1.
Proper orbital elements
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The proper orbital elements of an orbit are constants of motion of an object in space that remain practically unchanged over an astronomically long timescale. The term is used to describe the three quantities, proper semimajor axis, proper eccentricity, and proper inclination. The proper elements can be contrasted with the osculating Keplerian orbital elements observed at a time or epoch, such as the semi-major axis, eccentricity. Those osculating elements change in a quasi-periodic and predictable due to such effects as perturbations from planets or other bodies. In the Solar System, such changes usually occur on timescales of thousands of years, for most bodies, the osculating elements are relatively close to the proper elements because precession and perturbation effects are relatively small. For over 99% of asteroids in the belt, the differences are less than 0.02 AU,0.1. Nevertheless, this difference is non-negligible for any purposes where precision is of importance, to obtain proper elements for an object, one usually conducts a detailed simulation of its motion over timespans of several millions of years. Such a simulation must take into account many details of celestial mechanics including perturbations by the planets, subsequently, one extracts quantities from the simulation which remain unchanged over this long timespan, for example, the mean inclination, eccentricity, and semi-major axis. These are the orbital elements. Historically, various approximate analytic calculations were made, starting with those of Kiyotsugu Hirayama in the early 20th century, later analytic methods often included thousands of perturbing corrections for each particular object. At present the most prominent use of orbital elements is in the study of asteroid families. A Mars-crosser asteroid 132 Aethra is the lowest numbered asteroid to not have any proper orbital elements, the Determination of Asteroid Proper Elements, p. 603-612 in Asteroids III, University of Arizona Press. Latest calculations of proper elements for numbered minor planets at astDys
2.
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
3.
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
4.
Kirkwood gap
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A Kirkwood gap is a gap or dip in the distribution of the semi-major axes of the orbits of main-belt asteroids. They correspond to the locations of orbital resonances with Jupiter, for example, there are very few asteroids with semimajor axis near 2.50 AU, period 3.95 years, which would make three orbits for each orbit of Jupiter. Other orbital resonances correspond to orbital periods whose lengths are simple fractions of Jupiters, the weaker resonances lead only to a depletion of asteroids, while spikes in the histogram are often due to the presence of a prominent asteroid family. The orbital elements of the asteroids vary chaotically as a result, the 2,1 MMR has a few relatively stable islands within the resonance, however. These islands are depleted due to slow diffusion onto less stable orbits and this process, which has been linked to Jupiter and Saturn being near a 5,2 resonance, may have been more rapid when Jupiters and Saturns orbits were closer together. More recently, a small number of asteroids have been found to possess high eccentricity orbits which do lie within the Kirkwood gaps. Examples include the Alinda family and the Griqua family and these orbits slowly increase their eccentricity on a timescale of tens of millions of years, and will eventually break out of the resonance due to close encounters with a major planet. The most prominent Kirkwood gaps are located at mean orbital radii of,2.06 AU2.5 AU, home to the Alinda family of asteroids 2.82 AU2.95 AU3.27 AU, home to the Griqua family of asteroids. Weaker and/or narrower gaps are found at,1.9 AU2.25 AU2.33 AU2.71 AU3.03 AU3.075 AU3.47 AU3.7 AU. Orbital resonance Alinda family Griqua family Article on Kirkwood gaps at Wolframs scienceworld
5.
Asteroid
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Asteroids are minor planets, especially those of the inner Solar System. The larger ones have also been called planetoids and these terms have historically been applied to any astronomical object orbiting the Sun that did not show the disc of a planet and was not observed to have the characteristics of an active comet. As minor planets in the outer Solar System were discovered and found to have volatile-based surfaces that resemble those of comets, in this article, the term asteroid refers to the minor planets of the inner Solar System including those co-orbital with Jupiter. There are millions of asteroids, many thought to be the remnants of planetesimals. The large majority of known asteroids orbit in the belt between the orbits of Mars and Jupiter, or are co-orbital with Jupiter. However, other orbital families exist with significant populations, including the near-Earth objects, individual asteroids are classified by their characteristic spectra, with the majority falling into three main groups, C-type, M-type, and S-type. These were named after and are identified with carbon-rich, metallic. The size of asteroids varies greatly, some reaching as much as 1000 km across, asteroids are differentiated from comets and meteoroids. In the case of comets, the difference is one of composition, while asteroids are composed of mineral and rock, comets are composed of dust. In addition, asteroids formed closer to the sun, preventing the development of the aforementioned cometary ice, the difference between asteroids and meteoroids is mainly one of size, meteoroids have a diameter of less than one meter, whereas asteroids have a diameter of greater than one meter. Finally, meteoroids can be composed of either cometary or asteroidal materials, only one asteroid,4 Vesta, which has a relatively reflective surface, is normally visible to the naked eye, and this only in very dark skies when it is favorably positioned. Rarely, small asteroids passing close to Earth may be visible to the eye for a short time. As of March 2016, the Minor Planet Center had data on more than 1.3 million objects in the inner and outer Solar System, the United Nations declared June 30 as International Asteroid Day to educate the public about asteroids. The date of International Asteroid Day commemorates the anniversary of the Tunguska asteroid impact over Siberia, the first asteroid to be discovered, Ceres, was found in 1801 by Giuseppe Piazzi, and was originally considered to be a new planet. In the early half of the nineteenth century, the terms asteroid. Asteroid discovery methods have improved over the past two centuries. This task required that hand-drawn sky charts be prepared for all stars in the band down to an agreed-upon limit of faintness. On subsequent nights, the sky would be charted again and any moving object would, hopefully, the expected motion of the missing planet was about 30 seconds of arc per hour, readily discernible by observers
6.
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
7.
Asteroid belt
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The asteroid belt is the circumstellar disc in the Solar System located roughly between the orbits of the planets Mars and Jupiter. It is occupied by numerous irregularly shaped bodies called asteroids or minor planets, the asteroid belt is also termed the main asteroid belt or main belt to distinguish it from other asteroid populations in the Solar System such as near-Earth asteroids and trojan asteroids. About half the mass of the belt is contained in the four largest asteroids, Ceres, Vesta, Pallas, the total mass of the asteroid belt is approximately 4% that of the Moon, or 22% that of Pluto, and roughly twice that of Plutos moon Charon. Ceres, the belts only dwarf planet, is about 950 km in diameter, whereas Vesta, Pallas. The remaining bodies range down to the size of a dust particle, the asteroid material is so thinly distributed that numerous unmanned spacecraft have traversed it without incident. Nonetheless, collisions between large asteroids do occur, and these can form a family whose members have similar orbital characteristics. Individual asteroids within the belt are categorized by their spectra. The asteroid belt formed from the solar nebula as a group of planetesimals. Planetesimals are the precursors of the protoplanets. Between Mars and Jupiter, however, gravitational perturbations from Jupiter imbued the protoplanets with too much energy for them to accrete into a planet. Collisions became too violent, and instead of fusing together, the planetesimals, as a result,99. 9% of the asteroid belts original mass was lost in the first 100 million years of the Solar Systems history. Some fragments eventually found their way into the inner Solar System, Asteroid orbits continue to be appreciably perturbed whenever their period of revolution about the Sun forms an orbital resonance with Jupiter. At these orbital distances, a Kirkwood gap occurs as they are swept into other orbits. Classes of small Solar System bodies in other regions are the objects, the centaurs, the Kuiper belt objects, the scattered disc objects, the sednoids. On 22 January 2014, ESA scientists reported the detection, for the first definitive time, of water vapor on Ceres, the detection was made by using the far-infrared abilities of the Herschel Space Observatory. The finding was unexpected because comets, not asteroids, are considered to sprout jets. According to one of the scientists, The lines are becoming more and more blurred between comets and asteroids. This pattern, now known as the Titius–Bode law, predicted the semi-major axes of the six planets of the provided one allowed for a gap between the orbits of Mars and Jupiter
8.
