1.
Indiana University Bloomington
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Indiana University Bloomington is a public research university located in Bloomington, Indiana, United States. With over 48,000 students, IU Bloomington is the institution of the Indiana University system. As of Fall 2015,48,514 students attend Indiana University, while 55. 2% of the student body was from Indiana, students from 49 of the 50 states, Washington D. C. and 165 foreign nations were also enrolled. The university is home to a student life program, with more than 750 student organizations on campus. Indiana athletic teams compete in Division I of the NCAA and are known as the Indiana Hoosiers, the university is a member of the Big Ten Conference. Among IU Bloomington’s many graduate-level programs are the Kelley School of Business, School of Education, School of Public and Environmental Affairs, indiana’s law school has a program with a first-year team-based approach, a diversion from the typical legal education. In terms of academics and other criteria, IU Bloomington ranks in top 100 national universities in the United States and the top 50 public universities in the country. The schools sports teams are notorious competitors in the NCAA Division I Big Ten Conference, there are more than 650 student organizations on campus, and more than 5,000 students go Greek in the school’s large community of fraternities and sororities. Indianas state government in Corydon established Indiana University on January 20,1820, construction began in 1822 at what is now called Seminary Square Park near the intersection of Second Street and College Avenue. The first professor was Baynard Rush Hall, a Presbyterian minister who taught all of the classes in 1825–27, in the first year, he taught twelve students and was paid $250. Hall was a classicist who focused on Greek and Latin and believed that the study of classical philosophy, the first class graduated in 1830. From 1820 to 1889 a legal-political battle was fought between IU and Vincennes University as to which was the state university. In 1829, Andrew Wylie became the first president, serving until his death in 1851, the schools name was changed to Indiana College in 1829, and to Indiana University in 1839. Wylie and David Maxwell, president of the board of trustees, were devout Presbyterians and they spoke of the nonsectarian status of the school but generally hired fellow Presbyterians. Presidents and professors were expected to set an example for their charges. After six ministers in a row, the first non-clergyman to become president was the young biology professor David Starr Jordan, Jordan followed Baptist theologian Lemuel Moss, who resigned after a scandal broke regarding his involvement with a female professor. Jordan improved the finances and public image, doubled its enrollment. Jordan became president of Stanford University in June 1891, growth of the college was slow
2.
Herman Wells
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Herman B Wells, a native of Boone County, Indiana, was the eleventh president of Indiana University and its first university chancellor. He remained steadfast in his support of IUs faculty and students, especially in the areas of academic freedom and civil rights. Wells served in numerous other appointed positions, economic analyst for the U. S. State Departments Office of Foreign Economic Cooperation in Washington, D. C. cultural affairs adviser to the U. S. Military Government in West Germany, U. S. delegate to the Twelfth Session of the United Nations General Assembly, a recipient of numerous honors and awards, including twenty-six honorary degrees, Wells received many tributes to his long career. IU student scholarships and student recognition awards, as well as memorials on the IU Bloomington campus, Wells was also the subject of a PBS documentary film. His autobiography, Being Lucky, Reminiscences and Reflections, was published in 1980, Herman B Wells was born on June 7,1902, in Jamestown, Boone County, Indiana. He was the child of Joseph Granville Wells, a bank cashier and a former teacher and elementary school principal, and Anna Bernice Wells. Herman was not given a name, only the letter B not followed by a period. Wellss father committed suicide in 1948, his mother died in 1973, Wells grew up in Jamestown, attended a local Methodist church, and played alto horn in the Jamestown Boys Band. In 1917 the family moved to Lebanon, Indiana, the seat of government for Boone County, after school and on Saturdays, Herman helped out at a local bank where his father worked. Wells graduated from Lebanon High School in 1920 and was voted Funniest and Best All-Around Boy his senior year, Wells served as treasurer for the high schools yearbook and was involved in the schools newspaper, theater productions, and various fundraisers. After graduation Wells worked at a bank in nearby Whitestown, Indiana, although Wellss parents were supportive of his desire to continue his education, they had limited financial resources to pay for his college tuition and other expenses. Wells initially enrolled at the University of Illinois at Urbana–Champaign in 1920, Wells also pointed out that the connections he developed at IU would be useful to his future career. Wells was active in life as an IU undergraduate, he pledged Sigma Nu fraternity, lived in its chapter house at 322 East Kirkwood. Wells served as the fraternity chapters treasurer and was elected as his fraternity chapters president in his senior year and he was also treasurer of IUs Union Board, a student organization established in 1909. Wells earned a Bachelor of Science degree in commerce in 1924, Wells earned Master of Arts degree in economics from IU in 1927. His masters thesis, Service Charges for Small or So-Called Country Banks, was published in The Hoosier Banker in 1927, Wells began doctoral studies in economics at the University of Wisconsin–Madison, but his schooling ended in 1928, when he took a job with the Indiana Bankers Association. In 1928 Wells left his studies at Wisconsin to take a job as a field secretary for the Indiana Bankers Association
3.
