1.
James Craig Watson
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James Craig Watson was a Canadian-American astronomer, discoverer of comets and minor planets, director of the Ann Arbor Observatory, and awarded with the Lalande Prize in 1869. He was born in the village of Fingal, Ontario Canada and his family relocated to Ann Arbor, Michigan in 1850. At age 15 he was matriculated at the University of Michigan and he graduated with a BA in 1857 and received a masters degree on examination after two years study in astronomy under professor Franz Brünnow. He became Professor of Physics and instructor in Mathematics, and in 1863, succeeded him as professor of Astronomy and he wrote the textbook Theoretical Astronomy in 1868. He discovered 22 asteroids, beginning with 79 Eurynome in 1863, one of his asteroid discoveries,139 Juewa was made in Beijing when Watson was there to observe the 1874 transit of Venus. The name Juewa was chosen by Chinese officials, another was 121 Hermione in 1872, from Ann Arbor, Michigan, and this asteroid was found to have a small asteroid moon in 2002. He was a member of the most important expeditions for astronomical observation sent out by the United States Government during his time. He was a believer in the existence of the planet Vulcan, a hypothetical planet closer to the Sun than Mercury. He believed he had seen such two such planets during his observation of the 1878 solar eclipse and he died of peritonitis at the age of only 42 and was buried at Forest Hill, Ann Arbor. He had amassed a considerable amount of money through non-astronomical business activities, by bequest he established the James Craig Watson Medal, awarded every two years by the National Academy of Sciences for contributions to astronomy. Watson won the Lalande Prize given by the French Academy of Sciences for 1869 and he was a member of the National Academy of Sciences and the American Philosophical Society. He received the degree of Doctor of Philosophy from the University of Leipzig in 1870, and from Yale College in 1871. The main-belt asteroid 729 Watsonia is named in his honour, as is the lunar crater Watson, in Search of Planet Vulcan, The Ghost in Newtons Clockwork Machine
2.
Hermione (mythology)
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In Greek mythology, Hermione was the only child of King Menelaus of Sparta and his wife, Helen of Troy. Prior to the Trojan War, Hermione was betrothed by Tyndareus, her grandfather, however, during the Trojan War, Menelaus promised her to Neoptolemus, also known as Pyrrhus, son of Achilles. Ancient poets disagree over whether Menelaus was involved in both betrothals, euripides has Orestes say, ″Because, in fact, you were rightfully mine, from a long time ago. But Menelaus, my father, made a promise of me, shortly after settling into the domestic life, conflict arose between Hermione and Andromache, the concubine Neoptolemus had obtained as a prize after the sack of Troy. Hermione blamed Andromache for her inability to become pregnant, claiming that she was casting spells on her to keep her barren. She asked her father to kill Andromache while Neoptolemus was away at war, Hermione and Orestes were married, and she gave birth to his heir Tisamenus. The myths do not mention Hermione after that, though it is said that Orestes later married his half-sister Erigone, daughter of Clytemnestra and Aigisthus and she, in turn, was the inspiration for Hermione Grangers name in the Harry Potter franchise. British actress Emma Watson portrayed Hermione in all eight of the movies
3.
Minor planet
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A minor planet is an astronomical object in direct orbit around the Sun that is neither a planet nor exclusively classified as a comet. Minor planets can be dwarf planets, asteroids, trojans, centaurs, Kuiper belt objects, as of 2016, the orbits of 709,706 minor planets were archived at the Minor Planet Center,469,275 of which had received permanent numbers. The first minor planet to be discovered was Ceres in 1801, the term minor planet has been used since the 19th century to describe these objects. The term planetoid has also used, especially for larger objects such as those the International Astronomical Union has called dwarf planets since 2006. Historically, the asteroid, minor planet, and planetoid have been more or less synonymous. This terminology has become complicated by the discovery of numerous minor planets beyond the orbit of Jupiter. A Minor planet seen releasing gas may be classified as a comet. Before 2006, the IAU had officially used the term minor planet, during its 2006 meeting, the IAU reclassified minor planets and comets into dwarf planets and small Solar System bodies. Objects are called dwarf planets if their self-gravity is sufficient to achieve hydrostatic equilibrium, all other minor planets and comets are called small Solar System bodies. The IAU stated that the minor planet may still be used. However, for purposes of numbering and naming, the distinction between minor planet and comet is still used. Hundreds of thousands of planets have been discovered within the Solar System. The Minor Planet Center has documented over 167 million observations and 729,626 minor planets, of these,20,570 have official names. As of March 2017, the lowest-numbered unnamed minor planet is 1974 FV1, as of March 2017, the highest-numbered named minor planet is 458063 Gustavomuler. There are various broad minor-planet populations, Asteroids, traditionally, most have been bodies in the inner Solar System. Near-Earth asteroids, those whose orbits take them inside the orbit of Mars. Further subclassification of these, based on distance, is used, Apohele asteroids orbit inside of Earths perihelion distance. Aten asteroids, those that have semi-major axes of less than Earths, Apollo asteroids are those asteroids with a semimajor axis greater than Earths, while having a perihelion distance of 1.017 AU or less. Like Aten asteroids, Apollo asteroids are Earth-crossers, amor asteroids are those near-Earth asteroids that approach the orbit of Earth from beyond, but do not cross it
4.
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
5.
Cybele asteroid
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Cybele asteroids are a group of asteroids in the outer asteroid belt with a semi-major axis between 3.27 AU and 3.7 AU, an eccentricity less than 0.3, and an inclination less than 25°. The group is named for the asteroid 65 Cybele, as of 2010, the group is thought to have formed from the breakup of a larger object in the distant past. Some of the largest Cybele asteroids are 87 Sylvia,65 Cybele,107 Camilla,121 Hermione,76 Freia,790 Pretoria, some of the group also have asteroid moons, such as 121 Hermione
6.
Perihelion and aphelion
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The perihelion is the point in the orbit of a celestial body where it is nearest to its orbital focus, generally a star. It is the opposite of aphelion, which is the point in the orbit where the body is farthest from its focus. The word perihelion stems from the Ancient Greek words peri, meaning around or surrounding, aphelion derives from the preposition apo, meaning away, off, apart. According to Keplers first law of motion, all planets, comets. Hence, a body has a closest and a farthest point from its parent object, that is, a perihelion. Each extreme is known as an apsis, orbital eccentricity measures the flatness of the orbit. Because of the distance at aphelion, only 93. 55% of the solar radiation from the Sun falls on a given area of land as does at perihelion. However, this fluctuation does not account for the seasons, as it is summer in the northern hemisphere when it is winter in the southern hemisphere and vice versa. Instead, seasons result from the tilt of Earths axis, which is 23.4 degrees away from perpendicular to the plane of Earths orbit around the sun. Winter falls on the hemisphere where sunlight strikes least directly, and summer falls where sunlight strikes most directly, in the northern hemisphere, summer occurs at the same time as aphelion. Despite this, there are larger land masses in the northern hemisphere, consequently, summers are 2.3 °C warmer in the northern hemisphere than in the southern hemisphere under similar conditions. Apsis Ellipse Solstice Dates and times of Earths perihelion and aphelion, 2000–2025 from the United States Naval Observatory
7.
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
8.