Pallas family
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The Pallas or Palladian family of asteroids is a grouping of B-type asteroids at very high inclinations in the intermediate asteroid belt. It was first noted by Kiyotsugu Hirayama in 1928, the namesake of the family is 2 Pallas, an extremely large asteroid with a mean diameter of about 550 km. The remaining bodies are far smaller, the largest is 5222 Ioffe with a diameter of 22 km. This, along with the preponderance of the otherwise rare B spectral type among its members, another suspected Palladian is 3200 Phaethon, the parent body of the Geminid meteor shower. Kozai Secular perturbations of asteroids and comets In, Dynamics of the system, Proceedings of the Symposium, Tokyo, Japan. 1979, p. 231-236, Discussion, p.236,237, spectroscopic Properties of Asteroid Families, in Asteroids III, p. 633-643, University of Arizona Press
9.
Hungaria group
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The Hungaria family is a group of asteroids in the asteroid belt. The Hungaria asteroids orbit the Sun with an axis between 1.78 and 2.00 astronomical units. They are the innermost dense concentration of asteroids in the Solar System—the near-Earth asteroids are much more sparse—and derive their name from their largest member 434 Hungaria. The Hungaria asteroids typically share the following parameters, Semi-major axis between 1.78 and 2.00 AU Orbital period of approximately 2.5 years Low eccentricity of below 0. For comparison the majority of asteroids are in region of the asteroid belt. Most Hungarias are E-type asteroids, which means they have extremely bright enstatite surfaces, despite their high albedos, none can be seen with binoculars because they are far too small, the largest is only about 11 km in size. They are, however, the smallest asteroids that can regularly be glimpsed with amateur telescopes, the origin of the Hungaria group of asteroids is well known. Interior to this 4,1 resonance, asteroids in low inclination orbits are, unlike those outside the 4,1 Kirkwood gap, strongly influenced by the gravitational field of Mars. This has left a situation where the remaining concentration of asteroids inward of the 4,1 resonance lies at high inclination orbits. However, even at the present time in Solar System history some Hungaria asteroids cross the orbit of Mars and are still in the process of being ejected from the Solar System due to Marss influence. Long-term changes in the orbit of Mars are believed to be a factor in the current removal of Hungaria asteroids. This ultimately leads over millions of years to the formation of the short-lived Amor asteroids, the Hungaria asteroids are thought to be the remains of the hypothetical E-belt asteroid population. E-type asteroid Aubrite 2004 VD1764 Angelina 434 Hungaria 44 Nysa 55 Pandora 2867 Šteins
10.
Haumea family
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Calculations indicate that it is probably the only trans-Neptunian collisional family. The dispersion of the orbital elements of the members is a few percent or less. The diagram illustrates the orbital elements of the members of the family in relation to other TNOs, the objects common physical characteristics include neutral colours and deep infrared absorption features typical of water ice. Collisional formation of the family requires a progenitor some 1660 km in diameter, with a density of ~2.0 g/cm3, similar to Pluto, during the formational collision, Haumea lost roughly 20% of its mass, mostly ice, and became denser. The current orbits of the members of the family cannot be accounted for by the formational collision alone, to explain the spread of the orbital elements, an initial velocity dispersion of ~400 m/s is required, but such a velocity spread should have dispersed the fragments much further. This problem applies only to Haumea itself, the elements of all the other objects in the family require an initial velocity dispersion of ~140 m/s. Unlike the other members of the family, Haumea is in an orbit, near the 7,12 resonance with Neptune. Haumea may not be the only elongated, rapidly rotating, large object in the Kuiper belt, in 2002, Jewitt and Sheppard suggested that Varuna should be elongated, based on its rapid rotation. In the early history of the Solar System, the region would have contained many more objects than it does at present. Gravitational interaction with Neptune has since scattered many objects out of the Kuiper belt to the scattered disc, the presence of the collisional family hints that Haumea and its offspring might have originated in the scattered disc. In todays sparsely populated Kuiper belt, the chance of such a collision occurring over the age of the Solar System is less than 0.1 percent. Simulations suggest the probability of one family in the Solar System is approximately 50%. Over a timescale as long as a billion years, energy from the Sun would have reddened and darkened their surfaces and this high amount of amorphous ice on the surface confirms that the collisional event must have happened more than 100 million years ago. This result agrees with the studies and discards the assumption that the surfaces of these objects are young. Asteroid family Haumea Moons of Haumea http, //news. softpedia. com/news/New-Body-Parts-From-Kuiper-Belt-039-s-Haumea-95833. shtml
11.
Dwarf planet
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A dwarf planet is a planetary-mass object that is neither a planet nor a natural satellite. The International Astronomical Union currently recognizes five dwarf planets, Ceres, Pluto, Haumea, Makemake, another hundred or so known objects in the Solar System are suspected to be dwarf planets. Individual astronomers recognize several of these, and in August 2011 Mike Brown published a list of 390 candidate objects, Stern states that there are more than a dozen known dwarf planets. Only two of these bodies, Ceres and Pluto, have observed in enough detail to demonstrate that they actually fit the IAUs definition. The IAU accepted Eris as a dwarf planet because it is more massive than Pluto and they subsequently decided that unnamed trans-Neptunian objects with an absolute magnitude brighter than +1 are to be named under the assumption that they are dwarf planets. The classification of bodies in other systems with the characteristics of dwarf planets has not been addressed. Starting in 1801, astronomers discovered Ceres and other bodies between Mars and Jupiter which were for some decades considered to be planets. Between then and around 1851, when the number of planets had reached 23, astronomers started using the asteroid for the smaller bodies. With the discovery of Pluto in 1930, most astronomers considered the Solar System to have nine planets and it was roughly one-twentieth the mass of Mercury, which made Pluto by far the smallest planet. Although it was more than ten times as massive as the largest object in the asteroid belt, Ceres. In the 1990s, astronomers began to find objects in the region of space as Pluto. Many of these shared several of Plutos key orbital characteristics, and Pluto started being seen as the largest member of a new class of objects and this led some astronomers to stop referring to Pluto as a planet. Several terms, including subplanet and planetoid, started to be used for the now known as dwarf planets. By 2005, three trans-Neptunian objects comparable in size to Pluto had been reported and it became clear that either they would also have to be classified as planets, or Pluto would have to be reclassified. Astronomers were also confident that more objects as large as Pluto would be discovered, Eris was discovered in January 2005, it was thought to be slightly larger than Pluto, and some reports informally referred to it as the tenth planet. As a consequence, the became a matter of intense debate during the IAU General Assembly in August 2006. The IAUs initial draft proposal included Charon, Eris, and Ceres in the list of planets, dropping Charon from the list, the new proposal also removed Pluto, Ceres, and Eris, because they have not cleared their orbits. The IAUs final Resolution 5A preserved this three-category system for the bodies orbiting the Sun
12.