Indiana University
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Indiana University is a multi-campus public university system in the state of Indiana, United States. The core campuses of Indiana University are located in Bloomington and Indianapolis, Indiana University Bloomington is the flagship campus of Indiana University. Indiana University – Purdue University Indianapolis is the urban campus of Indiana University. The campus is operated in cooperation with Purdue University, but is administered by Indiana University, in addition to its two core campuses, Indiana University comprises seven smaller campuses and two extensions spread throughout Indiana. The smaller campuses are, Indiana University East is located in Richmond, Indiana University Kokomo is located in Kokomo, Indiana. Indiana University Northwest is located in Gary, Indiana, Indiana University South Bend is located in South Bend, Indiana. Indiana University Southeast is located in New Albany, Indiana, Indiana University – Purdue University Fort Wayne is located in Fort Wayne, Indiana. IPFW is operated in cooperation with, and is administered by, Indiana University – Purdue University Columbus is located in Columbus, Indiana. The centers/extensions are, The Danielson Center is located in New Castle, the Elkhart Center is located in Elkhart, Indiana. Future projects include, A medical school complex near downtown Evansville, according to the National Association of College and University Business Officers, the value of the endowment of the Indiana University and affiliated foundations is over $1.57 billion. Mark Cuban Brad Stephens Indiana University has three medals to recognize individuals, the University Medal, the only IU medal that requires approval from the Board of Trustees, was created in 1982 by then IU President John W. Ryan and is the highest award bestowed by the University. It honors individuals for singular or noteworthy contributions, including service to the university and achievement in arts, letters, science, the first recipient was Thomas T. Solley, former director of the IU Art Museum. Indiana University Presidents Medal for Excellence, a reproduction in silver of the symbolic jewel of office worn by the president at ceremonial occasions, is rich in meaning. The first recipients were member of the Beaux Arts Trio on September 20,1985, Thomas Hart Benton Mural Medallion recognizes individuals who are shining examples of the values of IU and the universal academic community. President Ryan was the first to award this honor and it was first awarded to the president of Nanjing University on July 21,1986. Indiana University has a number of ways to recognize the accomplishments of faculty, the recipient is also the IU nominee for the national Campus Compact Thomas Ehrlich Award for Service Learning. The Mace, a symbol of authority dating back to medieval times and it later would be used in processions of city mayors and other dignitaries, and became an emblem of order and authority during academic ceremonies. The staff of IUs Mace is 30 inches long and made of polished ebony encircled with four brass, gold-plated collars, atop the staff is a globe of plated brass with four flat sides
4.
