|
Clélie
In mathematics, a Clélie or Clelia curve is a curve on a sphere with the property: * If the surface of a sphere is described as usual by the longitude (angle \varphi) and the colatitude In a spherical coordinate system, a colatitude is the complementary angle of a given latitude, i.e. the difference between a right angle and the latitude. Here Southern latitudes are defined to be negative, and as a result the colatitude is a non- ... (angle \theta) then : \varphi=c\;\theta, \quad c>0. The curve was named by Luigi Guido Grandi after Clelia Borromeo. Viviani's curve and spherical spirals are special cases of Clelia curves. In practice Clelia curves occur as polar orbits of satellites with circular orbits, whose traces on the earth include the poles. If the orbit is a geosynchronous one, then c=1 and the trace is a Viviani's curve. Parametric representation If the sphere is parametrized by : \begin x &= r \cdot \cos \theta \cdot \cos \varphi \\ y &= r \cdot \cos ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Celia Grillo Borromeo
Clelia Grillo Borromeo Arese or Celia Grillo Borromeo (1684 – 23 August 1777) was an Italian (Genovese) natural philosopher, mathematician and scientist. Life and education Borromeo was born in Genoa, the daughter of duke Marcantonio of Mondragone and Maria Antonia, the marquise Imperial. Borromeo was educated in several languages, mathematics, natural science and mechanics. She spoke eight languages and was interested in geometry, natural science and mathematics. She was educated first by her mother and then in a convent, but it is unknown where she received education in the subjects she became known for. In 1707, she married count Giovanni Borromeo Arese Benedict (1679–1744), and became the mother of eight children. Borromeo died in Milan. Contributions She was famous for her ability to solve every mathematical problem presented to her. Borromeo was described as an independent person, which was regarded as eccentric because it was not considered natural for her gender. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Longitude
Longitude (, ) is a geographic coordinate that specifies the east–west position of a point on the surface of the Earth, or another celestial body. It is an angular measurement, usually expressed in degrees and denoted by the Greek letter lambda (λ). Meridians are semicircular lines running from pole to pole that connect points with the same longitude. The prime meridian defines 0° longitude; by convention the International Reference Meridian for the Earth passes near the Royal Observatory in Greenwich, England on the island of Great Britain. Positive longitudes are east of the prime meridian, and negative ones are west. Because of the Earth's rotation, there is a close connection between longitude and time measurement. Scientifically precise local time varies with longitude: a difference of 15° longitude corresponds to a one-hour difference in local time, due to the differing position in relation to the Sun. Comparing local time to an absolute measure of time allows ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Colatitude
In a spherical coordinate system, a colatitude is the complementary angle of a given latitude, i.e. the difference between a right angle and the latitude. Here Southern latitudes are defined to be negative, and as a result the colatitude is a non-negative quantity, ranging from zero at the North pole to 180° at the South pole. The colatitude corresponds to the conventional 3D polar angle in spherical coordinates, as opposed to the latitude as used in cartography. Examples Latitude and colatitude sum up to 90°. Astronomical use The colatitude is most useful in astronomy because it refers to the zenith distance of the celestial poles. For example, at latitude 42°N, Polaris (approximately on the North celestial pole) has an altitude of 42°, so the distance from the zenith (overhead point) to Polaris is . Adding the declination of a star to the observer's colatitude gives the maximum latitude of that star (its angle from the horizon at culmination or upper transit). For ex ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Luigi Guido Grandi
Guido Grandi Dom Guido Grandi, O.S.B. Cam. (1 October 1671 – 4 July 1742) was an Italian monk, priest, philosopher, theologian, mathematician, and engineer. Life Grandi was born on 1 October 1671 in Cremona, Italy and christened Luigi Francesco Lodovico. When he was of age, he was educated at the Jesuit college there. After he completed his studies there in 1687, he entered the novitiate of the Camaldolese monks at Ferrara and took the name of Guido. In 1693 he was sent to the Monastery of St. Gregory the Great, the Camaldolese house in Rome, to complete his studies in philosophy and theology in preparation for Holy Orders. A year later, Grandi was assigned as professor of both fields at the Camaldolese Monastery of St. Mary of the Angels in Florence. It appears that it was during this period of his life that he took an interest in mathematics. He did his research privately, however, as he was appointed professor of philosophy at St. Gregory Monastery in 1700, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Viviani's Curve