Haumea
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Haumea, minor-planet designation 136108 Haumea, is a dwarf planet located beyond Neptunes orbit. On September 17,2008, it was recognized as a planet by the International Astronomical Union and named after Haumea. Haumeas mass is about one-third that of Pluto, and 1/1400 that of Earth, although its shape has not been directly observed, calculations from its light curve indicate that it is a triaxial ellipsoid, with its major axis twice as long as its minor. Its gravity is thought to be sufficient for it to have relaxed into hydrostatic equilibrium, two teams claim credit for the discovery of Haumea. Mike Brown and his team at Caltech discovered Haumea in December 2004 on images they had taken on May 6,2004, on July 20,2005, they published an online abstract of a report intended to announce the discovery at a conference in September 2005. At around this time, José Luis Ortiz Moreno and his team at the Instituto de Astrofísica de Andalucía at Sierra Nevada Observatory in Spain found Haumea on images taken on March 7–10,2003. Ortiz emailed the Minor Planet Center with their discovery on the night of July 27,2005, Ortiz later admitted he had accessed the Caltech observation logs but denied any wrongdoing, stating he was merely verifying whether they had discovered a new object. However, the IAU announcement on September 17,2008, that Haumea had been accepted as a dwarf planet, did not mention a discoverer. Until it was given a permanent name, the Caltech discovery team used the nickname Santa among themselves, because they had discovered Haumea on December 28,2004, the Spanish team were the first to file a claim for discovery to the Minor Planet Center, in July 2005. On July 29,2005, Haumea was given the provisional designation 2003 EL61, on September 7,2006, it was numbered and admitted into the official minor planet catalogue as 2003 EL61. The names were proposed by David Rabinowitz of the Caltech team, Haumea is the matron goddess of the island of Hawaiʻi, where the Mauna Kea Observatory is located. The two known moons, also believed to have formed in this manner, are named after two of Haumeas daughters, Hiʻiaka and Nāmaka. The proposal by the Ortiz team, Ataecina, did not meet IAU naming requirements, Haumea is a plutoid, a dwarf planet beyond Neptunes orbit. Haumea appears to have an ellipsoid shape resulting its rapid rotation complicated by tidal interactions with its moons. This contrasts with the simpler oblate shape typically assumed by less rapidly rotating astronomical bodies such as the Earth, in other words, Haumea is spinning so fast that if it spun much faster these bulges would distort into a dumbbell shape and split the planet in two. Haumea was initially listed as a classical Kuiper belt object in 2006 by the Minor Planet Center, the nominal trajectory suggests that it is in the weak 7,12 resonance with Neptune, because its perihelion distance of 35 AU is near the limit of stability with Neptune. There are precovery images of Haumea dating back to March 22,1955 from the Palomar Mountain Digitized Sky Survey, further observations of the orbit will be required to verify its dynamic status. Haumea has a period of 284 Earth years, a perihelion of 35 AU
13.
Trojan (astronomy)
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In astronomy, a trojan is a minor planet or moon that shares the orbit of a planet or larger moon, wherein the trojan remains in the same, stable position relative to the larger object. In particular, a trojan remains near one of the two points of stability – designated L4 and L5 – which lie approximately 60° ahead of and behind the larger body. Trojan points make up two of five types of Lagrangian points, and a trojan is a type of Lagrangian object and they are one type of co-orbital object. In this arrangement, the star and the smaller planet orbit about their common barycenter. A much smaller mass located at one of the Lagrangian points is subject to a gravitational force that acts through this barycenter. Hence the object can orbit around the barycenter with the orbital period as the planet. The Jupiter trojans account for most known trojans in the Solar System and they are divided into the Greek camp in front of and the Trojan camp trailing behind Jupiter in their orbit. Numerical calculations of the dynamics involved indicate that Saturn and Uranus probably do not have any primordial trojans. The discovery of the first Earth trojan,2010 TK7, was announced by NASA in 2011, unlike trojan minor planets that share the orbit with a planet, a trojan moon is a moon orbiting near the trojan point of another, larger moon. All known trojan moons are part of the Saturn system, telesto and Calypso are trojans of Tethys, and Helene and Polydeuces of Dione. There is also a concept of a trojan planet, a planet that orbits at the trojan point of another, larger planet. Such a pair of co-orbital exoplanets was already thought to exist in another star system, in 1772, the Italian–French mathematician and astronomer Joseph-Louis Lagrange obtained two constant-pattern solutions of the general three-body problem. In the restricted problem, with one mass negligible, the five possible positions of that mass are now termed Lagrangian points. The term trojan originally referred to the asteroids that orbit close to the Lagrangian points of Jupiter. These have long been named after characters from the Trojan War of Greek mythology, there are two exceptions, which were named before the convention was put in place, the Greek-themed 617 Patroclus and the Trojan-themed 624 Hektor, which were assigned to the wrong sides. Astronomers estimate that the Jupiter trojans are about as numerous as the asteroids of the asteroid belt, later on, objects were found orbiting near the Lagrangian points of Neptune, Mars, Earth, Uranus, and Venus. Minor planets at the Lagrangian points of other than Jupiter may be called Lagrangian minor planets. 17 Neptune trojans are known, but large Neptune trojans are expected to outnumber the large Jupiter trojans by an order of magnitude,2010 TK7 was confirmed to be the first known Earth trojan in 2011
14.
Vesta family
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The Vesta or Vestian family of asteroids is a large and prominent grouping of mostly V-type asteroids in the inner asteroid belt in the vicinity of 4 Vesta. The Vestian asteroids consist of 4 Vesta, the second-most-massive of all asteroids, and many small asteroids below 10 km diameter. The brightest of these,1929 Kollaa and 2045 Peking, have a magnitude of 12.2. The family originated from an impact on asteroid 4 Vesta, with the giant south-polar crater the likely impact site, the family are thought to be the source of the HED meteorites. At the present epoch, the range of osculating orbital elements of these members is The Zappala 1995 analysis found 235 core members. A search of a recent proper-element database for 96944 minor planets in 2005 yielded 6051 objects lying within the Vesta-family region as per the first table above, Spectroscopic analyses have shown that some of the largest Vestians are in fact interlopers. They are not of the V or J spectral class, but have similar elements by coincidence. These include 306 Unitas,442 Eichsfeldia,1697 Koskenniemi,1781 Van Biesbroeck,2024 McLaughlin,2029 Binomi,2086 Newell,2346 Lilio, phase II of the Small Main-Belt Asteroid Spectroscopic Survey, Icarus Vo. Proper elements for 96944 numbered minor planets
15.
Hygiea family
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The Hygiea or Hygiean family of asteroids is a grouping of dark, carbonaceous C-type and B-type asteroids in outer asteroid belt, the largest member of which is 10 Hygiea. About 1% of all asteroids in the asteroid belt belong to this family. By far the largest member is 10 Hygiea, a 400 km diameter C-type asteroid that is the fourth largest in the belt, the remaining members are much smaller so Hygiea contains about 94–98% of the mass in the family. The two next largest members are 333 Badenia, and 538 Friederike, both just over 70 km in diameter, after that, the remaining members have diameters of less than 30 km. The Hygiea family is thought to be of the cratering type, however, the two 70-kilometer-diameter bodies are still surprisingly large to have been excavated in an impact that did not disrupt the parent body. They may be interlopers despite having a similar type to Hygiea. The family contains a significant number of objects of the otherwise rare B spectral type, the largest of these is the previously mentioned 538 Friederike. There are some indications that this family is quite old. This would give about 1% of all asteroids in the asteroid belt and this family contains quite a large number of identified interlopers. In fact, some of the asteroids of the C spectral type are probably interlopers as well. Possible candidates include 333 Badenia and 538 Friederike, based on their large size for cratering family members. 52 Europa, a very large 300 km diameter asteroid orbits nearby with an inclination of 6. 37°, and was sometimes considered part of the Hygiea family in the past. A better sampling of asteroids in the area in recent years has shown that it orbits well beyond the Hygiea family clump. Asteroid Families, Old and Young, ASP Conference Series, Vol.107, rotationally Resolved Spectra of 10 Hygiea and a Spectroscopic Study of the Hygiea Family, Icarus, Vol.152, p.117. On the Size Distribution of Asteroid Families, The Role of Geometry, Icarus, Vol.141, proper elements for 96944 numbered minor planets
16.