Minor planet
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A minor planet is an astronomical object in direct orbit around the Sun that is neither a planet nor exclusively classified as a comet. Minor planets can be dwarf planets, asteroids, trojans, centaurs, Kuiper belt objects, as of 2016, the orbits of 709,706 minor planets were archived at the Minor Planet Center,469,275 of which had received permanent numbers. The first minor planet to be discovered was Ceres in 1801, the term minor planet has been used since the 19th century to describe these objects. The term planetoid has also used, especially for larger objects such as those the International Astronomical Union has called dwarf planets since 2006. Historically, the asteroid, minor planet, and planetoid have been more or less synonymous. This terminology has become complicated by the discovery of numerous minor planets beyond the orbit of Jupiter. A Minor planet seen releasing gas may be classified as a comet. Before 2006, the IAU had officially used the term minor planet, during its 2006 meeting, the IAU reclassified minor planets and comets into dwarf planets and small Solar System bodies. Objects are called dwarf planets if their self-gravity is sufficient to achieve hydrostatic equilibrium, all other minor planets and comets are called small Solar System bodies. The IAU stated that the minor planet may still be used. However, for purposes of numbering and naming, the distinction between minor planet and comet is still used. Hundreds of thousands of planets have been discovered within the Solar System. The Minor Planet Center has documented over 167 million observations and 729,626 minor planets, of these,20,570 have official names. As of March 2017, the lowest-numbered unnamed minor planet is 1974 FV1, as of March 2017, the highest-numbered named minor planet is 458063 Gustavomuler. There are various broad minor-planet populations, Asteroids, traditionally, most have been bodies in the inner Solar System. Near-Earth asteroids, those whose orbits take them inside the orbit of Mars. Further subclassification of these, based on distance, is used, Apohele asteroids orbit inside of Earths perihelion distance. Aten asteroids, those that have semi-major axes of less than Earths, Apollo asteroids are those asteroids with a semimajor axis greater than Earths, while having a perihelion distance of 1.017 AU or less. Like Aten asteroids, Apollo asteroids are Earth-crossers, amor asteroids are those near-Earth asteroids that approach the orbit of Earth from beyond, but do not cross it
5.
Asteroid belt
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The asteroid belt is the circumstellar disc in the Solar System located roughly between the orbits of the planets Mars and Jupiter. It is occupied by numerous irregularly shaped bodies called asteroids or minor planets, the asteroid belt is also termed the main asteroid belt or main belt to distinguish it from other asteroid populations in the Solar System such as near-Earth asteroids and trojan asteroids. About half the mass of the belt is contained in the four largest asteroids, Ceres, Vesta, Pallas, the total mass of the asteroid belt is approximately 4% that of the Moon, or 22% that of Pluto, and roughly twice that of Plutos moon Charon. Ceres, the belts only dwarf planet, is about 950 km in diameter, whereas Vesta, Pallas. The remaining bodies range down to the size of a dust particle, the asteroid material is so thinly distributed that numerous unmanned spacecraft have traversed it without incident. Nonetheless, collisions between large asteroids do occur, and these can form a family whose members have similar orbital characteristics. Individual asteroids within the belt are categorized by their spectra. The asteroid belt formed from the solar nebula as a group of planetesimals. Planetesimals are the precursors of the protoplanets. Between Mars and Jupiter, however, gravitational perturbations from Jupiter imbued the protoplanets with too much energy for them to accrete into a planet. Collisions became too violent, and instead of fusing together, the planetesimals, as a result,99. 9% of the asteroid belts original mass was lost in the first 100 million years of the Solar Systems history. Some fragments eventually found their way into the inner Solar System, Asteroid orbits continue to be appreciably perturbed whenever their period of revolution about the Sun forms an orbital resonance with Jupiter. At these orbital distances, a Kirkwood gap occurs as they are swept into other orbits. Classes of small Solar System bodies in other regions are the objects, the centaurs, the Kuiper belt objects, the scattered disc objects, the sednoids. On 22 January 2014, ESA scientists reported the detection, for the first definitive time, of water vapor on Ceres, the detection was made by using the far-infrared abilities of the Herschel Space Observatory. The finding was unexpected because comets, not asteroids, are considered to sprout jets. According to one of the scientists, The lines are becoming more and more blurred between comets and asteroids. This pattern, now known as the Titius–Bode law, predicted the semi-major axes of the six planets of the provided one allowed for a gap between the orbits of Mars and Jupiter
6.