Astronomical unit
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The astronomical unit is a unit of length, roughly the distance from Earth to the Sun. However, that varies as Earth orbits the Sun, from a maximum to a minimum. Originally conceived as the average of Earths aphelion and perihelion, it is now defined as exactly 149597870700 metres, the astronomical unit is used primarily as a convenient yardstick for measuring distances within the Solar System or around other stars. However, it is also a component in the definition of another unit of astronomical length. A variety of symbols and abbreviations have been in use for the astronomical unit. In a 1976 resolution, the International Astronomical Union used the symbol A for the astronomical unit, in 2006, the International Bureau of Weights and Measures recommended ua as the symbol for the unit. In 2012, the IAU, noting that various symbols are presently in use for the astronomical unit, in the 2014 revision of the SI Brochure, the BIPM used the unit symbol au. In ISO 80000-3, the symbol of the unit is ua. Earths orbit around the Sun is an ellipse, the semi-major axis of this ellipse is defined to be half of the straight line segment that joins the aphelion and perihelion. The centre of the sun lies on this line segment. In addition, it mapped out exactly the largest straight-line distance that Earth traverses over the course of a year, knowing Earths shift and a stars shift enabled the stars distance to be calculated. But all measurements are subject to some degree of error or uncertainty, improvements in precision have always been a key to improving astronomical understanding. Improving measurements were continually checked and cross-checked by means of our understanding of the laws of celestial mechanics, the expected positions and distances of objects at an established time are calculated from these laws, and assembled into a collection of data called an ephemeris. NASAs Jet Propulsion Laboratory provides one of several ephemeris computation services, in 1976, in order to establish a yet more precise measure for the astronomical unit, the IAU formally adopted a new definition. Equivalently, by definition, one AU is the radius of an unperturbed circular Newtonian orbit about the sun of a particle having infinitesimal mass. As with all measurements, these rely on measuring the time taken for photons to be reflected from an object. However, for precision the calculations require adjustment for such as the motions of the probe. In addition, the measurement of the time itself must be translated to a scale that accounts for relativistic time dilation
9.
Orbital eccentricity
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The orbital eccentricity of an astronomical object is a parameter that determines the amount by which its orbit around another body deviates from a perfect circle. A value of 0 is an orbit, values between 0 and 1 form an elliptical orbit,1 is a parabolic escape orbit. The term derives its name from the parameters of conic sections and it is normally used for the isolated two-body problem, but extensions exist for objects following a rosette orbit through the galaxy. In a two-body problem with inverse-square-law force, every orbit is a Kepler orbit, the eccentricity of this Kepler orbit is a non-negative number that defines its shape. The limit case between an ellipse and a hyperbola, when e equals 1, is parabola, radial trajectories are classified as elliptic, parabolic, or hyperbolic based on the energy of the orbit, not the eccentricity. Radial orbits have zero angular momentum and hence eccentricity equal to one, keeping the energy constant and reducing the angular momentum, elliptic, parabolic, and hyperbolic orbits each tend to the corresponding type of radial trajectory while e tends to 1. For a repulsive force only the trajectory, including the radial version, is applicable. For elliptical orbits, a simple proof shows that arcsin yields the projection angle of a circle to an ellipse of eccentricity e. For example, to view the eccentricity of the planet Mercury, next, tilt any circular object by that angle and the apparent ellipse projected to your eye will be of that same eccentricity. From Medieval Latin eccentricus, derived from Greek ἔκκεντρος ekkentros out of the center, from ἐκ- ek-, eccentric first appeared in English in 1551, with the definition a circle in which the earth, sun. Five years later, in 1556, a form of the word was added. The eccentricity of an orbit can be calculated from the state vectors as the magnitude of the eccentricity vector, e = | e | where. For elliptical orbits it can also be calculated from the periapsis and apoapsis since rp = a and ra = a, where a is the semimajor axis. E = r a − r p r a + r p =1 −2 r a r p +1 where, rp is the radius at periapsis. For Earths annual orbit path, ra/rp ratio = longest_radius / shortest_radius ≈1.034 relative to center point of path, the eccentricity of the Earths orbit is currently about 0.0167, the Earths orbit is nearly circular. Venus and Neptune have even lower eccentricity, over hundreds of thousands of years, the eccentricity of the Earths orbit varies from nearly 0.0034 to almost 0.058 as a result of gravitational attractions among the planets. The table lists the values for all planets and dwarf planets, Mercury has the greatest orbital eccentricity of any planet in the Solar System. Such eccentricity is sufficient for Mercury to receive twice as much solar irradiation at perihelion compared to aphelion, before its demotion from planet status in 2006, Pluto was considered to be the planet with the most eccentric orbit
10.
Mean anomaly
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In celestial mechanics, the mean anomaly is an angle used in calculating the position of a body in an elliptical orbit in the classical two-body problem. Define T as the time required for a body to complete one orbit. In time T, the radius vector sweeps out 2π radians or 360°. The average rate of sweep, n, is then n =2 π T or n =360 ∘ T, define τ as the time at which the body is at the pericenter. From the above definitions, a new quantity, M, the mean anomaly can be defined M = n, because the rate of increase, n, is a constant average, the mean anomaly increases uniformly from 0 to 2π radians or 0° to 360° during each orbit. It is equal to 0 when the body is at the pericenter, π radians at the apocenter, if the mean anomaly is known at any given instant, it can be calculated at any later instant by simply adding n δt where δt represents the time difference. Mean anomaly does not measure an angle between any physical objects and it is simply a convenient uniform measure of how far around its orbit a body has progressed since pericenter. The mean anomaly is one of three parameters that define a position along an orbit, the other two being the eccentric anomaly and the true anomaly. Define l as the longitude, the angular distance of the body from the same reference direction. Thus mean anomaly is also M = l − ϖ, mean angular motion can also be expressed, n = μ a 3, where μ is a gravitational parameter which varies with the masses of the objects, and a is the semi-major axis of the orbit. Mean anomaly can then be expanded, M = μ a 3, and here mean anomaly represents uniform angular motion on a circle of radius a
11.
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
12.
Longitude of the ascending node
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The longitude of the ascending node is one of the orbital elements used to specify the orbit of an object in space. It is the angle from a direction, called the origin of longitude, to the direction of the ascending node. The ascending node is the point where the orbit of the passes through the plane of reference. Commonly used reference planes and origins of longitude include, For a geocentric orbit, Earths equatorial plane as the plane. In this case, the longitude is called the right ascension of the ascending node. The angle is measured eastwards from the First Point of Aries to the node, for a heliocentric orbit, the ecliptic as the reference plane, and the First Point of Aries as the origin of longitude. The angle is measured counterclockwise from the First Point of Aries to the node, the angle is measured eastwards from north to the node. pp.40,72,137, chap. In the case of a star known only from visual observations, it is not possible to tell which node is ascending. In this case the orbital parameter which is recorded is the longitude of the node, Ω, here, n=<nx, ny, nz> is a vector pointing towards the ascending node. The reference plane is assumed to be the xy-plane, and the origin of longitude is taken to be the positive x-axis, K is the unit vector, which is the normal vector to the xy reference plane. For non-inclined orbits, Ω is undefined, for computation it is then, by convention, set equal to zero, that is, the ascending node is placed in the reference direction, which is equivalent to letting n point towards the positive x-axis. Kepler orbits Equinox Orbital node perturbation of the plane can cause revolution of the ascending node
13.
Argument of periapsis
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The argument of periapsis, symbolized as ω, is one of the orbital elements of an orbiting body. Parametrically, ω is the angle from the ascending node to its periapsis. For specific types of orbits, words such as perihelion, perigee, periastron, an argument of periapsis of 0° means that the orbiting body will be at its closest approach to the central body at the same moment that it crosses the plane of reference from South to North. An argument of periapsis of 90° means that the body will reach periapsis at its northmost distance from the plane of reference. Adding the argument of periapsis to the longitude of the ascending node gives the longitude of the periapsis, however, especially in discussions of binary stars and exoplanets, the terms longitude of periapsis or longitude of periastron are often used synonymously with argument of periapsis. In the case of equatorial orbits, the argument is strictly undefined, where, ex and ey are the x- and y-components of the eccentricity vector e. In the case of circular orbits it is assumed that the periapsis is placed at the ascending node. Kepler orbit Orbital mechanics Orbital node
14.
