1.
Cupid and Psyche
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Cupid and Psyche is a story originally from Metamorphoses, written in the 2nd Century AD by Lucius Apuleius Madaurensis. It concerns the overcoming of obstacles to the love between Psyche and Cupid or Amor, and their union in a sacred marriage. Although the only extended narrative from antiquity is that of Apuleius, Eros, since the rediscovery of Apuleiuss novel in the Renaissance, the reception of Cupid and Psyche in the classical tradition has been extensive. The story has been retold in poetry, drama, and opera, and depicted widely in painting, sculpture, Psyches Roman name through direct translation is Anima. The tale of Cupid and Psyche is placed at the midpoint of Apuleiuss novel, the novel itself is a first-person narrative by the protagonist Lucius. Transformed into a donkey by magic gone wrong, Lucius undergoes various trials and adventures, Psyches story has some similarities, including the theme of dangerous curiosity, punishments and tests, and redemption through divine favor. As a structural mirror of the plot, the tale is an example of mise en abyme. The happy ending for Psyche is supposed to assuage Charites fear of rape, there were once a king and queen, rulers of an unnamed city, who had three daughters of conspicuous beauty. The youngest and most beautiful was Psyche, whose admirers, neglecting the worship of the love goddess Venus, instead prayed. It was rumored that she was the coming of Venus. Venus is offended, and commissions Cupid to work her revenge, Cupid instead scratches himself with his own dart, which makes any living thing fall in love with the first thing it sees. As soon as Cupid scratches himself he falls deeply in love with Psyche, although her two humanly beautiful sisters have married, the idolized Psyche has yet to find love. Her father suspects that they have incurred the wrath of the gods, Psyche is arrayed in funeral attire, conveyed by a procession to the peak of a rocky crag, and exposed. Marriage and death are merged into a rite of passage. Zephyr the West Wind bears her up to meet her match, and deposits her in a lovely meadow. The transported girl awakes to find herself at the edge of a cultivated grove, exploring, she finds a marvelous house with golden columns, a carved ceiling of citrus wood and ivory, silver walls embossed with wild and domesticated animals, and jeweled mosaic floors. A disembodied voice tells her to make herself comfortable, and she is entertained at a feast that serves itself, although fearful and without sexual experience, she allows herself to be guided to a bedroom, where in the darkness a being she cannot see makes her his wife. She gradually learns to look forward to his visits, though he always departs before sunrise and forbids her to look upon him, and soon she becomes pregnant
2.
Minor planet
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A minor planet is an astronomical object in direct orbit around the Sun that is neither a planet nor exclusively classified as a comet. Minor planets can be dwarf planets, asteroids, trojans, centaurs, Kuiper belt objects, as of 2016, the orbits of 709,706 minor planets were archived at the Minor Planet Center,469,275 of which had received permanent numbers. The first minor planet to be discovered was Ceres in 1801, the term minor planet has been used since the 19th century to describe these objects. The term planetoid has also used, especially for larger objects such as those the International Astronomical Union has called dwarf planets since 2006. Historically, the asteroid, minor planet, and planetoid have been more or less synonymous. This terminology has become complicated by the discovery of numerous minor planets beyond the orbit of Jupiter. A Minor planet seen releasing gas may be classified as a comet. Before 2006, the IAU had officially used the term minor planet, during its 2006 meeting, the IAU reclassified minor planets and comets into dwarf planets and small Solar System bodies. Objects are called dwarf planets if their self-gravity is sufficient to achieve hydrostatic equilibrium, all other minor planets and comets are called small Solar System bodies. The IAU stated that the minor planet may still be used. However, for purposes of numbering and naming, the distinction between minor planet and comet is still used. Hundreds of thousands of planets have been discovered within the Solar System. The Minor Planet Center has documented over 167 million observations and 729,626 minor planets, of these,20,570 have official names. As of March 2017, the lowest-numbered unnamed minor planet is 1974 FV1, as of March 2017, the highest-numbered named minor planet is 458063 Gustavomuler. There are various broad minor-planet populations, Asteroids, traditionally, most have been bodies in the inner Solar System. Near-Earth asteroids, those whose orbits take them inside the orbit of Mars. Further subclassification of these, based on distance, is used, Apohele asteroids orbit inside of Earths perihelion distance. Aten asteroids, those that have semi-major axes of less than Earths, Apollo asteroids are those asteroids with a semimajor axis greater than Earths, while having a perihelion distance of 1.017 AU or less. Like Aten asteroids, Apollo asteroids are Earth-crossers, amor asteroids are those near-Earth asteroids that approach the orbit of Earth from beyond, but do not cross it
3.