Kirkwood gap
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A Kirkwood gap is a gap or dip in the distribution of the semi-major axes of the orbits of main-belt asteroids. They correspond to the locations of orbital resonances with Jupiter, for example, there are very few asteroids with semimajor axis near 2.50 AU, period 3.95 years, which would make three orbits for each orbit of Jupiter. Other orbital resonances correspond to orbital periods whose lengths are simple fractions of Jupiters, the weaker resonances lead only to a depletion of asteroids, while spikes in the histogram are often due to the presence of a prominent asteroid family. The orbital elements of the asteroids vary chaotically as a result, the 2,1 MMR has a few relatively stable islands within the resonance, however. These islands are depleted due to slow diffusion onto less stable orbits and this process, which has been linked to Jupiter and Saturn being near a 5,2 resonance, may have been more rapid when Jupiters and Saturns orbits were closer together. More recently, a small number of asteroids have been found to possess high eccentricity orbits which do lie within the Kirkwood gaps. Examples include the Alinda family and the Griqua family and these orbits slowly increase their eccentricity on a timescale of tens of millions of years, and will eventually break out of the resonance due to close encounters with a major planet. The most prominent Kirkwood gaps are located at mean orbital radii of,2.06 AU2.5 AU, home to the Alinda family of asteroids 2.82 AU2.95 AU3.27 AU, home to the Griqua family of asteroids. Weaker and/or narrower gaps are found at,1.9 AU2.25 AU2.33 AU2.71 AU3.03 AU3.075 AU3.47 AU3.7 AU. Orbital resonance Alinda family Griqua family Article on Kirkwood gaps at Wolframs scienceworld
7.
Perihelion and aphelion
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The perihelion is the point in the orbit of a celestial body where it is nearest to its orbital focus, generally a star. It is the opposite of aphelion, which is the point in the orbit where the body is farthest from its focus. The word perihelion stems from the Ancient Greek words peri, meaning around or surrounding, aphelion derives from the preposition apo, meaning away, off, apart. According to Keplers first law of motion, all planets, comets. Hence, a body has a closest and a farthest point from its parent object, that is, a perihelion. Each extreme is known as an apsis, orbital eccentricity measures the flatness of the orbit. Because of the distance at aphelion, only 93. 55% of the solar radiation from the Sun falls on a given area of land as does at perihelion. However, this fluctuation does not account for the seasons, as it is summer in the northern hemisphere when it is winter in the southern hemisphere and vice versa. Instead, seasons result from the tilt of Earths axis, which is 23.4 degrees away from perpendicular to the plane of Earths orbit around the sun. Winter falls on the hemisphere where sunlight strikes least directly, and summer falls where sunlight strikes most directly, in the northern hemisphere, summer occurs at the same time as aphelion. Despite this, there are larger land masses in the northern hemisphere, consequently, summers are 2.3 °C warmer in the northern hemisphere than in the southern hemisphere under similar conditions. Apsis Ellipse Solstice Dates and times of Earths perihelion and aphelion, 2000–2025 from the United States Naval Observatory
8.
Astronomical unit
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The astronomical unit is a unit of length, roughly the distance from Earth to the Sun. However, that varies as Earth orbits the Sun, from a maximum to a minimum. Originally conceived as the average of Earths aphelion and perihelion, it is now defined as exactly 149597870700 metres, the astronomical unit is used primarily as a convenient yardstick for measuring distances within the Solar System or around other stars. However, it is also a component in the definition of another unit of astronomical length. A variety of symbols and abbreviations have been in use for the astronomical unit. In a 1976 resolution, the International Astronomical Union used the symbol A for the astronomical unit, in 2006, the International Bureau of Weights and Measures recommended ua as the symbol for the unit. In 2012, the IAU, noting that various symbols are presently in use for the astronomical unit, in the 2014 revision of the SI Brochure, the BIPM used the unit symbol au. In ISO 80000-3, the symbol of the unit is ua. Earths orbit around the Sun is an ellipse, the semi-major axis of this ellipse is defined to be half of the straight line segment that joins the aphelion and perihelion. The centre of the sun lies on this line segment. In addition, it mapped out exactly the largest straight-line distance that Earth traverses over the course of a year, knowing Earths shift and a stars shift enabled the stars distance to be calculated. But all measurements are subject to some degree of error or uncertainty, improvements in precision have always been a key to improving astronomical understanding. Improving measurements were continually checked and cross-checked by means of our understanding of the laws of celestial mechanics, the expected positions and distances of objects at an established time are calculated from these laws, and assembled into a collection of data called an ephemeris. NASAs Jet Propulsion Laboratory provides one of several ephemeris computation services, in 1976, in order to establish a yet more precise measure for the astronomical unit, the IAU formally adopted a new definition. Equivalently, by definition, one AU is the radius of an unperturbed circular Newtonian orbit about the sun of a particle having infinitesimal mass. As with all measurements, these rely on measuring the time taken for photons to be reflected from an object. However, for precision the calculations require adjustment for such as the motions of the probe. In addition, the measurement of the time itself must be translated to a scale that accounts for relativistic time dilation
9.