Natural satellite
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A natural satellite or moon is, in the most common usage, an astronomical body that orbits a planet or minor planet. In the Solar System there are six planetary satellite systems containing 178 known natural satellites, four IAU-listed dwarf planets are also known to have natural satellites, Pluto, Haumea, Makemake, and Eris. As of January 2012, over 200 minor-planet moons have been discovered, the Earth–Moon system is unique in that the ratio of the mass of the Moon to the mass of Earth is much greater than that of any other natural-satellite–planet ratio in the Solar System. At 3,474 km across, Earths Moon is 0.27 times the diameter of Earth, the first known natural satellite was the Moon, but it was considered a planet until Copernicus introduction of heliocentrism in 1543. Until the discovery of the Galilean satellites in 1610, however, galileo chose to refer to his discoveries as Planetæ, but later discoverers chose other terms to distinguish them from the objects they orbited. The first to use of the satellite to describe orbiting bodies was the German astronomer Johannes Kepler in his pamphlet Narratio de Observatis a se quatuor Iouis satellitibus erronibus in 1610. He derived the term from the Latin word satelles, meaning guard, attendant, or companion, the term satellite thus became the normal one for referring to an object orbiting a planet, as it avoided the ambiguity of moon. In 1957, however, the launching of the artificial object Sputnik created a need for new terminology, to further avoid ambiguity, the convention is to capitalize the word Moon when referring to Earths natural satellite, but not when referring to other natural satellites. A few recent authors define moon as a satellite of a planet or minor planet, there is no established lower limit on what is considered a moon. Small asteroid moons, such as Dactyl, have also been called moonlets, the upper limit is also vague. Two orbiting bodies are described as a double body rather than primary. Asteroids such as 90 Antiope are considered double asteroids, but they have not forced a clear definition of what constitutes a moon, some authors consider the Pluto–Charon system to be a double planet. In contrast, irregular satellites are thought to be captured asteroids possibly further fragmented by collisions, most of the major natural satellites of the Solar System have regular orbits, while most of the small natural satellites have irregular orbits. The Moon and possibly Charon are exceptions among large bodies in that they are thought to have originated by the collision of two large proto-planetary objects. The material that would have placed in orbit around the central body is predicted to have reaccreted to form one or more orbiting natural satellites. As opposed to planetary-sized bodies, asteroid moons are thought to form by this process. Triton is another exception, although large and in a close, circular orbit, its motion is retrograde, most regular moons in the Solar System are tidally locked to their respective primaries, meaning that the same side of the natural satellite always faces its planet. The only known exception is Saturns natural satellite Hyperion, which rotates chaotically because of the influence of Titan
15.
S/2002 (121) 1
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121 Hermione is a very large asteroid discovered in 1872. It orbits in the Cybele group in the far outer asteroid belt, as an asteroid of the dark C spectral type, it is probably composed of carbonaceous materials. In 2002, a small moon was found to be orbiting Hermione, Hermione was discovered by J. C. Watson on May 12,1872, from Ann Arbor, and named after Hermione, daughter of Menelaus and Helen in Greek mythology. Hermione is a Cybele asteroid and orbits beyond most of the main-belt asteroids, a satellite of Hermione was discovered in 2002 with the Keck II telescope. It is about 8 miles in diameter, the satellite is provisionally designated S/20021. The asteroid has a shape, as evidenced by adaptive optics images. Of several proposed models that agreed with the images, a snowman-like shape was found to best fit the observed precession rate of Hermiones satellite. In this snowman model, the shape can be approximated by two partially overlapping spheres of radii 80 and 60 km, whose centers are separated by a distance of 115 km. A simple ellipsoid shape was ruled out, observation of the satellites orbit has made possible an accurate determination of Hermiones mass. Occultations by Hermione have been successfully observed three times so far, the last time in February 2004,121 Hermione and S/20021, orbit data website maintained by F. Marchis. Includes adaptive optics images, orbit diagrams, and shape models
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Mass
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In physics, mass is a property of a physical body. It is the measure of a resistance to acceleration when a net force is applied. It also determines the strength of its gravitational attraction to other bodies. The basic SI unit of mass is the kilogram, Mass is not the same as weight, even though mass is often determined by measuring the objects weight using a spring scale, rather than comparing it directly with known masses. An object on the Moon would weigh less than it does on Earth because of the lower gravity and this is because weight is a force, while mass is the property that determines the strength of this force. In Newtonian physics, mass can be generalized as the amount of matter in an object, however, at very high speeds, special relativity postulates that energy is an additional source of mass. Thus, any body having mass has an equivalent amount of energy. In addition, matter is a defined term in science. There are several distinct phenomena which can be used to measure mass, active gravitational mass measures the gravitational force exerted by an object. Passive gravitational mass measures the force exerted on an object in a known gravitational field. The mass of an object determines its acceleration in the presence of an applied force, according to Newtons second law of motion, if a body of fixed mass m is subjected to a single force F, its acceleration a is given by F/m. A bodys mass also determines the degree to which it generates or is affected by a gravitational field and this is sometimes referred to as gravitational mass. The standard International System of Units unit of mass is the kilogram, the kilogram is 1000 grams, first defined in 1795 as one cubic decimeter of water at the melting point of ice. Then in 1889, the kilogram was redefined as the mass of the prototype kilogram. As of January 2013, there are proposals for redefining the kilogram yet again. In this context, the mass has units of eV/c2, the electronvolt and its multiples, such as the MeV, are commonly used in particle physics. The atomic mass unit is 1/12 of the mass of a carbon-12 atom, the atomic mass unit is convenient for expressing the masses of atoms and molecules. Outside the SI system, other units of mass include, the slug is an Imperial unit of mass, the pound is a unit of both mass and force, used mainly in the United States
17.
Density
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The density, or more precisely, the volumetric mass density, of a substance is its mass per unit volume. The symbol most often used for density is ρ, although the Latin letter D can also be used. Mathematically, density is defined as mass divided by volume, ρ = m V, where ρ is the density, m is the mass, and V is the volume. In some cases, density is defined as its weight per unit volume. For a pure substance the density has the numerical value as its mass concentration. Different materials usually have different densities, and density may be relevant to buoyancy, purity, osmium and iridium are the densest known elements at standard conditions for temperature and pressure but certain chemical compounds may be denser. Thus a relative density less than one means that the floats in water. The density of a material varies with temperature and pressure and this variation is typically small for solids and liquids but much greater for gases. Increasing the pressure on an object decreases the volume of the object, increasing the temperature of a substance decreases its density by increasing its volume. In most materials, heating the bottom of a results in convection of the heat from the bottom to the top. This causes it to rise relative to more dense unheated material, the reciprocal of the density of a substance is occasionally called its specific volume, a term sometimes used in thermodynamics. Density is a property in that increasing the amount of a substance does not increase its density. Archimedes knew that the irregularly shaped wreath could be crushed into a cube whose volume could be calculated easily and compared with the mass, upon this discovery, he leapt from his bath and ran naked through the streets shouting, Eureka. As a result, the term eureka entered common parlance and is used today to indicate a moment of enlightenment, the story first appeared in written form in Vitruvius books of architecture, two centuries after it supposedly took place. Some scholars have doubted the accuracy of this tale, saying among other things that the method would have required precise measurements that would have been difficult to make at the time, from the equation for density, mass density has units of mass divided by volume. As there are units of mass and volume covering many different magnitudes there are a large number of units for mass density in use. The SI unit of kilogram per metre and the cgs unit of gram per cubic centimetre are probably the most commonly used units for density.1,000 kg/m3 equals 1 g/cm3. In industry, other larger or smaller units of mass and or volume are often more practical, see below for a list of some of the most common units of density
18.
Escape velocity
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The escape velocity from Earth is about 11.186 km/s at the surface. More generally, escape velocity is the speed at which the sum of a kinetic energy. With escape velocity in a direction pointing away from the ground of a massive body, once escape velocity is achieved, no further impulse need be applied for it to continue in its escape. When given a speed V greater than the speed v e. In these equations atmospheric friction is not taken into account, escape velocity is only required to send a ballistic object on a trajectory that will allow the object to escape the gravity well of the mass M. The existence of escape velocity is a consequence of conservation of energy, by adding speed to the object it expands the possible places that can be reached until with enough energy they become infinite. For a given gravitational potential energy at a position, the escape velocity is the minimum speed an object without propulsion needs to be able to escape from the gravity. Escape velocity is actually a speed because it does not specify a direction, no matter what the direction of travel is, the simplest way of deriving the formula for escape velocity is to use conservation of energy. Imagine that a spaceship of mass m is at a distance r from the center of mass of the planet and its initial speed is equal to its escape velocity, v e. At its final state, it will be a distance away from the planet. The same result is obtained by a calculation, in which case the variable r represents the radial coordinate or reduced circumference of the Schwarzschild metric. All speeds and velocities measured with respect to the field, additionally, the escape velocity at a point in space is equal to the speed that an object would have if it started at rest from an infinite distance and was pulled by gravity to that point. In common usage, the point is on the surface of a planet or moon. On the surface of the Earth, the velocity is about 11.2 km/s. However, at 9,000 km altitude in space, it is less than 7.1 km/s. The escape velocity is independent of the mass of the escaping object and it does not matter if the mass is 1 kg or 1,000 kg, what differs is the amount of energy required. For an object of mass m the energy required to escape the Earths gravitational field is GMm / r, a related quantity is the specific orbital energy which is essentially the sum of the kinetic and potential energy divided by the mass. An object has reached escape velocity when the orbital energy is greater or equal to zero
19.