Massalia family
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The Massalia or Massalian family of asteroids is a grouping of S-type asteroids in the inner main belt at very low inclination. About 0. 8% of known asteroids belong to this family and this is a definite cratering family consisting of 20 Massalia and a mass of small fragments excavated from Massalias surface by an impact. Massalia is by far the largest member with a diameter of about 150 km, the mass of all the small members is negligible, less than about 1%, compared to Massalia. The family is fairly young, estimated to have created by an impact 150 to 200 million years ago. The bodies in the lobes tend to be smaller on average than those in the central region and it has been shown that this structure is likely caused by slow drift of the semi-major axis caused by the Yarkovsky and YORP effects. Details of the lobes were used to calculate the age of the family, a strong 1,2 orbital resonance with Mars crosses the family at 2.42 AU, and appears responsible for some leakage of family members away from the area into higher inclination orbits. The Massalia family or a recent minor collision within it may be the source for the prominent α dust band, the Massalian asteroids are located at very low inclinations, straddling the 1,2 resonances with Mars. This would give about 0. 8% of all main belt asteroids, a number of interlopers have been identified, which share the same orbital elements as the true family members, but cannot have come from the same cratering event because of spectral differences. Muchachos is larger than any of the family members apart from Massalia itself
17.
Flora family
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The Flora or Florian family of asteroids is a large grouping of S-type asteroids in the inner main belt, whose origin and properties are relatively poorly understood at present. Roughly 4–5% of all main belt asteroids belong to this family, the Flora family of asteroids may be the source of the Chicxulub impactor, the likely culprit in the extinction of the dinosaurs. The largest member is 8 Flora, which measures 140 km in diameter, nevertheless, the parent body was almost certainly disrupted by the impact/s that formed the family, and Flora is probably a gravitational aggregate of most of the pieces. 43 Ariadne makes up much of the mass, with the remaining family members being fairly small. A noticeable fraction of the parent body has been lost from the family since the original impact, for example, it has been estimated that Flora contains only about 57% of the parent bodys mass, but about 80% of the mass in the present family. The Flora family is broad and gradually fades into the background population in such a way that its boundaries are very poorly defined. There are also several non-uniformities or lobes within the family, one cause of which may have been later secondary collisions between family members, hence, it is a classical example of a so-called asteroid clan. Curiously, the largest members,8 Flora and 43 Ariadne, are located near the edge of the family, the reason for this unusual mass distribution within the family is unknown at present. 951 Gaspra, a core family member was visited by the Galileo spacecraft on its way to Jupiter. Studies of Gaspra suggests that the age is of the order of 200 million years. The Flora family members are considered candidates for being the parent bodies of the L chondrite meteorites. The Flora family was one of the five original Hirayama families that were first identified and it has a high number of early discovered members both because S-type asteroids tend to have high albedo, and because it is the closest major asteroid grouping to Earth. A HCM numerical analysis determined a large group of family members, whose proper orbital elements lie in the approximate ranges The boundaries of the family are, however. At the present epoch, the range of osculating orbital elements of these members is Zappalas 1995 analysis found 604 core members. A search of a recent proper element database for 96944 minor planets in 2005 yielded 7438 objects lying within the region defined by the first table above. However, this includes parts of the Vesta and Nysa families in the corners so that a more likely membership estimate is 4000–5000 objects. This means that the Flora family represents 4–5% of all main belt asteroids, because of the high background density of asteroids in this part of space, one might expect that a great number of interlopers would be present. This is because interlopers are hard to distinguish family members because the family is of the same spectral type that dominates the inner main belt overall
18.
Planetary differentiation
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Such a process tends to create a core and mantle. Sometimes a chemically distinct crust forms on top of the mantle, the process of planetary differentiation has occurred on planets, dwarf planets, the asteroid 4 Vesta, and natural satellites. When the Sun ignited in the nebula, hydrogen, helium. The solar wind and radiation pressure forced these low-density materials away from the Sun, rocks, and the elements comprising them, were stripped of their early atmospheres, but themselves remained, to accumulate into protoplanets. Protoplanets had higher concentrations of radioactive elements early in their history, heating due to radioactivity, impacts, and gravitational pressure melted parts of protoplanets as they grew toward being planets. In melted zones, it was possible for denser materials to sink towards the center, the compositions of some meteorites show that differentiation also took place in some asteroids, that are parental bodies for meteoroids. The short-lived radioactive isotope 26Al was probably the source of heat. When protoplanets accrete more material, the energy of impact causes local heating, in addition to this temporary heating, the gravitational force in a sufficiently large body creates pressures and temperatures which are sufficient to melt some of the materials. This allows chemical reactions and density differences to mix and separate materials, on Earth, a large piece of molten iron is sufficiently denser than continental crust material to force its way down through the crust to the mantle. In the outer Solar System a similar process may take place but with lighter materials, they may be such as methane, water as liquid or ice. High-density materials tend to sink through lighter materials and this tendency is affected by the relative structural strengths, but such strength is reduced at temperatures where both materials are plastic or molten. Iron, the most common element that is likely to form a dense molten metal phase. With it, many siderophile elements also travel downward, however, not all heavy elements make this transition as some chalcophilic heavy elements bind into low-density silicate and oxide compounds, which differentiate in the opposite direction. Even lighter still are the watery liquid hydrosphere and the gaseous, lighter materials tend to rise through material with a higher density. They may take on dome-shaped forms called diapirs when doing so, on Earth, salt domes are salt diapirs in the crust which rise through surrounding rock. Diapirs of molten low-density silicate rocks such as granite are abundant in the Earths upper crust, the hydrated, low-density serpentinite formed by alteration of mantle material at subduction zones can also rise to the surface as diapirs. Other materials do likewise, a low-temperature, near-surface example is provided by mud volcanos and it is also high in uranium and thorium. Magma in the Earth is produced by melting of a source rock
19.
Yarkovsky effect
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The Yarkovsky effect is a force acting on a rotating body in space caused by the anisotropic emission of thermal photons, which carry momentum. It is usually considered in relation to meteoroids or small asteroids, the effect was discovered by the Russian civil engineer Ivan Osipovich Yarkovsky, who worked on scientific problems in his spare time. Yarkovskys insight would have been forgotten had it not been for the Estonian astronomer Ernst J. Öpik, decades later, Öpik, recalling the pamphlet from memory, discussed the possible importance of the Yarkovsky effect on movement of meteoroids about the Solar System. The Yarkovsky effect is a consequence of the fact that change in the temperature of an object warmed by radiation lags behind changes in the incoming radiation. That is, the surface of the object takes time to warm when first illuminated. In general there are two components to the effect, Diurnal effect, On a rotating body illuminated by the Sun, the surface is warmed by radiation during the day. This results in a difference between the directions of absorption and re-emission of radiation, which yields a net force along the direction of motion of the orbit. If the object is a rotator, the force is in the direction of motion of the orbit, and causes the semi-major axis of the orbit to increase steadily. The diurnal effect is the dominant component for bodies with greater than about 100 m. Seasonal effect, This is easiest to understand for the case of a non-rotating body orbiting the Sun. As it travels around its orbit, the hemisphere which has been heated over a long preceding time period is invariably in the direction of orbital motion. The excess of radiation in this direction causes a braking force which always causes spiraling inward toward the Sun. In practice, for rotating bodies, this effect increases along with the axial tilt. It dominates only if the effect is small enough. This may occur because of rapid rotation, small size or an axial tilt close to 90°. The seasonal effect is important for smaller asteroid fragments, provided their surfaces are not covered by an insulating regolith layer. Additionally, on long timescales over which the spin axis of the body may be repeatedly changed due to collisions. In general, the effect is dependent, and will affect the semi-major axis of smaller asteroids
20.