Semi-major and semi-minor axes
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In geometry, the major axis of an ellipse is its longest diameter, a line segment that runs through the center and both foci, with ends at the widest points of the perimeter. The semi-major axis is one half of the axis, and thus runs from the centre, through a focus. Essentially, it is the radius of an orbit at the two most distant points. For the special case of a circle, the axis is the radius. One can think of the axis as an ellipses long radius. The semi-major axis of a hyperbola is, depending on the convention, thus it is the distance from the center to either vertex of the hyperbola. A parabola can be obtained as the limit of a sequence of ellipses where one focus is fixed as the other is allowed to move arbitrarily far away in one direction. Thus a and b tend to infinity, a faster than b, the semi-minor axis is a line segment associated with most conic sections that is at right angles with the semi-major axis and has one end at the center of the conic section. It is one of the axes of symmetry for the curve, in an ellipse, the one, in a hyperbola. The semi-major axis is the value of the maximum and minimum distances r max and r min of the ellipse from a focus — that is. In astronomy these extreme points are called apsis, the semi-minor axis of an ellipse is the geometric mean of these distances, b = r max r min. The eccentricity of an ellipse is defined as e =1 − b 2 a 2 so r min = a, r max = a. Now consider the equation in polar coordinates, with one focus at the origin, the mean value of r = ℓ / and r = ℓ /, for θ = π and θ =0 is a = ℓ1 − e 2. In an ellipse, the axis is the geometric mean of the distance from the center to either focus. The semi-minor axis of an ellipse runs from the center of the ellipse to the edge of the ellipse, the semi-minor axis is half of the minor axis. The minor axis is the longest line segment perpendicular to the axis that connects two points on the ellipses edge. The semi-minor axis b is related to the axis a through the eccentricity e. A parabola can be obtained as the limit of a sequence of ellipses where one focus is fixed as the other is allowed to move arbitrarily far away in one direction
10.
Orbital eccentricity
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The orbital eccentricity of an astronomical object is a parameter that determines the amount by which its orbit around another body deviates from a perfect circle. A value of 0 is an orbit, values between 0 and 1 form an elliptical orbit,1 is a parabolic escape orbit. The term derives its name from the parameters of conic sections and it is normally used for the isolated two-body problem, but extensions exist for objects following a rosette orbit through the galaxy. In a two-body problem with inverse-square-law force, every orbit is a Kepler orbit, the eccentricity of this Kepler orbit is a non-negative number that defines its shape. The limit case between an ellipse and a hyperbola, when e equals 1, is parabola, radial trajectories are classified as elliptic, parabolic, or hyperbolic based on the energy of the orbit, not the eccentricity. Radial orbits have zero angular momentum and hence eccentricity equal to one, keeping the energy constant and reducing the angular momentum, elliptic, parabolic, and hyperbolic orbits each tend to the corresponding type of radial trajectory while e tends to 1. For a repulsive force only the trajectory, including the radial version, is applicable. For elliptical orbits, a simple proof shows that arcsin yields the projection angle of a circle to an ellipse of eccentricity e. For example, to view the eccentricity of the planet Mercury, next, tilt any circular object by that angle and the apparent ellipse projected to your eye will be of that same eccentricity. From Medieval Latin eccentricus, derived from Greek ἔκκεντρος ekkentros out of the center, from ἐκ- ek-, eccentric first appeared in English in 1551, with the definition a circle in which the earth, sun. Five years later, in 1556, a form of the word was added. The eccentricity of an orbit can be calculated from the state vectors as the magnitude of the eccentricity vector, e = | e | where. For elliptical orbits it can also be calculated from the periapsis and apoapsis since rp = a and ra = a, where a is the semimajor axis. E = r a − r p r a + r p =1 −2 r a r p +1 where, rp is the radius at periapsis. For Earths annual orbit path, ra/rp ratio = longest_radius / shortest_radius ≈1.034 relative to center point of path, the eccentricity of the Earths orbit is currently about 0.0167, the Earths orbit is nearly circular. Venus and Neptune have even lower eccentricity, over hundreds of thousands of years, the eccentricity of the Earths orbit varies from nearly 0.0034 to almost 0.058 as a result of gravitational attractions among the planets. The table lists the values for all planets and dwarf planets, Mercury has the greatest orbital eccentricity of any planet in the Solar System. Such eccentricity is sufficient for Mercury to receive twice as much solar irradiation at perihelion compared to aphelion, before its demotion from planet status in 2006, Pluto was considered to be the planet with the most eccentric orbit
11.