Axial tilt
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In astronomy, axial tilt, also known as obliquity, is the angle between an objects rotational axis and its orbital axis, or, equivalently, the angle between its equatorial plane and orbital plane. At an obliquity of zero, the two axes point in the direction, i. e. the rotational axis is perpendicular to the orbital plane. Over the course of an orbit, the obliquity usually does not change considerably, and this causes one pole to be directed more toward the Sun on one side of the orbit, and the other pole on the other side — the cause of the seasons on the Earth. Earths obliquity oscillates between 22.1 and 24.5 degrees on a 41, 000-year cycle, the mean obliquity is currently 23°26′13. 4″. There are two methods of specifying tilt. The IAU also uses the rule to define a positive pole for the purpose of determining orientation. Using this convention, Venus is tilted 177° and it is denoted by the Greek letter ε. Earth currently has a tilt of about 23. 4°. This value remains about the relative to a stationary orbital plane throughout the cycles of axial precession. But the ecliptic due to planetary perturbations, and the obliquity of the ecliptic is not a fixed quantity. At present, it is decreasing at a rate of about 47″ per century, Earths obliquity may have been reasonably accurately measured as early as 1100 BC in India and China. The ancient Greeks had good measurements of the obliquity since about 350 BC, about 830 AD, the Caliph Al-Mamun of Baghdad directed his astronomers to measure the obliquity, and the result was used in the Arab world for many years. It was widely believed, during the Middle Ages, that both precession and Earths obliquity oscillated around a value, with a period of 672 years. Earths axis remains tilted in the direction with reference to the background stars throughout a year. This means that one pole will be directed away from the Sun at one side of the orbit and this is the cause of Earths seasons. Summer occurs in the Northern hemisphere when the pole is directed toward the Sun. Variations in Earths axial tilt can influence the seasons and is likely a factor in climate change. The exact angular value of the obliquity is found by observation of the motions of Earth, from 1984, the Jet Propulsion Laboratorys DE series of computer-generated ephemerides took over as the fundamental ephemeris of the Astronomical Almanac
20.
Ecliptic coordinate system
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The ecliptic coordinate system is a celestial coordinate system commonly used for representing the positions and orbits of Solar System objects. Because most planets, and many small Solar System bodies have orbits with small inclinations to the ecliptic, using it as the fundamental plane is convenient. The systems origin can be either the center of the Sun or the center of the Earth, its direction is towards the vernal equinox. It may be implemented in spherical coordinates or rectangular coordinates, a slow motion of Earths axis, precession, causes a slow, continuous turning of the coordinate system westward about the poles of the ecliptic, completing one circuit in about 26,000 years. Superimposed on this is a motion of the ecliptic. The three most commonly used are, Mean equinox of an epoch is a fixed standard direction. Mean equinox of date is the intersection of the ecliptic of date with the mean equator, commonly used in planetary orbit calculation. True equinox of date is the intersection of the ecliptic of date with the true equator and this is the actual intersection of the two planes at any particular moment, with all motions accounted for. A position in the coordinate system is thus typically specified true equinox and ecliptic of date, mean equinox and ecliptic of J2000.0. Note that there is no mean ecliptic, as the ecliptic is not subject to small periodic oscillations, ecliptic longitude or celestial longitude measures the angular distance of an object along the ecliptic from the primary direction. Like right ascension in the coordinate system, the primary direction points from the Earth towards the Sun at the vernal equinox of the Northern Hemisphere. Because it is a system, ecliptic longitude is measured positive eastwards in the fundamental plane from 0° to 360°. Because of axial precession, the longitude of most fixed stars increases by about 50.3 arcseconds per year, or 83.8 arcminutes per century. Ecliptic latitude or celestial latitude, measures the distance of an object from the ecliptic towards the north or south ecliptic pole. For example, the ecliptic pole has a celestial latitude of +90°. Ecliptic latitude for fixed stars is not affected by precession, distance is also necessary for a complete spherical position. Different distance units are used for different objects, within the Solar System, astronomical units are used, and for objects near the Earth, Earth radii or kilometers are used. From antiquity through the 18th century, ecliptic longitude was measured using twelve zodiacal signs, each of 30° longitude
21.
Temperature
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A temperature is an objective comparative measurement of hot or cold. It is measured by a thermometer, several scales and units exist for measuring temperature, the most common being Celsius, Fahrenheit, and, especially in science, Kelvin. Absolute zero is denoted as 0 K on the Kelvin scale, −273.15 °C on the Celsius scale, the kinetic theory offers a valuable but limited account of the behavior of the materials of macroscopic bodies, especially of fluids. Temperature is important in all fields of science including physics, geology, chemistry, atmospheric sciences, medicine. The Celsius scale is used for temperature measurements in most of the world. Because of the 100 degree interval, it is called a centigrade scale.15, the United States commonly uses the Fahrenheit scale, on which water freezes at 32°F and boils at 212°F at sea-level atmospheric pressure. Many scientific measurements use the Kelvin temperature scale, named in honor of the Scottish physicist who first defined it and it is a thermodynamic or absolute temperature scale. Its zero point, 0K, is defined to coincide with the coldest physically-possible temperature and its degrees are defined through thermodynamics. The temperature of zero occurs at 0K = −273. 15°C. For historical reasons, the triple point temperature of water is fixed at 273.16 units of the measurement increment, Temperature is one of the principal quantities in the study of thermodynamics. There is a variety of kinds of temperature scale and it may be convenient to classify them as empirically and theoretically based. Empirical temperature scales are historically older, while theoretically based scales arose in the middle of the nineteenth century, empirically based temperature scales rely directly on measurements of simple physical properties of materials. For example, the length of a column of mercury, confined in a capillary tube, is dependent largely on temperature. Such scales are only within convenient ranges of temperature. For example, above the point of mercury, a mercury-in-glass thermometer is impracticable. A material is of no use as a thermometer near one of its phase-change temperatures, in spite of these restrictions, most generally used practical thermometers are of the empirically based kind. Especially, it was used for calorimetry, which contributed greatly to the discovery of thermodynamics, nevertheless, empirical thermometry has serious drawbacks when judged as a basis for theoretical physics. Theoretically based temperature scales are based directly on theoretical arguments, especially those of thermodynamics, kinetic theory and they rely on theoretical properties of idealized devices and materials
22.