Orbital resonance
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Orbital resonances greatly enhance the mutual gravitational influence of the bodies, i. e. their ability to alter or constrain each others orbits. In most cases, this results in an interaction, in which the bodies exchange momentum. Under some circumstances, a resonant system can be stable and self-correcting, examples are the 1,2,4 resonance of Jupiters moons Ganymede, Europa and Io, and the 2,3 resonance between Pluto and Neptune. Unstable resonances with Saturns inner moons give rise to gaps in the rings of Saturn, thus the 2,3 ratio above means Pluto completes two orbits in the time it takes Neptune to complete three. In the case of resonance relationships between three or more bodies, either type of ratio may be used and the type of ratio will be specified. Since the discovery of Newtons law of gravitation in the 17th century. The stable orbits that arise in a two-body approximation ignore the influence of other bodies and it was Laplace who found the first answers explaining the remarkable dance of the Galilean moons. It is fair to say that this field of study has remained very active since then. Before Newton, there was consideration of ratios and proportions in orbital motions, in what was called the music of the spheres. In general, a resonance may involve one or any combination of the orbit parameters. Act on any scale from short term, commensurable with the orbit periods, to secular. Lead to either long-term stabilization of the orbits or be the cause of their destabilization, a mean-motion orbital resonance occurs when two bodies have periods of revolution that are a simple integer ratio of each other. Depending on the details, this can either stabilize or destabilize the orbit, stabilization may occur when the two bodies move in such a synchronised fashion that they never closely approach. For instance, The orbits of Pluto and the plutinos are stable, despite crossing that of the much larger Neptune, the resonance ensures that, when they approach perihelion and Neptunes orbit, Neptune is consistently distant. Other Neptune-crossing bodies that were not in resonance were ejected from that region by strong perturbations due to Neptune. There are also smaller but significant groups of resonant trans-Neptunian objects occupying the 1,1,3,5,4,7,1,2 and 2,5 resonances, among others, with respect to Neptune. In the asteroid belt beyond 3.5 AU from the Sun, orbital resonances can also destabilize one of the orbits. For small bodies, destabilization is actually far more likely, for instance, In the asteroid belt within 3.5 AU from the Sun, the major mean-motion resonances with Jupiter are locations of gaps in the asteroid distribution, the Kirkwood gaps
21.
9 Metis
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For the moon of Jupiter, see Metis. 9 Metis is one of the larger main-belt asteroids and it is composed of silicates and metallic nickel-iron, and may be the core remnant of a large asteroid that was destroyed by an ancient collision. Metis is estimated to contain just under half a percent of the mass of the asteroid belt. Metis was discovered by Andrew Graham on 25 April 1848, at Markree Observatory in Ireland and its name comes from the mythological Metis, a Titaness and Oceanid, daughter of Tethys and Oceanus. The name Thetis was also considered and rejected, Metis direction of rotation is unknown at present, due to ambiguous data. Lightcurve analysis indicates that the Metidian pole points towards ecliptic coordinates = or with a 10° uncertainty. The equivalent equatorial coordinates are = or and this gives an axial tilt of 72° or 76°, respectively. Hubble space telescope images and lightcurve analyses are in agreement that Metis has an elongated shape with one pointed. Radar observations suggest the presence of a significant flat area, in agreement with the model from lightcurves. The Metidian surface composition has been estimated as 30–40% metal-bearing olivine, light curve data on Metis led to an assumption that it could have a satellite. However, subsequent observations failed to confirm this, later searches with the Hubble Space Telescope in 1993 found no satellites. In 2007, Baer and Chesley estimated Metis to have a mass of 1. 6-to-2. 5×1019 kg and this would give this stony asteroid a density of about 6 g/cm³. A more recent estimate by Baer suggests it has a mass of ×1019 kg, Metis appears to be more dense than most other asteroids with a diameter close to 200 km. This may support the theory that Metis is the remnant of a large evolved asteroid for which 90% of the original mass has been lost. Metis passed within 0. 034AU, or 5,000,000 kilometres, the putative parent body is estimated to have been 300 to 600 km in diameter and differentiated. Metis would be the intact core remnant, and Amalthea a fragment of the mantle. Coincidentally, both Metis and Amalthea have namesakes among Jupiters inner moons, in 1984 an occultation of a star produced seven chords that Kristensen used to derive an ellipsoidal profile of 210x170km. On 6 August 1989, Metis occulted a magnitude 8.7 star producing five chords suggesting a diameter of 173.5 km, observations of an occultation on 11 February 2006, produced only two chords indicating a minimum diameter 156 km
22.
Iron meteorite
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Iron meteorites are meteorites that consist overwhelmingly of an iron–nickel alloy known as meteoric iron that usually consists of two mineral phases, kamacite and taenite. Iron meteorites originate from planetary cores of planetesimals, the iron found in iron meteorites was one of the earliest sources of usable iron available to humans, before the development of smelting that signaled the beginning of the iron age. Although they are rare compared to the stony meteorites, comprising only about 5. 7% of witnessed falls. This is due to several factors, They are easily recognized as unusual even by laymen, modern-day searches for meteorites in deserts and Antarctica yield a much more representative sample of meteorites overall. They are much more resistant to weathering and they are much more likely to survive atmospheric entry, and are more resistant to the resulting ablation. Hence, they are likely to be found as large pieces. They are able to be even when buried by use of surface metal detecting equipment. Because they are denser than stony meteorites, iron meteorites also account for almost 90% of the mass of all known meteorites. All the largest known meteorites are of type, including the largest—the Hoba meteorite. Iron meteorites have been linked to M-type asteroids because both have similar characteristics in the visible and near-infrared. Iron meteorites are thought to be the fragments of the cores of larger ancient asteroids that have been shattered by impacts, the IIE iron meteorites may be a notable exception, in that they probably originate from the crust of S-type asteroid 6 Hebe. Chemical and isotope analysis indicates that at least about 50 distinct parent bodies were involved and this implies that there were once at least this many large, differentiated, asteroids in the asteroid belt – many more than today. The overwhelming bulk of these consists of the FeNi-alloys kamacite and taenite. Minor minerals, when occurring, often form rounded nodules of troilite or graphite, schreibersite and troilite also occur as plate shaped inclusions, which show up on cut surfaces as cm-long and mm-thick lamellae. The troilite plates are called Reichenbach lamellae, the chemical composition is dominated by the elements Fe, Ni and Co, which make up more than 95%. Ni is always present, the concentration is always higher than 5%. Iron meteorites were historically used for their meteoric iron, which was forged into cultural objects, with the advent of smelting and the beginning of the iron age the importance of iron meteorites as a resource decreased, at least in those cultures that developed those techniques. The Inuit used the Cape York meteorite for a longer time
23.