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
4.
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
5.
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
6.
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
7.
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
8.
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
9.
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
10.
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
11.
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
12.
Spheroid
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A spheroid, or ellipsoid of revolution, is a quadric surface obtained by rotating an ellipse about one of its principal axes, in other words, an ellipsoid with two equal semi-diameters. If the ellipse is rotated about its axis, the result is a prolate spheroid. If the ellipse is rotated about its axis, the result is an oblate spheroid. If the generating ellipse is a circle, the result is a sphere, because of the combined effects of gravity and rotation, the Earths shape is not quite a sphere but instead is slightly flattened in the direction of its axis of rotation. For that reason, in cartography the Earth is often approximated by an oblate spheroid instead of a sphere, the current World Geodetic System model uses a spheroid whose radius is 6,378.137 km at the equator and 6,356.752 km at the poles. The semi-major axis a is the radius of the spheroid. There are two cases, c < a, oblate spheroid c > a, prolate spheroid The case of a = c reduces to a sphere. An oblate spheroid with c < a has surface area S o b l a t e =2 π a 2 where e 2 =1 − c 2 a 2. The oblate spheroid is generated by rotation about the z-axis of an ellipse with semi-major axis a and semi-minor axis c, therefore e may be identified as the eccentricity. A prolate spheroid with c > a has surface area S p r o l a t e =2 π a 2 where e 2 =1 − a 2 c 2. The prolate spheroid is generated by rotation about the z-axis of an ellipse with semi-major axis c and semi-minor axis a and these formulas are identical in the sense that the formula for Soblate can be used to calculate the surface area of a prolate spheroid and vice versa. However, e then becomes imaginary and can no longer directly be identified with the eccentricity, both of these results may be cast into many other forms using standard mathematical identities and relations between parameters of the ellipse. The volume inside a spheroid is 4π/3a2c ≈4. 19a2c, if A = 2a is the equatorial diameter, and C = 2c is the polar diameter, the volume is π/6A2C ≈0. 523A2C. Both of these curvatures are always positive, so every point on a spheroid is elliptic. These are just two of different parameters used to define an ellipse and its solid body counterparts. The most common shapes for the density distribution of protons and neutrons in an atomic nucleus are spherical, prolate and oblate spheroidal, deformed nuclear shapes occur as a result of the competition between electromagnetic repulsion between protons, surface tension and quantum shell effects. An extreme example of a planet in science fiction is Mesklin, in Hal Clements novel Mission of Gravity. The prolate spheroid is the shape of the ball in several sports, several moons of the Solar system approximate prolate spheroids in shape, though they are actually triaxial ellipsoids
13.
Volume
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Volume is the quantity of three-dimensional space enclosed by a closed surface, for example, the space that a substance or shape occupies or contains. Volume is often quantified numerically using the SI derived unit, the cubic metre, three dimensional mathematical shapes are also assigned volumes. Volumes of some simple shapes, such as regular, straight-edged, Volumes of a complicated shape can be calculated by integral calculus if a formula exists for the shapes boundary. Where a variance in shape and volume occurs, such as those that exist between different human beings, these can be calculated using techniques such as the Body Volume Index. One-dimensional figures and two-dimensional shapes are assigned zero volume in the three-dimensional space, the volume of a solid can be determined by fluid displacement. Displacement of liquid can also be used to determine the volume of a gas, the combined volume of two substances is usually greater than the volume of one of the substances. However, sometimes one substance dissolves in the other and the volume is not additive. In differential geometry, volume is expressed by means of the volume form, in thermodynamics, volume is a fundamental parameter, and is a conjugate variable to pressure. Any unit of length gives a unit of volume, the volume of a cube whose sides have the given length. For example, a cubic centimetre is the volume of a cube whose sides are one centimetre in length, in the International System of Units, the standard unit of volume is the cubic metre. The metric system also includes the litre as a unit of volume, thus 1 litre =3 =1000 cubic centimetres =0.001 cubic metres, so 1 cubic metre =1000 litres. Small amounts of liquid are often measured in millilitres, where 1 millilitre =0.001 litres =1 cubic centimetre. Capacity is defined by the Oxford English Dictionary as the applied to the content of a vessel, and to liquids, grain, or the like. Capacity is not identical in meaning to volume, though closely related, Units of capacity are the SI litre and its derived units, and Imperial units such as gill, pint, gallon, and others. Units of volume are the cubes of units of length, in SI the units of volume and capacity are closely related, one litre is exactly 1 cubic decimetre, the capacity of a cube with a 10 cm side. In other systems the conversion is not trivial, the capacity of a fuel tank is rarely stated in cubic feet, for example. The density of an object is defined as the ratio of the mass to the volume, the inverse of density is specific volume which is defined as volume divided by mass. Specific volume is an important in thermodynamics where the volume of a working fluid is often an important parameter of a system being studied
14.