Kelvin
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The kelvin is a unit of measure for temperature based upon an absolute scale. It is one of the seven units in the International System of Units and is assigned the unit symbol K. The kelvin is defined as the fraction 1⁄273.16 of the temperature of the triple point of water. In other words, it is defined such that the point of water is exactly 273.16 K. The Kelvin scale is named after the Belfast-born, Glasgow University engineer and physicist William Lord Kelvin, unlike the degree Fahrenheit and degree Celsius, the kelvin is not referred to or typeset as a degree. The kelvin is the unit of temperature measurement in the physical sciences, but is often used in conjunction with the Celsius degree. The definition implies that absolute zero is equivalent to −273.15 °C, Kelvin calculated that absolute zero was equivalent to −273 °C on the air thermometers of the time. This absolute scale is known today as the Kelvin thermodynamic temperature scale, when spelled out or spoken, the unit is pluralised using the same grammatical rules as for other SI units such as the volt or ohm. When reference is made to the Kelvin scale, the word kelvin—which is normally a noun—functions adjectivally to modify the noun scale and is capitalized, as with most other SI unit symbols there is a space between the numeric value and the kelvin symbol. Before the 13th CGPM in 1967–1968, the unit kelvin was called a degree and it was distinguished from the other scales with either the adjective suffix Kelvin or with absolute and its symbol was °K. The latter term, which was the official name from 1948 until 1954, was ambiguous since it could also be interpreted as referring to the Rankine scale. Before the 13th CGPM, the form was degrees absolute. The 13th CGPM changed the name to simply kelvin. Its measured value was 7002273160280000000♠0.01028 °C with an uncertainty of 60 µK, the use of SI prefixed forms of the degree Celsius to express a temperature interval has not been widely adopted. In 2005 the CIPM embarked on a program to redefine the kelvin using a more experimentally rigorous methodology, the current definition as of 2016 is unsatisfactory for temperatures below 20 K and above 7003130000000000000♠1300 K. In particular, the committee proposed redefining the kelvin such that Boltzmanns constant takes the exact value 6977138065049999999♠1. 3806505×10−23 J/K, from a scientific point of view, this will link temperature to the rest of SI and result in a stable definition that is independent of any particular substance. From a practical point of view, the redefinition will pass unnoticed, the kelvin is often used in the measure of the colour temperature of light sources. Colour temperature is based upon the principle that a black body radiator emits light whose colour depends on the temperature of the radiator, black bodies with temperatures below about 7003400000000000000♠4000 K appear reddish, whereas those above about 7003750000000000000♠7500 K appear bluish
23.
C-type asteroid
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They are the most common variety, forming around 75% of known asteroids. They are distinguished by a low albedo because their composition includes a large amount of carbon, in addition to rocks. Asteroids of this class have very similar to those of carbonaceous chondrite meteorites. The latter are very close in composition to the Sun. C-type asteroids are extremely dark, with albedos typically in the 0.03 to 0.10 range, consequently, whereas a number of S-type asteroids can normally be viewed with binoculars at opposition, even the largest C-type asteroids require a small telescope. The potentially brightest C-type asteroid is 324 Bamberga, but that very high eccentricity means it rarely reaches its maximum magnitude. Their spectra contain moderately strong ultraviolet absorption at wavelengths below about 0.4 μm to 0.5 μm, while at longer wavelengths they are largely featureless but slightly reddish. The so-called water absorption feature around 3 μm, which can be an indication of content in minerals is also present
24.
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
25.
Carbonate
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In chemistry, a carbonate is a salt of carbonic acid, characterized by the presence of the carbonate ion, a polyatomic ion with the formula of CO2−3. The name may mean an ester of carbonic acid, an organic compound containing the carbonate group C2. In geology and mineralogy, the term carbonate can refer both to carbonate minerals and carbonate rock, and both are dominated by the ion, CO2−3. Carbonate minerals are extremely varied and ubiquitous in chemically precipitated sedimentary rock, sodium carbonate and potassium carbonate have been used since antiquity for cleaning and preservation, as well as for the manufacture of glass. Carbonates are widely used in industry, e. g. in iron smelting, as a raw material for Portland cement and lime manufacture, in the composition of ceramic glazes, the carbonate ion is the simplest oxocarbon anion. It consists of one carbon atom surrounded by three oxygen atoms, in a planar arrangement, with D3h molecular symmetry. It has a mass of 60.01 g/mol and carries a total formal charge of −2. It is the base of the hydrogen carbonate ion, HCO−3. The Lewis structure of the ion has two single bonds to negative oxygen atoms, and one short double bond to a neutral oxygen. This structure is incompatible with the symmetry of the ion. This process is called calcination, after calx, the Latin name of quicklime or calcium oxide, CaO, exceptions include lithium, sodium, potassium and ammonium carbonates, as well as many uranium carbonates. In aqueous solution, carbonate, bicarbonate, carbon dioxide, in strongly basic conditions, the carbonate ion predominates, while in weakly basic conditions, the bicarbonate ion is prevalent. In more acid conditions, aqueous carbon dioxide, CO2, is the main form, thus sodium carbonate is basic, sodium bicarbonate is weakly basic, while carbon dioxide itself is a weak acid. Carbonated water is formed by dissolving CO2 in water under pressure, in living systems an enzyme, carbonic anhydrase, speeds the interconversion of CO2 and carbonic acid. Although the carbonate salts of most metals are insoluble in water, in solution this equilibrium between carbonate, bicarbonate, carbon dioxide and carbonic acid changes consonant to changing temperature and pressure conditions. In the case of ions with insoluble carbonates, e. g. CaCO3. This is an explanation for the buildup of scale inside pipes caused by hard water, in organic chemistry a carbonate can also refer to a functional group within a larger molecule that contains a carbon atom bound to three oxygen atoms, one of which is double bonded. These compounds are known as organocarbonates or carbonate esters, and have the general formula ROCOOR′
26.
Minor-planet moon
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A minor-planet moon is an astronomical object that orbits a minor planet as its natural satellite. It is thought that many asteroids and Kuiper belt objects may possess moons, the first modern era mention of the possibility of an asteroid satellite was in connection with an occultation of the bright star Gamma Ceti by the minor planet Hebe in 1977. The observer, amateur astronomer Paul D. Maley, detected an unmistakable 0.5 second disappearance of this naked eye star from a site near Victoria, many hours later, several observations were reported in Mexico attributed to the occultation by Hebe itself. Although not confirmed this documents the first formally documented case of a companion of an asteroid. As of October 2016, there are over 300 minor planets known to have moons, in addition to the terms satellite and moon, the term binary is sometimes used for minor planets with moons, and triple for minor planets with two moons. If one object is much bigger it can be referred to as the primary, when binary minor planets are similar in size, the Minor Planet Center refers to them as binary companions instead of referring to the smaller body as a satellite. A good example of a true binary is the 90 Antiope system, small satellites are often referred to as moonlets. As of February 2017, over 330 moons of planets have been discovered. For example, in 1978, stellar occultation observations were claimed as evidence of a satellite for the asteroid 532 Herculina, however, later more-detailed imaging by the Hubble Telescope did not reveal a satellite, and the current consensus is that Herculina does not have a significant satellite. There were other reports of asteroids having companions in the following years. In 1993, the first asteroid moon was confirmed when the Galileo probe discovered the small Dactyl orbiting 243 Ida in the asteroid belt, the second was discovered around 45 Eugenia in 1998. In 2001,617 Patroclus and its same-sized companion Menoetius became the first known asteroids in the Jupiter trojans. The first trans-Neptunian binary after Pluto–Charon,1998 WW31, was resolved in 2002. Triple asteroids, or trinary asteroids, are known since 2005 and this was followed by the discovery of a second moon orbiting 45 Eugenia. Also in 2005, the Kuiper belt object Haumea was discovered to have two moons, making it the second KBO after Pluto known to have more than one moon, additionally,216 Kleopatra and 93 Minerva were discovered to be trinary asteroids in 2008 and 2009 respectively. Since the first few trinary asteroids were discovered, more continue to be discovered at a rate of one a year. Most recently discovered was a moon orbiting the belt asteroid 130 Elektra. List of multiple planets, The data about the populations of binary objects are still patchy
27.