Orbital elements
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Orbital elements are the parameters required to uniquely identify a specific orbit. In celestial mechanics these elements are considered in classical two-body systems. There are many different ways to describe the same orbit. A real orbit changes over time due to perturbations by other objects. A Keplerian orbit is merely an idealized, mathematical approximation at a particular time, the traditional orbital elements are the six Keplerian elements, after Johannes Kepler and his laws of planetary motion. When viewed from a frame, two orbiting bodies trace out distinct trajectories. Each of these trajectories has its focus at the center of mass. When viewed from a non-inertial frame centred on one of the bodies, only the trajectory of the body is apparent. An orbit has two sets of Keplerian elements depending on which body is used as the point of reference, the reference body is called the primary, the other body is called the secondary. The primary does not necessarily possess more mass than the secondary, and even when the bodies are of equal mass, the orbital elements depend on the choice of the primary. The main two elements that define the shape and size of the ellipse, Eccentricity —shape of the ellipse, semimajor axis —the sum of the periapsis and apoapsis distances divided by two. For circular orbits, the axis is the distance between the centers of the bodies, not the distance of the bodies from the center of mass. For paraboles or hyperboles, this is infinite, tilt angle is measured perpendicular to line of intersection between orbital plane and reference plane. Any three points on an ellipse will define the ellipse orbital plane, the plane and the ellipse are both two-dimensional objects defined in three-dimensional space. Longitude of the ascending node —horizontally orients the ascending node of the ellipse with respect to the reference frames vernal point, and finally, Argument of periapsis defines the orientation of the ellipse in the orbital plane, as an angle measured from the ascending node to the periapsis. True anomaly at epoch defines the position of the body along the ellipse at a specific time. The mean anomaly is a mathematically convenient angle which varies linearly with time and it can be converted into the true anomaly ν, which does represent the real geometric angle in the plane of the ellipse, between periapsis and the position of the orbiting object at any given time. Thus, the anomaly is shown as the red angle ν in the diagram
24.
Japan
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Japan is a sovereign island nation in Eastern Asia. Located in the Pacific Ocean, it lies off the eastern coast of the Asia Mainland and stretches from the Sea of Okhotsk in the north to the East China Sea, the kanji that make up Japans name mean sun origin. 日 can be read as ni and means sun while 本 can be read as hon, or pon, Japan is often referred to by the famous epithet Land of the Rising Sun in reference to its Japanese name. Japan is an archipelago consisting of about 6,852 islands. The four largest are Honshu, Hokkaido, Kyushu and Shikoku, the country is divided into 47 prefectures in eight regions. Hokkaido being the northernmost prefecture and Okinawa being the southernmost one, the population of 127 million is the worlds tenth largest. Japanese people make up 98. 5% of Japans total population, approximately 9.1 million people live in the city of Tokyo, the capital of Japan. Archaeological research indicates that Japan was inhabited as early as the Upper Paleolithic period, the first written mention of Japan is in Chinese history texts from the 1st century AD. Influence from other regions, mainly China, followed by periods of isolation, from the 12th century until 1868, Japan was ruled by successive feudal military shoguns who ruled in the name of the Emperor. Japan entered into a period of isolation in the early 17th century. The Second Sino-Japanese War of 1937 expanded into part of World War II in 1941, which came to an end in 1945 following the bombings of Hiroshima and Nagasaki. Japan is a member of the UN, the OECD, the G7, the G8, the country has the worlds third-largest economy by nominal GDP and the worlds fourth-largest economy by purchasing power parity. It is also the worlds fourth-largest exporter and fourth-largest importer, although Japan has officially renounced its right to declare war, it maintains a modern military with the worlds eighth-largest military budget, used for self-defense and peacekeeping roles. Japan is a country with a very high standard of living. Its population enjoys the highest life expectancy and the third lowest infant mortality rate in the world, in ancient China, Japan was called Wo 倭. It was mentioned in the third century Chinese historical text Records of the Three Kingdoms in the section for the Wei kingdom, Wa became disliked because it has the connotation of the character 矮, meaning dwarf. The 倭 kanji has been replaced with the homophone Wa, meaning harmony, the Japanese word for Japan is 日本, which is pronounced Nippon or Nihon and literally means the origin of the sun. The earliest record of the name Nihon appears in the Chinese historical records of the Tang dynasty, at the start of the seventh century, a delegation from Japan introduced their country as Nihon
25.
Astronomer
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An astronomer is a scientist in the field of astronomy who concentrates their studies on a specific question or field outside of the scope of Earth. They look at stars, planets, moons, comets and galaxies, as well as other celestial objects — either in observational astronomy. Examples of topics or fields astronomers work on include, planetary science, solar astronomy, there are also related but distinct subjects like physical cosmology which studies the Universe as a whole. Astronomers usually fit into two types, Observational astronomers make direct observations of planets, stars and galaxies, and analyze the data, theoretical astronomers create and investigate models of things that cannot be observed. They use this data to create models or simulations to theorize how different celestial bodies work, there are further subcategories inside these two main branches of astronomy such as planetary astronomy, galactic astronomy or physical cosmology. Today, that distinction has disappeared and the terms astronomer. Professional astronomers are highly educated individuals who typically have a Ph. D. in physics or astronomy and are employed by research institutions or universities. They spend the majority of their time working on research, although quite often have other duties such as teaching, building instruments. The number of astronomers in the United States is actually quite small. The American Astronomical Society, which is the organization of professional astronomers in North America, has approximately 7,000 members. This number includes scientists from other such as physics, geology. The International Astronomical Union comprises almost 10,145 members from 70 different countries who are involved in research at the Ph. D. level. Before CCDs, photographic plates were a method of observation. Modern astronomers spend relatively little time at telescopes usually just a few weeks per year, analysis of observed phenomena, along with making predictions as to the causes of what they observe, takes the majority of observational astronomers time. Astronomers who serve as faculty spend much of their time teaching undergraduate and graduate classes, most universities also have outreach programs including public telescope time and sometimes planetariums as a public service to encourage interest in the field. Those who become astronomers usually have a background in maths, sciences. Taking courses that teach how to research, write and present papers are also invaluable, in college/university most astronomers get a Ph. D. in astronomy or physics. Keeping in mind how few there are it is understood that graduate schools in this field are very competitive
26.
Hierarchical clustering
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In data mining and statistics, hierarchical clustering is a method of cluster analysis which seeks to build a hierarchy of clusters. Divisive, This is a top down approach, all start in one cluster. In general, the merges and splits are determined in a greedy manner, the results of hierarchical clustering are usually presented in a dendrogram. In the general case, the complexity of agglomerative clustering is O, divisive clustering with an exhaustive search is O, which is even worse. However, for special cases, optimal efficient agglomerative methods ) are known, SLINK for single-linkage. In order to decide which clusters should be combined, or where a cluster should be split, the choice of an appropriate metric will influence the shape of the clusters, as some elements may be close to one another according to one distance and farther away according to another. Some commonly used metrics for hierarchical clustering are, For text or other non-numeric data, the linkage criterion determines the distance between sets of observations as a function of the pairwise distances between observations. Some commonly used linkage criteria between two sets of observations A and B are, where d is the chosen metric, other linkage criteria include, The sum of all intra-cluster variance. The decrease in variance for the cluster being merged, the probability that candidate clusters spawn from the same distribution function. The product of in-degree and out-degree on a k-nearest-neighbour graph, the increment of some cluster descriptor after merging two clusters. Hierarchical clustering has the advantage that any valid measure of distance can be used. In fact, the observations themselves are not required, all that is used is a matrix of distances, for example, suppose this data is to be clustered, and the Euclidean distance is the distance metric. Cutting the tree at a height will give a partitioning clustering at a selected precision. In this example, cutting after the row of the dendrogram will yield clusters. Cutting after the row will yield clusters, which is a coarser clustering. The hierarchical clustering dendrogram would be as such, This method builds the hierarchy from the elements by progressively merging clusters. In our example, we have six elements and, the first step is to determine which elements to merge in a cluster. Usually, we want to take the two closest elements, according to the chosen distance, optionally, one can also construct a distance matrix at this stage, where the number in the i-th row j-th column is the distance between the i-th and j-th elements
27.
