1.
Wide-field Infrared Survey Explorer
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Wide-field Infrared Survey Explorer is a NASA infrared-wavelength astronomical space telescope launched in December 2009, and placed in hibernation in February 2011 when its transmitter turned off. WISE discovered thousands of planets and numerous star clusters. Its observations also supported the discovery of the first Y Dwarf, WISE performed an all-sky astronomical survey with images in 3.4,4.6,12 and 22 μm wavelength range bands, over ten months using a 40 cm diameter infrared telescope in Earth orbit. After its hydrogen coolant depleted, a mission extension called NEOWISE was conducted to search for near-Earth objects such as comets. The All-Sky data including processed images, source catalogs and raw data, was released to the public on March 14,2012, in August 2013, NASA announced it would reactivate the WISE telescope for a new three-year mission to search for asteroids that could collide with Earth. Science operations and data processing for WISE and NEOWISE take place at the Infrared Processing, the mission was planned to create infrared images of 99 percent of the sky, with at least eight images made of each position on the sky in order to increase accuracy. The spacecraft was placed in a 525 km, circular, polar, Sun-synchronous orbit for its mission, during which it has taken 1.5 million images. Each image covers a 47-arcminute field of view, which means a 6-arcsecond resolution, each area of the sky was scanned at least 10 times at the equator, the poles were scanned at theoretically every revolution due to the overlapping of the images. The produced image library contains data on the local Solar System, the Milky Way, among the objects WISE studied are asteroids, cool, dim stars such as brown dwarfs, and the most luminous infrared galaxies. Stellar nurseries, which are covered by interstellar dust, are detectable in infrared, Infrared measurements from the WISE astronomical survey have been particularly effective at unveiling previously undiscovered star clusters. Examples of such embedded star clusters are Camargo 18, Camargo 440, Majaess 101, in addition, galaxies of the young Universe and interacting galaxies, where star formation is intensive, are bright in infrared. On this wavelength the interstellar gas clouds are also detectable, as well as proto-planetary discs, WISE satellite was expected to find at least 1,000 of those proto-planetary discs. WISE was not able to detect Kuiper belt objects, because their temperatures are too low and it was able to detect any objects warmer than 70–100 K. A Neptune-sized object would be out to 700 AU, a Jupiter-mass object out to 1 light year. A larger object of 2–3 Jupiter masses would be visible at a distance of up to 7–10 light years and that translates to about 1000 new main-belt asteroids per day, and 1–3 NEOs per day. The peak of magnitude distribution for NEOs will be about 21–22 V, WISE would detect each typical Solar System object 10–12 times over about 36 hours in intervals of 3 hours. Construction of the WISE telescope was divided between Ball Aerospace & Technologies, SSG Precision Optronics, Inc, DRS and Rockwell, Lockheed Martin, and Space Dynamics Laboratory. The program was managed through the Jet Propulsion Laboratory, the WISE instrument was built by the Space Dynamics Laboratory in Logan, Utah
2.
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
3.
Trans-Neptunian object
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A trans-Neptunian object is any minor planet in the Solar System that orbits the Sun at a greater average distance than Neptune,30 astronomical units. Twelve minor planets with a semi-major axis greater than 150 AU and perihelion greater than 30 AU are known, the first trans-Neptunian object to be discovered was Pluto in 1930. It took until 1992 to discover a second trans-Neptunian object orbiting the Sun directly,1992 QB1, as of February 2017 over 2,300 trans-Neptunian objects appear on the Minor Planet Centers List of Transneptunian Objects. Of these TNOs,2,000 have a perihelion farther out than Neptune, as of November 2016,242 of these have their orbits well-enough determined that they have been given a permanent minor planet designation. The largest known object is Pluto, followed by Eris,2007 OR10, Makemake. The Kuiper belt, scattered disk, and Oort cloud are three divisions of this volume of space, though treatments vary and a few objects such as Sedna do not fit easily into any division. The orbit of each of the planets is slightly affected by the influences of the other planets. Discrepancies in the early 1900s between the observed and expected orbits of Uranus and Neptune suggested that there were one or more additional planets beyond Neptune, the search for these led to the discovery of Pluto in February 1930, which was too small to explain the discrepancies. Revised estimates of Neptunes mass from the Voyager 2 flyby in 1989 showed that the problem was spurious, Pluto was easiest to find because it has the highest apparent magnitude of all known trans-Neptunian objects. It also has an inclination to the ecliptic than most other large TNOs. After Plutos discovery, American astronomer Clyde Tombaugh continued searching for years for similar objects. For a long time, no one searched for other TNOs as it was believed that Pluto. Only after the 1992 discovery of a second TNO,1992 QB1, a broad strip of the sky around the ecliptic was photographed and digitally evaluated for slowly moving objects. Hundreds of TNOs were found, with diameters in the range of 50 to 2,500 kilometers, Pluto and Eris were eventually classified as dwarf planets by the International Astronomical Union. Kuiper belt objects are classified into the following two groups, Resonant objects are locked in an orbital resonance with Neptune. Objects with a 1,2 resonance are called twotinos, and objects with a 2,3 resonance are called plutinos, after their most prominent member, classical Kuiper belt objects have no such resonance, moving on almost circular orbits, unperturbed by Neptune. Examples are 1992 QB1,50000 Quaoar and Makemake, the scattered disc contains objects farther from the Sun, usually with very irregular orbits. A typical example is the most massive known TNO, Eris, scattered-extended —Scattered-extended objects have a Tisserand parameter greater than 3 and have a time-averaged eccentricity greater than 0
4.