In mathematics, Viviani's curve, also known as Viviani's window, is a figure eight shaped space curve named after the Italian mathematician Vincenzo Viviani. It is the intersection of a sphere with a cylinder that is tangent to the sphere and passes through two poles (a diameter) of the sphere (see diagram). Before Viviani this curve was studied by Simon de La Loubère and Gilles de Roberval. The orthographic projection of Viviani's curve onto a plane perpendicular to the line through the crossing point and the sphere center is the lemniscate of Gerono, while the stereographic projection is a hyperbola or the lemniscate of Bernoulli, depending on which point on the same line is used to project. . In 1692 Viviani solved the following task: Cut out of a half sphere (radius r) two windows, such that the remaining surface (of the half sphere) can be ''squared'', i.e. a square with the same area can be constructed using only compasses and ruler. His solution has an area of 4r^2 (se ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spherical Spiral
In mathematics, a spiral is a curve which emanates from a point, moving farther away as it revolves around the point. Helices Two major definitions of "spiral" in the American Heritage Dictionary are:Spiral ''American Heritage Dictionary of the English Language'', Houghton Mifflin Company, Fourth Edition, 2009. # a curve on a plane that winds around a fixed center point at a continuously increasing or decreasing distance from the point. # a three-dimensional curve that turns around an axis at a constant or continuously varying distance while moving parallel to the axis; a . The first definition describes a |
Polar Orbit
A polar orbit is one in which a satellite passes above or nearly above both poles of the body being orbited (usually a planet such as the Earth, but possibly another body such as the Moon or Sun) on each revolution. It has an inclination of about 60 - 90 degrees to the body's equator. Launching satellites into polar orbit requires a larger launch vehicle to launch a given payload to a given altitude than for a near-equatorial orbit at the same altitude, because it cannot take advantage of the Earth's rotational velocity. Depending on the location of the launch site and the inclination of the polar orbit, the launch vehicle may lose up to 460 m/s of Delta-v, approximately 5% of the Delta-v required to attain Low Earth orbit. Usage Polar orbits are used for Earth-mapping, reconnaissance satellites, as well as for some weather satellites.Science Focus 2nd Edition 2, pg. 297 The Iridium satellite constellation uses a polar orbit to provide telecommunications services. Near-polar orb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Satellite
A satellite or artificial satellite is an object intentionally placed into orbit in outer space. Except for passive satellites, most satellites have an electricity generation system for equipment on board, such as solar panels or radioisotope thermoelectric generators (RTGs). Most satellites also have a method of communication to ground stations, called Transponder (satellite communications), transponders. Many satellites use a Satellite bus, standardized bus to save cost and work, the most popular of which is small CubeSats. Similar satellites can work together as a group, forming Satellite constellation, constellations. Because of the high launch cost to space, satellites are designed to be as lightweight and robust as possible. Most communication satellites are radio Broadcast relay station, relay stations in orbit and carry dozens of transponders, each with a bandwidth of tens of megahertz. Satellites are placed from the surface to orbit by launch vehicles, high enough to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geosynchronous Orbit
A geosynchronous orbit (sometimes abbreviated GSO) is an Earth-centered orbit with an orbital period that matches Earth's rotation on its axis, 23 hours, 56 minutes, and 4 seconds (one sidereal day). The synchronization of rotation and orbital period means that, for an observer on Earth's surface, an object in geosynchronous orbit returns to exactly the same position in the sky after a period of one sidereal day. Over the course of a day, the object's position in the sky may remain still or trace out a path, typically in a figure-8 form, whose precise characteristics depend on the orbit's inclination and eccentricity. A circular geosynchronous orbit has a constant altitude of . A special case of geosynchronous orbit is the geostationary orbit, which is a circular geosynchronous orbit in Earth's equatorial plane with both inclination and eccentricity equal to 0. A satellite in a geostationary orbit remains in the same position in the sky to observers on the surface. Communicat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