Homogeneity and heterogeneity
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Homogeneity and heterogeneity are concepts often used in the sciences and statistics relating to the uniformity in a substance or organism. A material or image that is homogeneous is uniform in composition or character, the alternate spellings homogenous and heterogenous are commonly, but incorrectly, used. Heterogenous meanwhile is a term primarily confined to pathology which refers to the property of an object in the body having its origin outside the body, the concepts are the same to every level of complexity, from atoms to populations of animals or people, and galaxies. Hence, an element may be homogeneous on a larger scale and this is known as an effective medium approach, or effective medium approximations. Various disciplines understand heterogeneity, or being heterogeneous, in different ways, heterogeneous solids, liquids, and gases may be made homogeneous by melting, stirring, or by allowing time to pass for diffusion to distribute the molecules evenly. For example, adding dye to water will create a solution at first. Entropy allows for heterogeneous substances to become homogeneous over time, a heterogeneous mixture is a mixture of two or more compounds. Examples are, mixtures of sand and water or sand and iron filings, a rock, water and oil, a salad, trail mix. A mixture can be determined to be homogeneous when everything is settled and equal, various models have been proposed to model the concentrations in different phases. The phenomena to be considered are mass rates and reaction, homogeneous reactions are chemical reactions in which the reactants and products are in the same phase, while heterogeneous reactions have reactants in two or more phases. Reactions that take place on the surface of a catalyst of a different phase are also heterogeneous, a reaction between two gases or two miscible liquids is homogeneous. A reaction between a gas and a liquid, a gas and a solid or a liquid and a solid is heterogeneous, earth is a heterogeneous substance in many aspects. E. g. rocks are inherently heterogeneous, usually occurring at the micro-scale and mini-scale, in algebra, homogeneous polynomials have the same number of factors of a given kind. This can cause problems in attempts to summarize the meaning of the studies, in medicine and genetics, a genetic or allelic heterogeneous condition is one where the same disease or condition can be caused, or contributed to, by several factors. In the case of genetics, varying different genes or alleles, in cancer research, cancer cell heterogeneity is thought to be one of the underlying reasons that make treatment of cancer difficult. In physics, heterogeneous is understood to mean having physical properties that vary within the medium, in sociology, heterogeneous may refer to a society or group that includes individuals of differing ethnicities, cultural backgrounds, sexes, or ages. Academic Press Dictionary of Science and Technology
28.
Ceres (dwarf planet)
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Ceres is the largest object in the asteroid belt that lies between the orbits of Mars and Jupiter. Its diameter is approximately 945 kilometers, making it the largest of the planets within the orbit of Neptune. The 33rd-largest known body in the Solar System, it is the dwarf planet within the orbit of Neptune. Composed of rock and ice, Ceres is estimated to approximately one third of the mass of the entire asteroid belt. Ceres is the object in the asteroid belt known to be rounded by its own gravity. From Earth, the apparent magnitude of Ceres ranges from 6.7 to 9.3, Ceres was the first asteroid discovered, by Giuseppe Piazzi at Palermo on 1 January 1801. It was originally considered a planet, but was reclassified as an asteroid in the 1850s after many other objects in similar orbits were discovered. Ceres appears to be differentiated into a core and icy mantle. The surface is probably a mixture of ice and various hydrated minerals such as carbonates. In January 2014, emissions of water vapor were detected from several regions of Ceres and this was unexpected, because large bodies in the asteroid belt typically do not emit vapor, a hallmark of comets. The robotic NASA spacecraft Dawn entered orbit around Ceres on 6 March 2015, pictures with a resolution previously unattained were taken during imaging sessions starting in January 2015 as Dawn approached Ceres, showing a cratered surface. Two distinct bright spots inside a crater were seen in a 19 February 2015 image, on 11 May 2015, NASA released a higher-resolution image showing that, instead of one or two spots, there are actually several. In October 2015, NASA released a true portrait of Ceres made by Dawn. In February 2017, organics were reported to have been detected on Ceres in Ernutet crater, Johann Elert Bode, in 1772, first suggested that an undiscovered planet could exist between the orbits of Mars and Jupiter. Kepler had already noticed the gap between Mars and Jupiter in 1596, the pattern predicted that the missing planet ought to have an orbit with a semi-major axis near 2.8 astronomical units. Although they did not discover Ceres, they found several large asteroids. One of the selected for the search was Giuseppe Piazzi. Before receiving his invitation to join the group, Piazzi discovered Ceres on 1 January 1801 and he was searching for the 87th of the Catalogue of the Zodiacal stars of Mr la Caille, but found that it was preceded by another
29.
Gefion family
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The Gefion or Gefionian family of asteroids is a grouping of S-type asteroids in the intermediate asteroid belt. The members have proper orbital elements in the approximate ranges At the present epoch, the family is fairly large, e. g. the Zappala 1995 analysis found about a hundred core members. A search of a recent proper element database found 766 objects lying within the region defined by the first table above.025, the core members identified by the Zappalà HCM method survey are shown in the table at right. Until recently, this family was known as the Ceres family or the Minerva family after 1 Ceres or 93 Minerva, however, spectroscopic analyses showed that these largest members were in fact interlopers in their own family, having a different spectral class from the bulk of the members. Other known interlopers are 255 Oppavia,374 Burgundia,2507 Bobone and this left the fairly minor asteroid 1272 Gefion as the lowest-numbered member. This is a list of the family members, without the above mentioned interlopers
30.
Koronis family
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The Koronis or Koronian family is a family of asteroids in the main belt between Mars and Jupiter. They are thought to have formed at least two billion years ago in a catastrophic collision between two larger bodies. The family is named after 158 Koronis, and the largest known member is about 41 km in diameter, the Koronis family travels in a cluster along the same orbit. Over 300 have been found but only about 20 are larger than 20 km in diameter, on August 28,1993, the Galileo spacecraft visited a member of this family,243 Ida. Asteroid family Karin cluster Astronomical studies of the Koronis Family Spins on Koronis family
31.
Eunomia family
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The Eunomia or Eunomian family of asteroids is a large grouping of S-type asteroids named after the asteroid 15 Eunomia. It is the most prominent family in the asteroid belt. About 5% of all asteroids in the asteroid belt belong to this family, Eunomia has been estimated to contain about 70–75% of the matter from the original parent body. This had a diameter of about 280 km and was disrupted by the catastrophic impact that created the family. It is likely that the parent body was at least partly differentiated, because the surface of Eunomia, the impactor was probably a smaller, yet still very substantial asteroid of 50 km diameter that hit at a speed of about 22,000 km/h. The other Eunomian asteroids are regularly distributed in orbital space around Eunomia. The next largest member identified by the analysis was 258 Tyche of 65 km diameter, however, its orbit lies at the very margin of what can be considered the family region, and it may well be an interloper. The largest clear family members are about 30 km diameter, with several asteroids in this size range, spectroscopic studies have shown that the family members span a noticeable range of compositions, although all remain within the S spectral class. As such they are of generally stony surface composition that includes silicates and some nickel-iron, the family contains relatively large numbers of small objects. The Cassini-Huygens spacecraft flew by 2685 Masursky, a family member. However, the distance of about one million kilometers was too large for surface features to be resolved. The Eunomia family is located between the 3,1 and 8,3 resonances with Jupiter, at relatively high inclinations, a HCM numerical analysis by Zappalà et al. This would give about 5% of all main belt asteroids, a number of interlopers have been identified, which share the same orbital elements as the true family members, but can not have come from the same breakup because of spectral differences
32.