Scattered disc
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The scattered disc is a distant circumstellar disc in the Solar System that is sparsely populated by icy minor planets, a subset of the broader family of trans-Neptunian objects. The scattered-disc objects have orbital eccentricities ranging as high as 0.8, inclinations as high as 40° and these extreme orbits are thought to be the result of gravitational scattering by the gas giants, and the objects continue to be subject to perturbation by the planet Neptune. Although the closest scattered-disc objects approach the Sun at about 30–35 AU and this makes scattered objects among the most distant and coldest objects in the Solar System. Eventually, perturbations from the giant planets send such objects towards the Sun, many Oort cloud objects are also thought to have originated in the scattered disc. Detached objects are not sharply distinct from scattered disc objects, during the 1980s, the use of CCD-based cameras in telescopes made it possible to directly produce electronic images that could then be readily digitized and transferred to digital images. Because the CCD captured more light than film and the blinking could now be done at a computer screen. A flood of new discoveries was the result, over a thousand objects were detected between 1992 and 2006. The first scattered-disc object to be recognised as such was 1996 TL66, three more were identified by the same survey in 1999,1999 CV118,1999 CY118, and 1999 CF119. The first object presently classified as an SDO to be discovered was 1995 TL8, as of 2011, over 200 SDOs have been identified, including 2007 UK126,2002 TC302, Eris, Sedna and 2004 VN112. Known trans-Neptunian objects are divided into two subpopulations, the Kuiper belt and the scattered disc. A third reservoir of trans-Neptunian objects, the Oort cloud, has been hypothesized, some researchers further suggest a transitional space between the scattered disc and the inner Oort cloud, populated with detached objects. Those in 3,2 resonances are known as plutinos, because Pluto is the largest member of their group, in contrast to the Kuiper belt, the scattered-disc population can be disturbed by Neptune. Scattered-disc objects come within range of Neptune at their closest approaches. Some objects, like 1999 TD10, blur the distinction and the Minor Planet Center, the MPC also makes a clear distinction between the Kuiper belt and the scattered disc, separating those objects in stable orbits from those in scattered orbits. Another term used is scattered Kuiper-belt object for bodies of the scattered disc and this delineation is inadequate over the age of the Solar System, since bodies trapped in resonances could pass from a scattering phase to a non-scattering phase numerous times. That is, trans-Neptunian objects could travel back and forth between the Kuiper belt and the disc over time. In the a >30 AU region, the region of the Solar System populated by objects with semi-major axes greater than 30 AU, the Minor Planet Center classifies the trans-Neptunian object 90377 Sedna as a scattered-disc object. Under this definition, an object with a greater than 40 AU could be classified as outside the scattered disc
5.
Centaur (minor planet)
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Centaurs are minor planets with a semi-major axis between those of the outer planets. They have unstable orbits that cross or have crossed the orbits of one or more of the giant planets, Centaurs typically behave with characteristics of both asteroids and comets. They are named after the centaurs that were a mixture of horse. It has been estimated there are around 44,000 centaurs in the Solar System with diameters larger than 1 km. The first centaur to be discovered, under the definition of the Jet Propulsion Laboratory, however, they were not recognized as a distinct population until the discovery of 2060 Chiron in 1977. The largest confirmed centaur is 10199 Chariklo, which at 260 km in diameter is as big as a mid-sized main-belt asteroid, however, the lost centaur 1995 SN55 may be somewhat larger. No centaur has been photographed up close, although there is evidence that Saturns moon Phoebe, imaged by the Cassini probe in 2004, in addition, the Hubble Space Telescope has gleaned some information about the surface features of 8405 Asbolus. As of 2008, three centaurs have been found to display comet-like comas, Chiron,60558 Echeclus, and 166P/NEAT, Chiron and Echeclus are therefore classified as both asteroids and comets. Other centaurs, such as 52872 Okyrhoe and 2012 CG, are suspected of having shown comas, any centaur that is perturbed close enough to the Sun is expected to become a comet. The generic definition of a centaur is a body that orbits the Sun between Jupiter and Neptune and crosses the orbits of one or more of the giant planets. Though nowadays the MPC often lists centaurs and scattered disc objects together as a single group, the Jet Propulsion Laboratory similarly defines centaurs as having a semi-major axis, a, between those of Jupiter and Neptune. In contrast, the Deep Ecliptic Survey defines centaurs using a classification scheme. These classifications are based on the change in behavior of the present orbit when extended over 10 million years. The DES defines centaurs as non-resonant objects whose instantaneous perihelia are less than the osculating semi-major axis of Neptune at any time during the simulation and this definition is intended to be synonymous with planet-crossing orbits and to suggest comparatively short lifetimes in the current orbit. The collection The Solar System Beyond Neptune defines objects with an axis between those of Jupiter and Neptune and a Jupiter – Tisserands parameter above 3. The JPL Small-Body Database lists 324 centaurs, there are an additional 65 trans-Neptunian objects with a perihelion closer than the orbit of Uranus. The Committee on Small Body Nomenclature of the International Astronomical Union has not formally weighed in on either side of the debate, thus far, only the binary objects Ceto and Phorcys and Typhon and Echidna have been named according to the new policy. Other objects caught between these differences in classification methods include 944 Hidalgo which was discovered in 1920 and is listed as a centaur in the JPL Small-Body Database
6.