Orbit
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In physics, an orbit is the gravitationally curved path of an object around a point in space, for example the orbit of a planet about a star or a natural satellite around a planet. Normally, orbit refers to a regularly repeating path around a body, to a close approximation, planets and satellites follow elliptical orbits, with the central mass being orbited at a focal point of the ellipse, as described by Keplers laws of planetary motion. For ease of calculation, in most situations orbital motion is adequately approximated by Newtonian Mechanics, historically, the apparent motions of the planets were described by European and Arabic philosophers using the idea of celestial spheres. This model posited the existence of perfect moving spheres or rings to which the stars and it assumed the heavens were fixed apart from the motion of the spheres, and was developed without any understanding of gravity. After the planets motions were accurately measured, theoretical mechanisms such as deferent. Originally geocentric it was modified by Copernicus to place the sun at the centre to help simplify the model, the model was further challenged during the 16th century, as comets were observed traversing the spheres. The basis for the understanding of orbits was first formulated by Johannes Kepler whose results are summarised in his three laws of planetary motion. Second, he found that the speed of each planet is not constant, as had previously been thought. Third, Kepler found a relationship between the orbital properties of all the planets orbiting the Sun. For the planets, the cubes of their distances from the Sun are proportional to the squares of their orbital periods. Jupiter and Venus, for example, are respectively about 5.2 and 0.723 AU distant from the Sun, their orbital periods respectively about 11.86 and 0.615 years. The proportionality is seen by the fact that the ratio for Jupiter,5. 23/11.862, is equal to that for Venus,0. 7233/0.6152. Idealised orbits meeting these rules are known as Kepler orbits, isaac Newton demonstrated that Keplers laws were derivable from his theory of gravitation and that, in general, the orbits of bodies subject to gravity were conic sections. Newton showed that, for a pair of bodies, the sizes are in inverse proportion to their masses. Where one body is more massive than the other, it is a convenient approximation to take the center of mass as coinciding with the center of the more massive body. Lagrange developed a new approach to Newtonian mechanics emphasizing energy more than force, in a dramatic vindication of classical mechanics, in 1846 le Verrier was able to predict the position of Neptune based on unexplained perturbations in the orbit of Uranus. This led astronomers to recognize that Newtonian mechanics did not provide the highest accuracy in understanding orbits, in relativity theory, orbits follow geodesic trajectories which are usually approximated very well by the Newtonian predictions but the differences are measurable. Essentially all the evidence that can distinguish between the theories agrees with relativity theory to within experimental measurement accuracy
28.
Ann Arbor, Michigan
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Ann Arbor is a city in the U. S. state of Michigan and the county seat of Washtenaw County. The 2010 census recorded its population to be 113,934, the citys population was estimated at 117,070 as of July 2015 by the U. S. Census Bureau. The Ann Arbor Metropolitan Statistical Area includes all of Washtenaw County, the city is also part of the larger Detroit–Ann Arbor–Flint, MI Combined Statistical Area with a population of 5,318,744. Ann Arbor was founded in 1824, named for wives of the villages founders, the University of Michigan moved from Detroit to Ann Arbor in 1837, and the city grew at a rapid rate in the early to mid-20th century. During the 1960s and 1970s, the city gained a reputation as a center for left-wing politics, Ann Arbor became a focal point for political activism and anti-Vietnam War movement, as well as various student movements. Ann Arbor is home to the University of Michigan, one of the foremost research universities in the United States, the university shapes Ann Arbors economy significantly as it employs about 30,000 workers, including about 12,000 in the medical center. The citys economy is centered on high technology, with several companies drawn to the area by the universitys research and development infrastructure. In about 1774, the Potawatomi founded two villages in the area of what is now Ann Arbor, Ann Arbor was founded in 1824 by land speculators John Allen and Elisha Walker Rumsey. On 25 May 1824, the plat was registered with Wayne County as Annarbour. Allen and Rumsey decided to name it for their wives, both named Ann, and for the stands of Bur Oak in the 640 acres of land purchased for $800 from the federal government at $1.25 per acre. The local Ojibwa named the settlement kaw-goosh-kaw-nick, after the sound of Allens sawmill, Ann Arbor became the seat of Washtenaw County in 1827, and was incorporated as a village in 1833. The Ann Arbor Land Company, a group of speculators, set aside 40 acres of undeveloped land and offered it to the state of Michigan as the site of the state capital, but lost the bid to Lansing. In 1837, the property was accepted instead as the site of the University of Michigan, since the universitys establishment in the city in 1837, the histories of the University of Michigan and Ann Arbor have been closely linked. Throughout the 1840s and the 1850s settlers continued to come to Ann Arbor, while the earlier settlers were primarily of British ancestry, the newer settlers also consisted of Germans, Irish, and African-Americans. In 1851, Ann Arbor was chartered as a city, though the city showed a drop in population during the Depression of 1873. It was not until the early 1880s that Ann Arbor again saw robust growth, with new immigrants coming from Greece, Italy, Russia, Ann Arbor saw increased growth in manufacturing, particularly in milling. Ann Arbors Jewish community also grew after the turn of the 20th century, during the 1960s and 1970s, the city gained a reputation as an important center for liberal politics. Ann Arbor also became a locus for left-wing activism and anti-Vietnam War movement, during the ensuing 15 years, many countercultural and New Left enterprises sprang up and developed large constituencies within the city
29.
Menelaus
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In Greek mythology, Menelaus was a king of Mycenaean Sparta, the husband of Helen of Troy, and a central figure in the Trojan War. He was the son of Atreus and Aerope, brother of Agamemnon, king of Mycenae and, according to the Iliad, although early authors such as Aeschylus refer in passing to Menelaus’ early life, detailed sources are quite late, post-dating 5th-century BC Greek tragedy. According to these sources, Menelaus father, Atreus, had been feuding with his brother Thyestes over the throne of Mycenae, after a back-and-forth struggle that featured adultery, incest and cannibalism, Thyestes gained the throne after his son Aegisthus murdered Atreus. As a result, Atreus’ sons, Menelaus and Agamemnon, went into exile and they first stayed with King Polyphides of Sicyon, and later with King Oeneus of Calydon. But when they thought the time was ripe to dethrone Mycenae’s hostile ruler, assisted by King Tyndareus of Sparta, they drove Thyestes away, and Agamemnon took the throne for himself. When it was time for Tyndareus’ step-daughter Helen to marry, many kings, among the contenders were Odysseus, Menestheus, Ajax the Great, Patroclus, and Idomeneus. Tyndareus would accept none of the gifts, nor would he send any of the suitors away for fear of offending them, Odysseus promised to solve the problem in a satisfactory manner if Tyndareus would support him in his courting of Tyndareus’s niece Penelope, the daughter of Icarius. Tyndareus readily agreed, and Odysseus proposed that, before the decision was made, then it was decreed that straws were to be drawn for Helen’s hand. The suitor who won was Menelaus, the rest of the suitors swore their oaths, and Helen and Menelaus were married, Menelaus becoming a ruler of Sparta with Helen after Tyndareus and Leda abdicated the thrones. Menelaus and Helen had a daughter Hermione as supported, for example, by Sappho and their palace has been discovered in Pellana, Laconia, to the north-west of modern Sparta. Other archaeologists consider that Pellana is too far away from other Mycenaean centres to have been the capital of Menelaus, in a return for awarding her a golden apple inscribed to the fairest, Aphrodite promised Paris the most beautiful woman in all the world. Homers Iliad is the most expansive source for Menelaus’s exploits during the Trojan War, in Book 3, Menelaus challenges Paris to a duel for Helen’s return. Menelaus soundly beats Paris, but before he can kill him and claim victory, in Book 4, while the Greeks and Trojans squabble over the duel’s winner, Athena inspires the Trojan Pandarus to shoot Menelaus with his bow and arrow. However, Athena never intended for Menelaus to die and she protects him from the arrow of Pandarus, Menelaus is wounded in the abdomen, and the fighting resumes. Later, in Book 17, Homer gives Menelaus an extended aristeia as the hero retrieves the corpse of Patroclus from the battlefield, according to Hyginus, Menelaus killed eight men in the war, and was one of the Greeks hidden inside the Trojan Horse. During the sack of Troy, Menelaus killed Deiphobus, who had married Helen after the death of Paris, there are four versions of Menelaus’ and Helen’s reunion on the night of the sack of Troy, Angry at Helen, Menelaus looked for and found her. In a fit of rage, he decided to kill her for leaving him for Paris, in a split second, Menelaus wrath went away instantly. He took pity on her, and decided to take her back as wife, Menelaus resolved to kill Helen but her striking beauty prompted him to drop his sword and take her back to his ship “to punish her at Sparta”, as he claimed
30.