Mean anomaly
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In celestial mechanics, the mean anomaly is an angle used in calculating the position of a body in an elliptical orbit in the classical two-body problem. Define T as the time required for a body to complete one orbit. In time T, the radius vector sweeps out 2π radians or 360°. The average rate of sweep, n, is then n =2 π T or n =360 ∘ T, define τ as the time at which the body is at the pericenter. From the above definitions, a new quantity, M, the mean anomaly can be defined M = n, because the rate of increase, n, is a constant average, the mean anomaly increases uniformly from 0 to 2π radians or 0° to 360° during each orbit. It is equal to 0 when the body is at the pericenter, π radians at the apocenter, if the mean anomaly is known at any given instant, it can be calculated at any later instant by simply adding n δt where δt represents the time difference. Mean anomaly does not measure an angle between any physical objects and it is simply a convenient uniform measure of how far around its orbit a body has progressed since pericenter. The mean anomaly is one of three parameters that define a position along an orbit, the other two being the eccentric anomaly and the true anomaly. Define l as the longitude, the angular distance of the body from the same reference direction. Thus mean anomaly is also M = l − ϖ, mean angular motion can also be expressed, n = μ a 3, where μ is a gravitational parameter which varies with the masses of the objects, and a is the semi-major axis of the orbit. Mean anomaly can then be expanded, M = μ a 3, and here mean anomaly represents uniform angular motion on a circle of radius a
12.
Degree (angle)
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A degree, usually denoted by °, is a measurement of a plane angle, defined so that a full rotation is 360 degrees. It is not an SI unit, as the SI unit of measure is the radian. Because a full rotation equals 2π radians, one degree is equivalent to π/180 radians, the original motivation for choosing the degree as a unit of rotations and angles is unknown. One theory states that it is related to the fact that 360 is approximately the number of days in a year. Ancient astronomers noticed that the sun, which follows through the path over the course of the year. Some ancient calendars, such as the Persian calendar, used 360 days for a year, the use of a calendar with 360 days may be related to the use of sexagesimal numbers. The earliest trigonometry, used by the Babylonian astronomers and their Greek successors, was based on chords of a circle, a chord of length equal to the radius made a natural base quantity. One sixtieth of this, using their standard sexagesimal divisions, was a degree, Aristarchus of Samos and Hipparchus seem to have been among the first Greek scientists to exploit Babylonian astronomical knowledge and techniques systematically. Timocharis, Aristarchus, Aristillus, Archimedes, and Hipparchus were the first Greeks known to divide the circle in 360 degrees of 60 arc minutes, eratosthenes used a simpler sexagesimal system dividing a circle into 60 parts. Furthermore, it is divisible by every number from 1 to 10 except 7 and this property has many useful applications, such as dividing the world into 24 time zones, each of which is nominally 15° of longitude, to correlate with the established 24-hour day convention. Finally, it may be the case more than one of these factors has come into play. For many practical purposes, a degree is a small enough angle that whole degrees provide sufficient precision. When this is not the case, as in astronomy or for geographic coordinates, degree measurements may be written using decimal degrees, with the symbol behind the decimals. Alternatively, the sexagesimal unit subdivisions can be used. One degree is divided into 60 minutes, and one minute into 60 seconds, use of degrees-minutes-seconds is also called DMS notation. These subdivisions, also called the arcminute and arcsecond, are represented by a single and double prime. For example,40. 1875° = 40° 11′ 15″, or, using quotation mark characters, additional precision can be provided using decimals for the arcseconds component. The older system of thirds, fourths, etc. which continues the sexagesimal unit subdivision, was used by al-Kashi and other ancient astronomers, but is rarely used today
13.