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
7.
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
8.
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
9.
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
10.
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
11.
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
12.
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
13.
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
14.
Argument of periapsis
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The argument of periapsis, symbolized as ω, is one of the orbital elements of an orbiting body. Parametrically, ω is the angle from the ascending node to its periapsis. For specific types of orbits, words such as perihelion, perigee, periastron, an argument of periapsis of 0° means that the orbiting body will be at its closest approach to the central body at the same moment that it crosses the plane of reference from South to North. An argument of periapsis of 90° means that the body will reach periapsis at its northmost distance from the plane of reference. Adding the argument of periapsis to the longitude of the ascending node gives the longitude of the periapsis, however, especially in discussions of binary stars and exoplanets, the terms longitude of periapsis or longitude of periastron are often used synonymously with argument of periapsis. In the case of equatorial orbits, the argument is strictly undefined, where, ex and ey are the x- and y-components of the eccentricity vector e. In the case of circular orbits it is assumed that the periapsis is placed at the ascending node. Kepler orbit Orbital mechanics Orbital node
15.
Minimum orbit intersection distance
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Minimum orbit intersection distance is a measure used in astronomy to assess potential close approaches and collision risks between astronomical objects. It is defined as the distance between the closest points of the orbits of two bodies. Of greatest interest is the risk of a collision with Earth, Earth MOID is often listed on comet and asteroid databases such as the JPL Small-Body Database. MOID values are defined with respect to other bodies as well, Jupiter MOID, Venus MOID. An object is classified as a hazardous object – that is, posing a possible risk to Earth – if, among other conditions. A low MOID does not mean that a collision is inevitable as the planets frequently perturb the orbit of small bodies. It is also necessary that the two bodies reach that point in their orbits at the time before the smaller body is perturbed into a different orbit with a different MOID value. Two Objects gravitationally locked in orbital resonance may never approach one another, numerical integrations become increasingly divergent as trajectories are projected further forward in time, especially beyond times where the smaller body is repeatedly perturbed by other planets. MOID has the convenience that it is obtained directly from the elements of the body. The only object that has ever been rated at 4 on the Torino Scale and this is not the smallest Earth MOID in the catalogues, many bodies with a small Earth MOID are not classed as PHOs because the objects are less than roughly 140 meters in diameter. Earth MOID values are more practical for asteroids less than 140 meters in diameter as those asteroids are very dim. It is even smaller at the more precise JPL Small Body Database
16.
