the presence of epidote and chlorites. High Taunus; the central region of the range where the highest peaks are found.
Its geological composition includes slates and sandstones. Farther Taunus at its northern end is the biggest part by area; the geological materials that compose it include greywacke and siltstones. The Taunus range originated during the Devonian period; the geological composition of the mountains was formed in a region covered by an ancient sea, a few hundred kilometers wide and are made up of phyllite, gneiss and sandstone. Großer Feldberg, Hochtaunuskreis. Being the highest point in the range, it provides the scenario for the Feldbergrennen hillclimbing and rallying contests, it should not be confused with the Feldberg in Hochtaunuskreis. It has an observatory on the summit. Altkönig, Hochtaunuskreis, it has the remains of a late Iron Age hill fort near the summit. Weilsberg, Hochtaunuskreis Glaskopf, Hochtaunuskreis Pferdskopf, Hochtaunuskreis Kolbenberg, Hochtaunuskreis Klingenkopf, Hochtaunuskreis Sängelberg, Hochtaunuskreis Pferdskopf, Hochtaunuskreis Weißeberg, Hochtaunuskreis Fauleberg, Hochtaunuskreis Großer Eichwald, Hochtaunuskreis Roßkopf, Hochtaunuskreis Kalte Herberge, Rheingau-Taunus-Kreis Hohe Wurzel, Rheingau-Taunus-Kreis Hohe Kanzel, Rheingau-Taunus-Kreis Hallgarter Zange, Rheingau-Taunus-Kreis Erbacher Kopf, Rheingau-Taunus-Kreis Steinkopf, Hochtaunuskreis Kuhbett, Kreis Limburg-Weilburg at Weilrod-Hasselbach Steinkopf, Wetteraukreis The Roman Limes was built across the Taunus.
The Saalburg, a restored Roman castellum, now houses a museum. After the fall of the Limes, the Alamanni settled in the range and for this reason there are some Alemannic cemeteries in the southern foothills of the Taunus; this area of the Taunus became part of the Frankish confederation of Germanic tribes after the Battle of Tolbiac around 500 AD. In past centuries the Taunus became famous among aristocrats for its therapeutic hot springs. Certain towns in the area, such as Bad Homburg vor der Höhe with its Kurpark, have geothermal spas that were renowned. Other spa towns in the Taunus range are Bad Schwalbach mentioned in documents dating back to the 16th century, Bad Ems, one of the most reputed therapeutic spas in Germany since the 17th century, as well as Bad Weilbach, where a spring reached wide fame for some time. By the 19th century the most famous spa towns in the area were Wiesbaden, Bad Homburg vor der Höhe, Bad Nauheim, Bad Soden am Taunus. Media related to Taunus at Wikimedia CommonsThere is literature about Taunus in the Hessian Bibliography Umweltatlas Hessen: → Natur und Landschaft → Die Naturräume Hessens bzw.
Naturräumliche Gliederung – Naturraum-Haupteinheit 30, auf atlas.umwelt.hessen.de Fremdenverkehrsinformationen, Taunus Tourist Service at taunus.info Webcams at taunus.info Taunus Nature Park at naturpark-taunus.de Feldberg Roman Fort circular path, at feldbergkastell.de Summits in the Taunus by isolation and prominence, at thehighrisepages.de Wehrheim, das Tor zur Bronzezeit im Usinger Land, Infos zu archäologischen Funden in Wehrheim, auf geschichtsverein-usingen.de Das Vortaunusmuseum at vortaunusmuseum.de map and aerial photo of the Taunus with boundaries and all important summits, at geographie.giersbeck.de#Taunus Placemarks
C-type asteroids are the most common variety, forming around 75% of known asteroids. They are distinguished by a low albedo because their composition includes a large amount of carbon, in addition to rocks and minerals, they occur most at the outer edge of the asteroid belt, 3.5 astronomical units from the Sun, where 80% of the asteroids are of this type, whereas only 40% of asteroids at 2 AU from the Sun are C-type. The proportion of C-types may be greater than this, because C-types are much darker than most other asteroid types except for D-types and others that are at the extreme outer edge of the asteroid belt. Asteroids of this class have spectra similar to those of carbonaceous chondrite meteorites; the latter are close in chemical composition to the Sun and the primitive solar nebula, except for the absence of hydrogen and other volatiles. Hydrated minerals are present. C-type asteroids are dark, with albedos in the 0.03 to 0.10 range. Whereas a number of S-type asteroids can be viewed with binoculars at opposition the largest C-type asteroids require a small telescope.
The brightest C-type asteroid is 324 Bamberga, but that object's high eccentricity means it reaches its maximum magnitude. Their spectra contain moderately strong ultraviolet absorption at wavelengths below about 0.4 μm to 0.5 μm, while at longer wavelengths they are featureless but reddish. The so-called "water" absorption feature of around 3 μm, which can be an indication of water content in minerals, is present; the largest unequivocally C-type asteroid is 10 Hygiea, although the SMASS classification places the largest asteroid, 1 Ceres, here as well, because that scheme lacks a G-type. In the Tholen classification, the C-type is grouped along with three less numerous types into a wider C-group of carbonaceous asteroids which contains: B-type C-type F-type G-type In the SMASS classification, the wider C-group contains the types: B-type corresponding to the Tholen B and F-types a core C-type for asteroids having the most "typical" spectra in the group Cg and Cgh types corresponding to the Tholen G-type Ch type with an absorption feature around 0.7μm Cb type corresponding to transition objects between the SMASS C and B types Asteroid spectral types