Helen of Troy
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In Greek mythology, Helen of Troy, also known as Helen of Sparta, or simply Helen, was the daughter of Zeus and Leda, and was a sister of Castor, Pollux, and Clytemnestra. In Greek myths, she was considered the most beautiful woman in the world, by marriage she was Queen of Laconia, a province within Homeric Greece, the wife of King Menelaus. Her abduction by Prince Paris of Troy brought about the Trojan War, elements of her putative biography come from classical authors such as Aristophanes, Cicero, Euripides and Homer. In her youth, she was abducted by Theseus, a competition between her suitors for her hand in marriage sees Menelaus emerge victorious. An oath sworn beforehand by all the suitors requires them to military assistance in the case of her abduction. When she marries Menelaus she is very young, whether her subsequent involvement with Paris is an abduction or a seduction is ambiguous. The legends recounting Helens fate in Troy are contradictory, Homer depicts her as a wistful figure, even a sorrowful one, who comes to regret her choice and wishes to be reunited with Menelaus. Other accounts have a treacherous Helen who simulates Bacchic rites and rejoices in the carnage, ultimately, Paris was killed in action, and in Homers account Helen was reunited with Menelaus, though other versions of the legend recount her ascending to Olympus instead. A cult associated with her developed in Hellenistic Laconia, both at Sparta and elsewhere, at Therapne she shared a shrine with Menelaus and she was also worshiped in Attica and on Rhodes. Her beauty inspired artists of all time to represent her, frequently as the personification of ideal beauty, Christopher Marlowes lines from his tragedy Doctor Faustus are frequently cited, Was this the face that launchd a thousand ships/And burnt the topless towers of Ilium. However, in the play this meeting and the ensuing temptation are not unambiguously positive, closely preceding death, images of her start appearing in the 7th century BC. In classical Greece, her abduction by—or elopement with—Paris was a popular motif, in medieval illustrations, this event was frequently portrayed as a seduction, whereas in Renaissance painting it is usually depicted as a rape by Paris. The fact that rape and kidnapping were interchangeable terms lends additional ambiguity to the story, the etymology of Helens name continues to be a problem for scholars. Georg Curtius related Helen to the moon, Émile Boisacq considered Ἑλένη to derive from the noun ἑλένη meaning torch. It has also suggested that the λ of Ἑλένη arose from an original ν. Linda Lee Clader, however, says none of the above suggestions offers much satisfaction. Inversely, others have connected this etymology to a hypothetical proto-indo-european sun goddess, in particular, her marriage myth may be connected to a broader indo-european marriage drama of the sun goddess, and she is related to the divine twins, just as many of these goddesses are. The origins of Helens myth date back to the Mycenaean age, the first record of her name appears in the poems of Homer, but scholars assume that such myths invented or received by the Mycenaean Greeks made their way to Homer
31.
Greek mythology
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It was a part of the religion in ancient Greece. Greek mythology is explicitly embodied in a collection of narratives. Greek myth attempts to explain the origins of the world, and details the lives and adventures of a variety of gods, goddesses, heroes, heroines. These accounts initially were disseminated in a tradition, today the Greek myths are known primarily from ancient Greek literature. The oldest known Greek literary sources, Homers epic poems Iliad and Odyssey, focus on the Trojan War, archaeological findings provide a principal source of detail about Greek mythology, with gods and heroes featured prominently in the decoration of many artifacts. Geometric designs on pottery of the eighth century BC depict scenes from the Trojan cycle as well as the adventures of Heracles, in the succeeding Archaic, Classical, and Hellenistic periods, Homeric and various other mythological scenes appear, supplementing the existing literary evidence. Greek mythology has had an influence on the culture, arts. Poets and artists from ancient times to the present have derived inspiration from Greek mythology and have discovered contemporary significance and relevance in the themes, Greek mythology is known today primarily from Greek literature and representations on visual media dating from the Geometric period from c. Mythical narration plays an important role in every genre of Greek literature. Nevertheless, the only general mythographical handbook to survive from Greek antiquity was the Library of Pseudo-Apollodorus and this work attempts to reconcile the contradictory tales of the poets and provides a grand summary of traditional Greek mythology and heroic legends. Apollodorus of Athens lived from c, 180–125 BC and wrote on many of these topics. His writings may have formed the basis for the collection, however the Library discusses events that occurred long after his death, among the earliest literary sources are Homers two epic poems, the Iliad and the Odyssey. Other poets completed the cycle, but these later and lesser poems now are lost almost entirely. Despite their traditional name, the Homeric Hymns have no connection with Homer. They are choral hymns from the part of the so-called Lyric age. Hesiods Works and Days, a poem about farming life, also includes the myths of Prometheus, Pandora. The poet gives advice on the best way to succeed in a dangerous world, lyrical poets often took their subjects from myth, but their treatment became gradually less narrative and more allusive. Greek lyric poets, including Pindar, Bacchylides and Simonides, and bucolic poets such as Theocritus and Bion, additionally, myth was central to classical Athenian drama
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Adaptive optics
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Adaptive optics works by measuring the distortions in a wavefront and compensating for them with a device that corrects those errors such as a deformable mirror or a liquid crystal array. Adaptive optics should not be confused with active optics, which works on a timescale to correct the primary mirror geometry. Adaptive optics was first envisioned by Horace W, some of the initial development work on adaptive optics was done by the US military during the Cold War and was intended for use in tracking Soviet satellites. The simplest form of adaptive optics is tip-tilt correction, which corresponds to correction of the tilts of the wavefront in two dimensions and this is performed using a rapidly moving tip–tilt mirror that makes small rotations around two of its axes. A significant fraction of the aberration introduced by the atmosphere can be removed in this way, tip–tilt mirrors are effectively segmented mirrors having only one segment which can tip and tilt, rather than having an array of multiple segments that can tip and tilt independently. Due to the simplicity of such mirrors and having a large stroke, meaning they have large correcting power, most AO systems use these, first. Higher order aberrations may then be corrected with deformable mirrors, when light from a star or another astronomical object enters the Earths atmosphere, atmospheric turbulence can distort and move the image in various ways. Visual images produced by any larger than approximately 20 centimeters are blurred by these distortions. In order to perform adaptive optics correction, the shape of the incoming wavefronts must be measured as a function of position in the aperture plane. The mean wavefront perturbation in each pixel is calculated and this pixelated map of the wavefronts is fed into the deformable mirror and used to correct the wavefront errors introduced by the atmosphere. The deformable mirror corrects incoming light so that the images appear sharp, because a science target is often too faint to be used as a reference star for measuring the shape of the optical wavefronts, a nearby brighter guide star can be used instead. This severely limits the application of the technique for astronomical observations, another major limitation is the small field of view over which the adaptive optics correction is good. As the angular distance from the star increases, the image quality degrades. A technique known as adaptive optics uses several deformable mirrors to achieve a greater field of view. An alternative is the use of a beam to generate a reference light source in the atmosphere. LGSs come in two flavors, Rayleigh guide stars and sodium guide stars, Rayleigh guide stars work by propagating a laser, usually at near ultraviolet wavelengths, and detecting the backscatter from air at altitudes between 15–25 km. Sodium guide stars use laser light at 589 nm to excite sodium atoms higher in the mesosphere and thermosphere, which then appear to glow. The LGS can then be used as a wavefront reference in the way as a natural guide star – except that natural reference stars are still required for image position information
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W. M. Keck Observatory