Apparent magnitude
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The apparent magnitude of a celestial object is a number that is a measure of its brightness as seen by an observer on Earth. The brighter an object appears, the lower its magnitude value, the Sun, at apparent magnitude of −27, is the brightest object in the sky. It is adjusted to the value it would have in the absence of the atmosphere, furthermore, the magnitude scale is logarithmic, a difference of one in magnitude corresponds to a change in brightness by a factor of 5√100, or about 2.512. The measurement of apparent magnitudes or brightnesses of celestial objects is known as photometry, apparent magnitudes are used to quantify the brightness of sources at ultraviolet, visible, and infrared wavelengths. An apparent magnitude is measured in a specific passband corresponding to some photometric system such as the UBV system. In standard astronomical notation, an apparent magnitude in the V filter band would be denoted either as mV or often simply as V, the scale used to indicate magnitude originates in the Hellenistic practice of dividing stars visible to the naked eye into six magnitudes. The brightest stars in the sky were said to be of first magnitude, whereas the faintest were of sixth magnitude. Each grade of magnitude was considered twice the brightness of the following grade and this rather crude scale for the brightness of stars was popularized by Ptolemy in his Almagest, and is generally believed to have originated with Hipparchus. This implies that a star of magnitude m is 2.512 times as bright as a star of magnitude m +1 and this figure, the fifth root of 100, became known as Pogsons Ratio. The zero point of Pogsons scale was defined by assigning Polaris a magnitude of exactly 2. However, with the advent of infrared astronomy it was revealed that Vegas radiation includes an Infrared excess presumably due to a disk consisting of dust at warm temperatures. At shorter wavelengths, there is negligible emission from dust at these temperatures, however, in order to properly extend the magnitude scale further into the infrared, this peculiarity of Vega should not affect the definition of the magnitude scale. Therefore, the scale was extrapolated to all wavelengths on the basis of the black body radiation curve for an ideal stellar surface at 11000 K uncontaminated by circumstellar radiation. On this basis the spectral irradiance for the zero magnitude point, with the modern magnitude systems, brightness over a very wide range is specified according to the logarithmic definition detailed below, using this zero reference. In practice such apparent magnitudes do not exceed 30, astronomers have developed other photometric zeropoint systems as alternatives to the Vega system. The AB magnitude zeropoint is defined such that an objects AB, the dimmer an object appears, the higher the numerical value given to its apparent magnitude, with a difference of 5 magnitudes corresponding to a brightness factor of exactly 100. Since an increase of 5 magnitudes corresponds to a decrease in brightness by a factor of exactly 100, each magnitude increase implies a decrease in brightness by the factor 5√100 ≈2.512. Inverting the above formula, a magnitude difference m1 − m2 = Δm implies a brightness factor of F2 F1 =100 Δ m 5 =100.4 Δ m ≈2.512 Δ m
17.
Numerical integration
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This article focuses on calculation of definite integrals. The term numerical quadrature is more or less a synonym for numerical integration, Some authors refer to numerical integration over more than one dimension as cubature, others take quadrature to include higher-dimensional integration. The basic problem in numerical integration is to compute an approximate solution to a definite integral ∫ a b f d x to a degree of accuracy. If f is a smooth function integrated over a number of dimensions. The term numerical integration first appears in 1915 in the publication A Course in Interpolation, Quadrature is a historical mathematical term that means calculating area. Quadrature problems have served as one of the sources of mathematical analysis. Mathematicians of Ancient Greece, according to the Pythagorean doctrine, understood calculation of area as the process of constructing geometrically a square having the same area and that is why the process was named quadrature. For example, a quadrature of the circle, Lune of Hippocrates and this construction must be performed only by means of compass and straightedge. The ancient Babylonians used the trapezoidal rule to integrate the motion of Jupiter along the ecliptic, for a quadrature of a rectangle with the sides a and b it is necessary to construct a square with the side x = a b. For this purpose it is possible to use the fact, if we draw the circle with the sum of a and b as the diameter. The similar geometrical construction solves a problem of a quadrature for a parallelogram, problems of quadrature for curvilinear figures are much more difficult. The quadrature of the circle with compass and straightedge had been proved in the 19th century to be impossible, nevertheless, for some figures a quadrature can be performed. The quadratures of a surface and a parabola segment done by Archimedes became the highest achievement of the antique analysis. The area of the surface of a sphere is equal to quadruple the area of a circle of this sphere. The area of a segment of the cut from it by a straight line is 4/3 the area of the triangle inscribed in this segment. For the proof of the results Archimedes used the Method of exhaustion of Eudoxus, in medieval Europe the quadrature meant calculation of area by any method. More often the Method of indivisibles was used, it was less rigorous, john Wallis algebrised this method, he wrote in his Arithmetica Infinitorum series that we now call the definite integral, and he calculated their values. Isaac Barrow and James Gregory made further progress, quadratures for some algebraic curves, christiaan Huygens successfully performed a quadrature of some Solids of revolution
18.
Curve fitting
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Curve fitting is the process of constructing a curve, or mathematical function, that has the best fit to a series of data points, possibly subject to constraints. Curve fitting can involve either interpolation, where an exact fit to the data is required, or smoothing, in which a smooth function is constructed that approximately fits the data. A related topic is regression analysis, which focuses more on questions of statistical inference such as how much uncertainty is present in a curve that is fit to data observed with random errors. Fitted curves can be used as an aid for data visualization, to infer values of a function where no data are available, most commonly, one fits a function of the form y=f. Starting with a first degree polynomial equation, y = a x + b and this is a line with slope a. A line will connect any two points, so a first degree polynomial equation is an exact fit through any two points with distinct x coordinates. If the order of the equation is increased to a second degree polynomial and this will exactly fit a simple curve to three points. If the order of the equation is increased to a third degree polynomial and this will exactly fit four points. A more general statement would be to say it will exactly fit four constraints, each constraint can be a point, angle, or curvature. Angle and curvature constraints are most often added to the ends of a curve, identical end conditions are frequently used to ensure a smooth transition between polynomial curves contained within a single spline. Higher-order constraints, such as the change in the rate of curvature, many other combinations of constraints are possible for these and for higher order polynomial equations. If there are more than n +1 constraints, the curve can still be run through those constraints. An exact fit to all constraints is not certain, in general, however, some method is then needed to evaluate each approximation. The least squares method is one way to compare the deviations, there are several reasons given to get an approximate fit when it is possible to simply increase the degree of the polynomial equation and get an exact match. Even if a match exists, it does not necessarily follow that it can be readily discovered. Depending on the algorithm used there may be a divergent case and this situation might require an approximate solution. The effect of averaging out questionable data points in a sample, rather than distorting the curve to fit them exactly, runges phenomenon, high order polynomials can be highly oscillatory. If a curve runs through two points A and B, it would be expected that the curve would run somewhat near the midpoint of A and B, as well
19.