Cubic kilometre
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The cubic metre or cubic meter is the SI derived unit of volume. It is the volume of a cube with one metre in length. An alternative name, which allowed a different usage with metric prefixes, was the stère, another alternative name, no longer widely used, was the kilolitre. A cubic metre of water at the temperature of maximum density and standard atmospheric pressure has a mass of 1000 kg. At 0 °C, the point of water, a cubic metre of water has slightly less mass,999.972 kilograms. It is sometimes abbreviated to cu m, m3, M3, m^3, m**3, CBM, abbreviated CBM and cbm in the freight business and MTQ in international trade. See Orders of magnitude for a comparison with other volumes
15.
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
16.
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
17.
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
18.
Hour
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An hour is a unit of time conventionally reckoned as 1⁄24 of a day and scientifically reckoned as 3, 599–3,601 seconds, depending on conditions. The seasonal, temporal, or unequal hour was established in the ancient Near East as 1⁄12 of the night or daytime, such hours varied by season, latitude, and weather. It was subsequently divided into 60 minutes, each of 60 seconds, the modern English word hour is a development of the Anglo-Norman houre and Middle English ure, first attested in the 13th century. It displaced the Old English tide and stound, the Anglo-Norman term was a borrowing of Old French ure, a variant of ore, which derived from Latin hōra and Greek hṓrā. Like Old English tīd and stund, hṓrā was originally a word for any span of time, including seasons. Its Proto-Indo-European root has been reconstructed as *yeh₁-, making hour distantly cognate with year, the time of day is typically expressed in English in terms of hours. Whole hours on a 12-hour clock are expressed using the contracted phrase oclock, Hours on a 24-hour clock are expressed as hundred or hundred hours. Fifteen and thirty minutes past the hour is expressed as a quarter past or after and half past, respectively, fifteen minutes before the hour may be expressed as a quarter to, of, till, or before the hour. Sumerian and Babylonian hours divided the day and night into 24 equal hours, the ancient Egyptians began dividing the night into wnwt at some time before the compilation of the Dynasty V Pyramid Texts in the 24th century BC. By 2150 BC, diagrams of stars inside Egyptian coffin lids—variously known as diagonal calendars or star clocks—attest that there were exactly 12 of these. The coffin diagrams show that the Egyptians took note of the risings of 36 stars or constellations. Each night, the rising of eleven of these decans were noted, the original decans used by the Egyptians would have fallen noticeably out of their proper places over a span of several centuries. By the time of Amenhotep III, the priests at Karnak were using water clocks to determine the hours and these were filled to the brim at sunset and the hour determined by comparing the water level against one of its twelve gauges, one for each month of the year. During the New Kingdom, another system of decans was used, the later division of the day into 12 hours was accomplished by sundials marked with ten equal divisions. The morning and evening periods when the failed to note time were observed as the first and last hours. The Egyptian hours were closely connected both with the priesthood of the gods and with their divine services, by the New Kingdom, each hour was conceived as a specific region of the sky or underworld through which Ras solar bark travelled. Protective deities were assigned to each and were used as the names of the hours, as the protectors and resurrectors of the sun, the goddesses of the night hours were considered to hold power over all lifespans and thus became part of Egyptian funerary rituals. The Egyptian for astronomer, used as a synonym for priest, was wnwty, the earliest forms of wnwt include one or three stars, with the later solar hours including the determinative hieroglyph for sun
19.