Orbital inclination
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Orbital inclination measures the tilt of an objects orbit around a celestial body. It is expressed as the angle between a plane and the orbital plane or axis of direction of the orbiting object. For a satellite orbiting the Earth directly above the equator, the plane of the orbit is the same as the Earths equatorial plane. The general case is that the orbit is tilted, it spends half an orbit over the northern hemisphere. If the orbit swung between 20° north latitude and 20° south latitude, then its orbital inclination would be 20°, the inclination is one of the six orbital elements describing the shape and orientation of a celestial orbit. It is the angle between the plane and the plane of reference, normally stated in degrees. For a satellite orbiting a planet, the plane of reference is usually the plane containing the planets equator, for planets in the Solar System, the plane of reference is usually the ecliptic, the plane in which the Earth orbits the Sun. This reference plane is most practical for Earth-based observers, therefore, Earths inclination is, by definition, zero. Inclination could instead be measured with respect to another plane, such as the Suns equator or the invariable plane, the inclination of orbits of natural or artificial satellites is measured relative to the equatorial plane of the body they orbit, if they orbit sufficiently closely. The equatorial plane is the perpendicular to the axis of rotation of the central body. An inclination of 30° could also be described using an angle of 150°, the convention is that the normal orbit is prograde, an orbit in the same direction as the planet rotates. Inclinations greater than 90° describe retrograde orbits, thus, An inclination of 0° means the orbiting body has a prograde orbit in the planets equatorial plane. An inclination greater than 0° and less than 90° also describe prograde orbits, an inclination of 63. 4° is often called a critical inclination, when describing artificial satellites orbiting the Earth, because they have zero apogee drift. An inclination of exactly 90° is an orbit, in which the spacecraft passes over the north and south poles of the planet. An inclination greater than 90° and less than 180° is a retrograde orbit, an inclination of exactly 180° is a retrograde equatorial orbit. For gas giants, the orbits of moons tend to be aligned with the giant planets equator, the inclination of exoplanets or members of multiple stars is the angle of the plane of the orbit relative to the plane perpendicular to the line-of-sight from Earth to the object. An inclination of 0° is an orbit, meaning the plane of its orbit is parallel to the sky. An inclination of 90° is an orbit, meaning the plane of its orbit is perpendicular to the sky
14.
Longitude of the ascending node
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The longitude of the ascending node is one of the orbital elements used to specify the orbit of an object in space. It is the angle from a direction, called the origin of longitude, to the direction of the ascending node. The ascending node is the point where the orbit of the passes through the plane of reference. Commonly used reference planes and origins of longitude include, For a geocentric orbit, Earths equatorial plane as the plane. In this case, the longitude is called the right ascension of the ascending node. The angle is measured eastwards from the First Point of Aries to the node, for a heliocentric orbit, the ecliptic as the reference plane, and the First Point of Aries as the origin of longitude. The angle is measured counterclockwise from the First Point of Aries to the node, the angle is measured eastwards from north to the node. pp.40,72,137, chap. In the case of a star known only from visual observations, it is not possible to tell which node is ascending. In this case the orbital parameter which is recorded is the longitude of the node, Ω, here, n=<nx, ny, nz> is a vector pointing towards the ascending node. The reference plane is assumed to be the xy-plane, and the origin of longitude is taken to be the positive x-axis, K is the unit vector, which is the normal vector to the xy reference plane. For non-inclined orbits, Ω is undefined, for computation it is then, by convention, set equal to zero, that is, the ascending node is placed in the reference direction, which is equivalent to letting n point towards the positive x-axis. Kepler orbits Equinox Orbital node perturbation of the plane can cause revolution of the ascending node