Albedo
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Albedo is a measure for reflectance or optical brightness. It is dimensionless and measured on a scale from zero to one, surface albedo is defined as the ratio of radiation reflected to the radiation incident on a surface. The proportion reflected is not only determined by properties of the surface itself and these factors vary with atmospheric composition, geographic location and time. While bi-hemispherical reflectance is calculated for an angle of incidence. The temporal resolution may range from seconds to daily, seasonal or annual averages, unless given for a specific wavelength, albedo refers to the entire spectrum of solar radiation. Due to measurement constraints, it is given for the spectrum in which most solar energy reaches the surface. This spectrum includes visible light, which explains why surfaces with a low albedo appear dark, albedo is an important concept in climatology, astronomy, and environmental management. The term albedo was introduced into optics by Johann Heinrich Lambert in his 1760 work Photometria, any albedo in visible light falls within a range of about 0.9 for fresh snow to about 0.04 for charcoal, one of the darkest substances. Deeply shadowed cavities can achieve an effective albedo approaching the zero of a black body, when seen from a distance, the ocean surface has a low albedo, as do most forests, whereas desert areas have some of the highest albedos among landforms. Most land areas are in a range of 0.1 to 0.4. The average albedo of Earth is about 0.3 and this is far higher than for the ocean primarily because of the contribution of clouds. Earths surface albedo is regularly estimated via Earth observation satellite sensors such as NASAs MODIS instruments on board the Terra, thereby, the BRDF allows to translate observations of reflectance into albedo. Earths average surface temperature due to its albedo and the effect is currently about 15 °C. If Earth were frozen entirely, the temperature of the planet would drop below −40 °C. If only the land masses became covered by glaciers, the mean temperature of the planet would drop to about 0 °C. In contrast, if the entire Earth was covered by water — a so-called aquaplanet — the average temperature on the planet would rise to almost 27 °C, hence, the actual albedo α can then be given as, α = α ¯ + D α ¯ ¯. Directional-hemispherical reflectance is sometimes referred to as black-sky albedo and bi-hemispherical reflectance as white-sky albedo and these terms are important because they allow the albedo to be calculated for any given illumination conditions from a knowledge of the intrinsic properties of the surface. The albedos of planets, satellites and asteroids can be used to infer much about their properties, the study of albedos, their dependence on wavelength, lighting angle, and variation in time comprises a major part of the astronomical field of photometry
20.
Two-body problem
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In classical mechanics, the two-body problem is to determine the motion of two point particles that interact only with each other. Common examples include a satellite orbiting a planet, a planet orbiting a star, the two-body problem can be re-formulated as two one-body problems, a trivial one and one that involves solving for the motion of one particle in an external potential. Since many one-body problems can be solved exactly, the corresponding two-body problem can also be solved, by contrast, the three-body problem cannot be solved in terms of first integrals, except in special cases. Let x1 and x2 be the positions of the two bodies, and m1 and m2 be their masses. The goal is to determine the trajectories x1 and x2 for all t, given the initial positions x1 and x2. The two dots on top of the x position vectors denote their second derivative with respect to time, adding and subtracting these two equations decouples them into two one-body problems, which can be solved independently. Adding equations and results in an equation describing the center of mass motion, by contrast, subtracting equation from equation results in an equation that describes how the vector r = x1 − x2 between the masses changes with time. The solutions of these independent one-body problems can be combined to obtain the solutions for the trajectories x1 and x2. The resulting equation, R ¨ =0 shows that the velocity V = dR/dt of the center of mass is constant, hence, the position R of the center of mass can be determined at all times from the initial positions and velocities. The motion of two bodies with respect to each other always lies in a plane, introducing the assumption that the force between two particles acts along the line between their positions, it follows that r × F =0 and the angular momentum vector L is constant. We now have, μ r ¨ = F r ^, Kepler orbit Energy drift Equation of the center Eulers three-body problem Gravitational two-body problem Kepler problem n-body problem Virial theorem Two-body problem Landau LD, Lifshitz EM. Two-body problem at Eric Weissteins World of Physics
21.
