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.
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
3.
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
4.
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
5.
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
6.
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
7.
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
8.
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
9.
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
10.
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
11.
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
12.
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