Asteroid family
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An asteroid family is a population of asteroids that share similar proper orbital elements, such as semimajor axis, eccentricity, and orbital inclination. The members of the families are thought to be fragments of past asteroid collisions, an asteroid family is a more specific term than asteroid group whose members, while sharing some broad orbital characteristics, may be otherwise unrelated to each other. Large prominent families contain several hundred recognized asteroids, small, compact families can have only about ten identified members. About 33% to 35% of asteroids in the belt are family members. There are about 20 to 30 reliably recognized families, with tens of less certain groupings. One family has been identified associated with the dwarf planet Haumea, some studies have tried to find evidence of collisional families among the trojan asteroids, but at present the evidence is inconclusive. The families are thought to form as a result of collisions between asteroids, in many or most cases the parent body was shattered, but there are also several families which resulted from a large cratering event which did not disrupt the parent body. Such cratering families typically consist of a large body and a swarm of asteroids that are much smaller. Some families have complex structures which are not satisfactorily explained at the moment. Due to the method of origin, all the members have closely matching compositions for most families, notable exceptions are those families which formed from a large differentiated parent body. Asteroid families are thought to have lifetimes of the order of a billion years and this is significantly shorter than the Solar Systems age, so few if any are relics of the early Solar System. Such small asteroids then become subject to such as the Yarkovsky effect that can push them towards orbital resonances with Jupiter over time. Once there, they are relatively rapidly ejected from the asteroid belt, tentative age estimates have been obtained for some families, ranging from hundreds of millions of years to less than several million years as for the compact Karin family. Old families are thought to contain few small members, and this is the basis of the age determinations and it is supposed that many very old families have lost all the smaller and medium-sized members, leaving only a few of the largest intact. A suggested example of old family remains are the 9 Metis and 113 Amalthea pair. Further evidence for a number of past families comes from analysis of chemical ratios in iron meteorites. These show that there must have once been at least 50 to 100 parent bodies large enough to be differentiated, when the orbital elements of main belt asteroids are plotted, a number of distinct concentrations are seen against the rather uniform background distribution of generic asteroids. These concentrations are the asteroid families, the proper elements are related constants of motion that remain almost constant for times of at least tens of millions of years, and perhaps longer
33.
S-type asteroid
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S-type asteroids, or silicaceous asteroids, are of a stony composition, hence the name. Approximately 17% of asteroids are of type, making it the second most common after the C-type. S-types are moderately bright and consist mainly of iron- and magnesium-silicates and they are dominant in the inner asteroid belt within 2.2 AU, common in the central belt within about 3 AU, but become rare farther out. The largest is 15 Eunomia, with the next largest members by diameter being 3 Juno,29 Amphitrite,532 Herculina and 7 Iris. Their spectrum has a steep slope at wavelengths shorter than 0.7 µm. The 1 µm absorption is indicative of the presence of silicates, often there is also a broad but shallow absorption feature centered near 0.63 µm. The composition of asteroids is similar to a variety of stony meteorites which share similar spectral characteristics. This whole S assemblage of asteroids is spectrally quite distinct from the carbonaceous C-group, Asteroid spectral types L-type asteroid K-type asteroid X-type asteroid Bus, S. J. Binzel, R. P. Phase II of the Small Main-belt Asteroid Spectroscopy Survey, A feature-based taxonomy
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15 Eunomia
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15 Eunomia is a very large asteroid in the inner asteroid belt. It is the largest of the asteroids, and somewhere between the 8th-to-12th-largest main-belt asteroid overall. It is the largest Eunomian asteroid, and is estimated to contain 1% of the mass of the asteroid belt. Eunomia was discovered by Annibale de Gasparis on July 29,1851, and named after Eunomia, one of the Horae, as the largest S-type asteroid, Eunomia has attracted a moderate amount of scientific attention. It contains slightly over one percent of the mass of the asteroid belt. Eunomia appears to be an elongated but fairly regularly shaped body, with what appear to be four sides of differing curvature and its elongation led to the suggestion that Eunomia may be a binary object, but this has been refuted. It is a retrograde rotator with its pole pointing towards ecliptic coordinates = with a 10° uncertainty and this gives an axial tilt of about 165°. Like other true members of the family, its surface is composed of silicates and some nickel-iron, calcium-rich pyroxenes and olivine, along with nickel-iron metal, have been detected on Eunomias surface. The range of compositions of the remaining Eunomian asteroids, formed by a collision of the parent body, is large enough to encompass all the surface variations on Eunomia itself. Interestingly, the majority of smaller Eunomian asteroids are more rich than Eunomias surface. However, there is uncertainty over Eunomias internal structure and relationship to the parent body, whatever the case in this respect, it appears that any metallic core region, if present, has not been exposed. These indicate that the largest fragment has about 70% of the mass of the parent body, the orbit of 15 Eunomia places it in a 7,16 mean-motion resonance with the planet Mars. Eunomia is used by the Minor Planet Center to calculate perturbations, the computed Lyapunov time for this asteroid is 25,000 years, indicating that it occupies a chaotic orbit that will change randomly over time because of gravitational perturbations of the planets. Eunomia has been observed occulting stars three times and it has a mean opposition magnitude of +8.5, about equal to the mean brightness of Titan, and can reach +7.9 at a near perihelion opposition. Asteroid 2000 CZ12 passed about 0.00037 AU from Eunomia on March 4,2002, one of the hidden levels in the videogame Descent is an expedition to a secret mine station on asteroid Eunomia. Eunomia is mentioned as one of the five largest asteroids in the science-fiction novel Rendezvous With Rama by Arthur C, one episode shows the study of gravitational waves at the expense of a chunk of Eunomia the size of Everest. 15 Eunomia is the inspiration for the look of the ships in Arrival. Former classification of planets shape model deduced from lightcurve, including composition variations across the surface JPL Ephemeris Elements,15 Eunomia at the JPL Small-Body Database Discovery · Orbit diagram · Orbital elements · Physical parameters
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8 Flora
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8 Flora is a large, bright main-belt asteroid. It is the seventh-brightest asteroid with an opposition magnitude of +8.7. Flora can reach a magnitude of +7.9 at an opposition near perihelion. Flora may be the core of an intensely heated, thermally evolved. Flora was discovered by J. R. Hind on October 18,1847 and it was his second asteroid discovery after 7 Iris. The name Flora was proposed by John Herschel, from Flora, the Latin goddess of flowers and gardens, wife of Zephyrus, the Greek equivalent is Chloris, who has her own asteroid,410 Chloris, but in Greek Flora is also called Chloris. Lightcurve analysis indicates that Floras pole points towards ecliptic coordinates = with a 10° uncertainty and this gives an axial tilt of 78°, plus or minus ten degrees. Flora is the parent body of the Flora family of asteroids, nevertheless, Flora was almost certainly disrupted by the impact that formed the family, and is probably a gravitational aggregate of most of the pieces. Floras spectrum indicates that its composition is a mixture of silicate rock. Flora, and the whole Flora family generally, are candidates for being the parent bodies of the L chondrite meteorites. This meteorite type comprises about 38% of all meteorites impacting the Earth, during an observation on March 25,1917,8 Flora was mistaken for the 15th-magnitude star TU Leonis, which led to that stars classification as a U Geminorum cataclysmic variable star. Flora had come to opposition on 1917 February 13,40 days earlier and this mistake was uncovered only in 1995. On July 26,2013, Flora at magnitude 8.8 occulted the star 2UCAC22807162 over parts of South America, Africa, in the 1968 science-fiction film The Green Slime, an orbital perturbation propels the asteroid Flora into a collision course with Earth
. Bibcode:2015aste.book..297N. doi:10.2458/azu_uapress_9780816532131-ch016. Retrieved 23 June 2017.