Barycenter
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The barycenter is the center of mass of two or more bodies that are orbiting each other, or the point around which they both orbit. It is an important concept in such as astronomy and astrophysics. The distance from a center of mass to the barycenter can be calculated as a simple two-body problem. In cases where one of the two objects is more massive than the other, the barycenter will typically be located within the more massive object. Rather than appearing to orbit a center of mass with the smaller body. This is the case for the Earth–Moon system, where the barycenter is located on average 4,671 km from the Earths center, when the two bodies are of similar masses, the barycenter will generally be located between them and both bodies will follow an orbit around it. This is the case for Pluto and Charon, as well as for many binary asteroids and it is also the case for Jupiter and the Sun, despite the thousandfold difference in mass, due to the relatively large distance between them. In astronomy, barycentric coordinates are non-rotating coordinates with the origin at the center of mass of two or more bodies, the International Celestial Reference System is a barycentric one, based on the barycenter of the Solar System. In geometry, the barycenter is synonymous with centroid, the geometric center of a two-dimensional shape. The barycenter is one of the foci of the orbit of each body. This is an important concept in the fields of astronomy and astrophysics. If a is the distance between the centers of the two bodies, r1 is the axis of the primarys orbit around the barycenter. When the barycenter is located within the massive body, that body will appear to wobble rather than to follow a discernible orbit. The following table sets out some examples from the Solar System, figures are given rounded to three significant figures. If Jupiter had Mercurys orbit, the Sun–Jupiter barycenter would be approximately 55,000 km from the center of the Sun, but even if the Earth had Eris orbit, the Sun–Earth barycenter would still be within the Sun. To calculate the motion of the Sun, you would need to sum all the influences from all the planets, comets, asteroids. If all the planets were aligned on the side of the Sun. The calculations above are based on the distance between the bodies and yield the mean value r1
22.
Jet Propulsion Laboratory
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The Jet Propulsion Laboratory is a federally funded research and development center and NASA field center in La Cañada Flintridge, California and Pasadena, California, United States. The JPL is managed by the nearby California Institute of Technology for NASA, the laboratorys primary function is the construction and operation of planetary robotic spacecraft, though it also conducts Earth-orbit and astronomy missions. It is also responsible for operating NASAs Deep Space Network and they are also responsible for managing the JPL Small-Body Database, and provides physical data and lists of publications for all known small Solar System bodies. The JPLs Space Flight Operations Facility and Twenty-Five-Foot Space Simulator are designated National Historic Landmarks, JPL traces its beginnings to 1936 in the Guggenheim Aeronautical Laboratory at the California Institute of Technology when the first set of rocket experiments were carried out in the Arroyo Seco. Malinas thesis advisor was engineer/aerodynamicist Theodore von Kármán, who arranged for U. S. Army financial support for this GALCIT Rocket Project in 1939. In 1941, Malina, Parsons, Forman, Martin Summerfield, in 1943, von Kármán, Malina, Parsons, and Forman established the Aerojet Corporation to manufacture JATO motors. The project took on the name Jet Propulsion Laboratory in November 1943, during JPLs Army years, the laboratory developed two deployed weapon systems, the MGM-5 Corporal and MGM-29 Sergeant intermediate range ballistic missiles. These missiles were the first US ballistic missiles developed at JPL and it also developed a number of other weapons system prototypes, such as the Loki anti-aircraft missile system, and the forerunner of the Aerobee sounding rocket. At various times, it carried out testing at the White Sands Proving Ground, Edwards Air Force Base. A lunar lander was developed in 1938-39 which influenced design of the Apollo Lunar Module in the 1960s. The team lost that proposal to Project Vanguard, and instead embarked on a project to demonstrate ablative re-entry technology using a Jupiter-C rocket. They carried out three successful flights in 1956 and 1957. Using a spare Juno I, the two organizations then launched the United States first satellite, Explorer 1, on February 1,1958, JPL was transferred to NASA in December 1958, becoming the agencys primary planetary spacecraft center. JPL engineers designed and operated Ranger and Surveyor missions to the Moon that prepared the way for Apollo, JPL also led the way in interplanetary exploration with the Mariner missions to Venus, Mars, and Mercury. In 1998, JPL opened the Near-Earth Object Program Office for NASA, as of 2013, it has found 95% of asteroids that are a kilometer or more in diameter that cross Earths orbit. JPL was early to employ women mathematicians, in the 1940s and 1950s, using mechanical calculators, women in an all-female computations group performed trajectory calculations. In 1961, JPL hired Dana Ulery as their first woman engineer to work alongside male engineers as part of the Ranger and Mariner mission tracking teams, when founded, JPLs site was a rocky flood-plain just outside the city limits of Pasadena. Almost all of the 177 acres of the U. S, the city of La Cañada Flintridge, California was incorporated in 1976, well after JPL attained international recognition with a Pasadena address
23.