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The W. M. Keck Observatory is a two-telescope astronomical observatory at an elevation of 4,145 meters near the summit of Mauna Kea in the U. S. state of Hawaii. Both telescopes feature 10 m primary mirrors, currently among the largest astronomical telescopes in use, the combination of an excellent site, large optics and innovative instruments has created the two most scientifically productive telescopes on Earth. With a design in hand a search for the funding began, Keck of the W. M. Keck Foundation gave $70 million to fund the construction of the Keck I telescope. Construction of Keck I began in September 1985, with first light occurring on 24 November 1990 using only nine of the eventual 36 segments, with construction of the first telescope well advanced, further donations allowed the construction of a second telescope starting in 1991. The Keck I telescope began observations in May 1993, while first light for Keck II occurred on October 23,1996. The key advance that allowed the construction of the Keck Observatorys large telescopes was the ability to operate smaller mirror segments as a single, in the case of the Keck Observatory telescopes each of the primary mirrors is composed of 36 hexagonal segments that work together as a single unit. Each segment is 1.8 meters wide,7.5 centimeters thick, the mirrors were made from Zerodur glass-ceramic by the German company Schott AG. On the telescope, each segment is kept stable by a system of active optics, during observation, the computer-controlled system of sensors and actuators adjusts the position of each segment, relative to its neighbors, to an accuracy of four nanometers. This twice-per-second adjustment counters the effect of gravity as the telescope moves, each Keck Observatory telescope sits on an altazimuth mount. Most current 8–10 m class telescopes use altazimuth designs due to the structural requirements compared to older equatorial designs. This mounting style provides the greatest strength and stiffness for the least amount of steel, the total weight of each telescope is more than 300 tons. Two of the designs for the next generation 30 and 40 m telescopes use the same basic technology pioneered at Keck Observatory. Because of this difference in design, Keck Observatorys telescopes arguably remain the largest steerable. The telescopes are equipped with a suite of instruments, both cameras and spectrometers that allow observations across much of the visible and near infrared spectrum, construction of the telescopes was made possible through private grants totaling more than $140 million provided by the W. M. Keck Foundation. The National Aeronautics and Space Administration joined the partnership in October 1996, telescope time is allocated by the partner institutions. Caltech, the University of Hawaii System, and the University of California accept proposals from their own researchers, NASA accepts proposals from researchers based in the United States, while the National Optical Astronomy Observatory accept proposals from researchers around the world. MOSFIRE MOSFIRE is a third generation instrument for the W. M. Keck Observatory, MOSFIRE was delivered to Keck Observatory on February 8,2012 and first light on the Keck I telescope was obtained on April 4,2012. Bars move in each side to form up to 46 short slits
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Precession
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Precession is a change in the orientation of the rotational axis of a rotating body. In an appropriate reference frame it can be defined as a change in the first Euler angle, in other words, if the axis of rotation of a body is itself rotating about a second axis, that body is said to be precessing about the second axis. A motion in which the second Euler angle changes is called nutation, in physics, there are two types of precession, torque-free and torque-induced. In astronomy, precession refers to any of several changes in an astronomical bodys rotational or orbital parameters. An important example is the change in the orientation of the axis of rotation of the Earth. Torque-free precession implies that no moment is applied to the body. In torque-free precession, the momentum is a constant. What makes this possible is a moment of inertia, or more precisely. The inertia matrix is composed of the moments of inertia of a body calculated with respect to coordinate axes. If an object is asymmetric about its axis of rotation. The result is that the component of the velocities of the body about each axis will vary inversely with each axis moment of inertia. When an object is not perfectly solid, internal vortices will tend to damp torque-free precession, R new = exp R old for the skew-symmetric matrix ×. Torque-induced precession is the phenomenon in which the axis of a spinning object describes a cone in space when a torque is applied to it. The phenomenon is seen in a spinning toy top. If the speed of the rotation and the magnitude of the external torque are constant, the spin axis will move at right angles to the direction that would intuitively result from the external torque. In the case of a toy top, its weight is acting downwards from its center of mass and these two opposite forces produce a torque which causes the top to precess. The device depicted on the right is gimbal mounted, from inside to outside there are three axes of rotation, the hub of the wheel, the gimbal axis, and the vertical pivot. To distinguish between the two axes, rotation around the wheel hub will be called spinning, and rotation around the gimbal axis will be called pitching
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Ellipsoid
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An ellipsoid is a surface that may be obtained from a sphere by deforming it by means of directional scalings, or more generally, of an affine transformation. An ellipsoid is a surface, that is a surface that may be defined as the zero set of a polynomial of degree two in three variables. Among quadric surfaces, an ellipsoid is characterized by any of the two following properties, every planar cross section is either an ellipse, or is empty, or is reduced to a single point. It is bounded, which means that it may be enclosed in a large sphere. An ellipsoid has three perpendicular axes of symmetry which intersect at a center of symmetry, called the center of the ellipsoid. The line segments that are delimited on the axes of symmetry by the ellipsoid are called the principal axes, if the three axes have different lengths, the ellipsoid is said to be tri-axial or scalene, and the axes are uniquely defined. If two of the axes have the length, then the ellipsoid is an ellipsoid of revolution. In this case, the ellipsoid is invariant under a rotation around the third axis, if the third axis is shorter, the ellipsoid is an oblate spheroid, if it is longer, it is prolate spheroid. If the three axes have the length, the ellipsoid is a sphere. The points, and lie on the surface, the line segments from the origin to these points are called the semi-principal axes of the ellipsoid, because a, b, c are half the length of the principal axes. They correspond to the axis and semi-minor axis of an ellipse. If a = b > c, one has an oblate spheroid, if a = b < c, one has a prolate spheroid, if a = b = c, one has a sphere. It is easy to check, The intersection of a plane, remark, The contour of an ellipsoid, seen from a point outside the ellipsoid or from infinity, is in any case a plane section, hence an ellipse. The ellipsoid may be parameterized in several ways, which are simpler to express when the ellipsoid axes coincide with coordinate axes. A common choice is x = a cos cos , y = b cos sin , z = c sin and these parameters may be interpreted as spherical coordinates. More precisely, π /2 − θ is the polar angle, and φ is the azimuth angle of the point of the ellipsoid. More generally, an arbitrarily oriented ellipsoid, centered at v, is defined by the x to the equation T A =1. The eigenvectors of A define the axes of the ellipsoid and the eigenvalues of A are the reciprocals of the squares of the semi-axes
36.
Occultation
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An occultation is an event that occurs when one object is hidden by another object that passes between it and the observer. The word is used in astronomy and it can also refer to any situation wherein an object in the foreground blocks from view an object in the background. In this general sense, occultation applies to the visual scene observed from low-flying aircraft wherein foreground objects obscure distant objects dynamically, as the scene changes over time. The term occultation is most frequently used to describe those relatively frequent occasions when the Moon passes in front of a star during the course of its orbital motion around the Earth. Events that take place on the Moons dark limb are of particular interest to observers, the Moons orbit is inclined to the ecliptic, and any stars with an ecliptic latitude of less than about 6.5 degrees may be occulted by it. There are three first magnitude stars that are close to the ecliptic that they may be occulted by the Moon and by planets – Regulus, Spica. Occultations of Aldebaran are presently only possible by the Moon, because the planets pass Aldebaran to the north, neither planetary nor lunar occultations of Pollux are currently possible. However, in the far future, occultations of Pollux will be possible, some deep-sky objects, such as the Pleiades, can also be occulted by the Moon. From an observational and scientific standpoint, these grazes are the most dynamic, the accurate timing of lunar occultations is performed regularly by astronomers. Lunar occultations timed to an accuracy of a few tenths of a second have various scientific uses, photoelectric analysis of lunar occultations have also discovered some stars to be very close visual or spectroscopic binaries. Some angular diameters of stars have been measured by timing of lunar occultations, several times during the year, someone on Earth can usually observe the Moon occulting a planet. Since planets, unlike stars, have significant angular sizes, lunar occultations of planets will create a zone on Earth from which a partial occultation of the planet will occur. An observer located within that narrow zone could observe the planets disk partly blocked by the moving moon. The same mechanic can be seen with the Sun, where observers on Earth will view it as a Solar Eclipse, therefore, a Total Solar Eclipse is effectively the same event as the Moon occulting the Sun. Stars may also be occulted by planets, uranuss rings were first discovered when that planet occulted a star in 1977. On 3 July 1989, Saturn passed in front of the 5th magnitude star 28 Sagittarii, pluto occulted stars in 1988,2002, and 2006, allowing its tenuous atmosphere to be studied via atmospheric limb sounding. In rare cases, one planet can pass in front of another, if the nearer planet appears larger than the more distant one, the event is called a mutual planetary occultation. An asteroid occultation occurs when an asteroid passes in front of a star, several events occur nearly every day over the world
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