Marc William Buie
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In 2008 Marc Buie moved to Boulder, Colorado to work at the Southwest Research Institute in the Space Science Department. Buie grew up in Baton Rouge, Louisiana and received his B. Sc. in physics from Louisiana State University in 1980 and he then switched fields and earned his Ph. D. in Planetary Science from the University of Arizona in 1984. Dr. Buie was a fellow at the University of Hawaii from 1985 to 1988. Dr. Buie joined the staff at Lowell Observatory in 1991, since 1983 Pluto has been a central theme of research done by Buie, who has published over 85 scientific papers and journal articles. His first result was to prove that the methane visible on Pluto was on its surface and he is also one of the co-discoverers of Plutos moons, Nix and Hydra. He has been working with the Deep Ecliptic Survey team who have been responsible for the discovery of over 1,000 of these distant objects, beyond the work of just locating these objects, he additionally seeks to develop a better picture of the structure and nature of them. A spin-off project from this endeavor is his participation in the project to locate a Kuiper belt object that is within the range of the New Horizons mission once it passes by Pluto. In an effort closer to home, he also studies near-Earth asteroids to try to more about these potentially dangerous solar system neighbors. Most of these research efforts involve the use of Lowell Observatory telescopes in addition to use of the Hubble. The inner main-belt asteroid 7553 Buie was named in the honor on 28 July 1999. He is also profiled as part of an article on Pluto in Air & Space Smithsonian magazine, from the desk of Marc W. Buie page from Lowell Portrait of Marc Buie by Dan Coogan
24.
ArXiv
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In many fields of mathematics and physics, almost all scientific papers are self-archived on the arXiv repository. Begun on August 14,1991, arXiv. org passed the half-million article milestone on October 3,2008, by 2014 the submission rate had grown to more than 8,000 per month. The arXiv was made possible by the low-bandwidth TeX file format, around 1990, Joanne Cohn began emailing physics preprints to colleagues as TeX files, but the number of papers being sent soon filled mailboxes to capacity. Additional modes of access were added, FTP in 1991, Gopher in 1992. The term e-print was quickly adopted to describe the articles and its original domain name was xxx. lanl. gov. Due to LANLs lack of interest in the rapidly expanding technology, in 1999 Ginsparg changed institutions to Cornell University and it is now hosted principally by Cornell, with 8 mirrors around the world. Its existence was one of the factors that led to the current movement in scientific publishing known as open access. Mathematicians and scientists regularly upload their papers to arXiv. org for worldwide access, Ginsparg was awarded a MacArthur Fellowship in 2002 for his establishment of arXiv. The annual budget for arXiv is approximately $826,000 for 2013 to 2017, funded jointly by Cornell University Library, annual donations were envisaged to vary in size between $2,300 to $4,000, based on each institution’s usage. As of 14 January 2014,174 institutions have pledged support for the period 2013–2017 on this basis, in September 2011, Cornell University Library took overall administrative and financial responsibility for arXivs operation and development. Ginsparg was quoted in the Chronicle of Higher Education as saying it was supposed to be a three-hour tour, however, Ginsparg remains on the arXiv Scientific Advisory Board and on the arXiv Physics Advisory Committee. The lists of moderators for many sections of the arXiv are publicly available, additionally, an endorsement system was introduced in 2004 as part of an effort to ensure content that is relevant and of interest to current research in the specified disciplines. Under the system, for categories that use it, an author must be endorsed by an established arXiv author before being allowed to submit papers to those categories. Endorsers are not asked to review the paper for errors, new authors from recognized academic institutions generally receive automatic endorsement, which in practice means that they do not need to deal with the endorsement system at all. However, the endorsement system has attracted criticism for allegedly restricting scientific inquiry, perelman appears content to forgo the traditional peer-reviewed journal process, stating, If anybody is interested in my way of solving the problem, its all there – let them go and read about it. The arXiv generally re-classifies these works, e. g. in General mathematics, papers can be submitted in any of several formats, including LaTeX, and PDF printed from a word processor other than TeX or LaTeX. The submission is rejected by the software if generating the final PDF file fails, if any image file is too large. ArXiv now allows one to store and modify an incomplete submission, the time stamp on the article is set when the submission is finalized
25.
Center of mass
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The distribution of mass is balanced around the center of mass and the average of the weighted position coordinates of the distributed mass defines its coordinates. Calculations in mechanics are simplified when formulated with respect to the center of mass. It is a point where entire mass of an object may be assumed to be concentrated to visualise its motion. In other words, the center of mass is the equivalent of a given object for application of Newtons laws of motion. In the case of a rigid body, the center of mass is fixed in relation to the body. The center of mass may be located outside the body, as is sometimes the case for hollow or open-shaped objects. In the case of a distribution of separate bodies, such as the planets of the Solar System, in orbital mechanics, the equations of motion of planets are formulated as point masses located at the centers of mass. The center of mass frame is a frame in which the center of mass of a system is at rest with respect to the origin of the coordinate system. The concept of center of mass in the form of the center of gravity was first introduced by the ancient Greek physicist, mathematician, and engineer Archimedes of Syracuse. He worked with simplified assumptions about gravity that amount to a uniform field, in work on floating bodies he demonstrated that the orientation of a floating object is the one that makes its center of mass as low as possible. He developed mathematical techniques for finding the centers of mass of objects of uniform density of various well-defined shapes, Newtons second law is reformulated with respect to the center of mass in Eulers first law. The center of mass is the point at the center of a distribution of mass in space that has the property that the weighted position vectors relative to this point sum to zero. In analogy to statistics, the center of mass is the location of a distribution of mass in space. Solving this equation for R yields the formula R =1 M ∑ i =1 n m i r i, solve this equation for the coordinates R to obtain R =1 M ∭ Q ρ r d V, where M is the total mass in the volume. If a continuous mass distribution has density, which means ρ is constant. The center of mass is not generally the point at which a plane separates the distribution of mass into two equal halves, in analogy with statistics, the median is not the same as the mean. The coordinates R of the center of mass of a system, P1 and P2, with masses m1. The percentages of mass at each point can be viewed as projective coordinates of the point R on this line, another way of interpreting the process here is the mechanical balancing of moments about an arbitrary point
26.
Small Solar System body
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A Small Solar System Body is an object in the Solar System that is neither a planet, nor a dwarf planet, nor a natural satellite. The term was first defined in 2006 by the International Astronomical Union, all other objects, except satellites, orbiting the Sun shall be referred to collectively as Small Solar System Bodies. These currently include most of the Solar System asteroids, most Trans-Neptunian Objects, comets and this encompasses all comets and all minor planets other than those that are dwarf planets. Except for the largest, which are in equilibrium, natural satellites differ from small Solar System bodies not in size. The orbits of satellites are not centered on the Sun, but around other Solar System objects such as planets, dwarf planets. Some of the larger small Solar System bodies may be reclassified in future as dwarf planets, the orbits of the vast majority of small Solar System bodies are located in two distinct areas, namely the asteroid belt and the Kuiper belt. These two belts possess some internal structure related to perturbations by the planets, and have fairly loosely defined boundaries. Other areas of the Solar System also encompass small bodies in smaller concentrations and these include the near-Earth asteroids, centaurs, comets, and scattered disc objects
27.
Minor-planet moon
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A minor-planet moon is an astronomical object that orbits a minor planet as its natural satellite. It is thought that many asteroids and Kuiper belt objects may possess moons, the first modern era mention of the possibility of an asteroid satellite was in connection with an occultation of the bright star Gamma Ceti by the minor planet Hebe in 1977. The observer, amateur astronomer Paul D. Maley, detected an unmistakable 0.5 second disappearance of this naked eye star from a site near Victoria, many hours later, several observations were reported in Mexico attributed to the occultation by Hebe itself. Although not confirmed this documents the first formally documented case of a companion of an asteroid. As of October 2016, there are over 300 minor planets known to have moons, in addition to the terms satellite and moon, the term binary is sometimes used for minor planets with moons, and triple for minor planets with two moons. If one object is much bigger it can be referred to as the primary, when binary minor planets are similar in size, the Minor Planet Center refers to them as binary companions instead of referring to the smaller body as a satellite. A good example of a true binary is the 90 Antiope system, small satellites are often referred to as moonlets. As of February 2017, over 330 moons of planets have been discovered. For example, in 1978, stellar occultation observations were claimed as evidence of a satellite for the asteroid 532 Herculina, however, later more-detailed imaging by the Hubble Telescope did not reveal a satellite, and the current consensus is that Herculina does not have a significant satellite. There were other reports of asteroids having companions in the following years. In 1993, the first asteroid moon was confirmed when the Galileo probe discovered the small Dactyl orbiting 243 Ida in the asteroid belt, the second was discovered around 45 Eugenia in 1998. In 2001,617 Patroclus and its same-sized companion Menoetius became the first known asteroids in the Jupiter trojans. The first trans-Neptunian binary after Pluto–Charon,1998 WW31, was resolved in 2002. Triple asteroids, or trinary asteroids, are known since 2005 and this was followed by the discovery of a second moon orbiting 45 Eugenia. Also in 2005, the Kuiper belt object Haumea was discovered to have two moons, making it the second KBO after Pluto known to have more than one moon, additionally,216 Kleopatra and 93 Minerva were discovered to be trinary asteroids in 2008 and 2009 respectively. Since the first few trinary asteroids were discovered, more continue to be discovered at a rate of one a year. Most recently discovered was a moon orbiting the belt asteroid 130 Elektra. List of multiple planets, The data about the populations of binary objects are still patchy