Apparent magnitude
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The apparent magnitude of a celestial object is a number that is a measure of its brightness as seen by an observer on Earth. The brighter an object appears, the lower its magnitude value, the Sun, at apparent magnitude of −27, is the brightest object in the sky. It is adjusted to the value it would have in the absence of the atmosphere, furthermore, the magnitude scale is logarithmic, a difference of one in magnitude corresponds to a change in brightness by a factor of 5√100, or about 2.512. The measurement of apparent magnitudes or brightnesses of celestial objects is known as photometry, apparent magnitudes are used to quantify the brightness of sources at ultraviolet, visible, and infrared wavelengths. An apparent magnitude is measured in a specific passband corresponding to some photometric system such as the UBV system. In standard astronomical notation, an apparent magnitude in the V filter band would be denoted either as mV or often simply as V, the scale used to indicate magnitude originates in the Hellenistic practice of dividing stars visible to the naked eye into six magnitudes. The brightest stars in the sky were said to be of first magnitude, whereas the faintest were of sixth magnitude. Each grade of magnitude was considered twice the brightness of the following grade and this rather crude scale for the brightness of stars was popularized by Ptolemy in his Almagest, and is generally believed to have originated with Hipparchus. This implies that a star of magnitude m is 2.512 times as bright as a star of magnitude m +1 and this figure, the fifth root of 100, became known as Pogsons Ratio. The zero point of Pogsons scale was defined by assigning Polaris a magnitude of exactly 2. However, with the advent of infrared astronomy it was revealed that Vegas radiation includes an Infrared excess presumably due to a disk consisting of dust at warm temperatures. At shorter wavelengths, there is negligible emission from dust at these temperatures, however, in order to properly extend the magnitude scale further into the infrared, this peculiarity of Vega should not affect the definition of the magnitude scale. Therefore, the scale was extrapolated to all wavelengths on the basis of the black body radiation curve for an ideal stellar surface at 11000 K uncontaminated by circumstellar radiation. On this basis the spectral irradiance for the zero magnitude point, with the modern magnitude systems, brightness over a very wide range is specified according to the logarithmic definition detailed below, using this zero reference. In practice such apparent magnitudes do not exceed 30, astronomers have developed other photometric zeropoint systems as alternatives to the Vega system. The AB magnitude zeropoint is defined such that an objects AB, the dimmer an object appears, the higher the numerical value given to its apparent magnitude, with a difference of 5 magnitudes corresponding to a brightness factor of exactly 100. Since an increase of 5 magnitudes corresponds to a decrease in brightness by a factor of exactly 100, each magnitude increase implies a decrease in brightness by the factor 5√100 ≈2.512. Inverting the above formula, a magnitude difference m1 − m2 = Δm implies a brightness factor of F2 F1 =100 Δ m 5 =100.4 Δ m ≈2.512 Δ m
20.
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
21.
Protoplanet
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A protoplanet is a large planetary embryo that originated within a protoplanetary disc and has undergone internal melting to produce a differentiated interior. Protoplanets are thought to form out of kilometer-sized planetesimals that gravitationally perturb each others orbits and collide, in the case of the Solar System, it is thought that the collisions of planetesimals created a few hundred planetary embryos. Such embryos were similar to Ceres and Pluto with masses of about 1022 to 1023 kg and were a few kilometers in diameter. Over the course of hundreds of millions of years, they collided with one another and these in their turn would have collided to create a third generation of fewer but even larger embryos. Eventually, only a handful of embryos were left, which collided to complete the assembly of the planets proper, early protoplanets had more radioactive elements, the quantity of which has been reduced over time due to radioactive decay. Heating due to radioactivity, impact, and gravitational pressure melted parts of protoplanets as they grew toward being planets, in melted zones their heavier elements sank to the center, whereas lighter elements rose to the surface. Such a process is known as planetary differentiation, the composition of some meteorites show that differentiation took place in some asteroids. According to the giant impact hypothesis the Moon formed from an impact of a hypothetical protoplanet called Theia with Earth. In the inner Solar System, the three protoplanets to survive intact are the asteroids Ceres, Pallas, and Vesta. Psyche is likely the survivor of a violent hit-and-run with another object that stripped off the outer, the asteroid Lutetia also has characteristics that resemble a protoplanet. Kuiper-belt dwarf planets have also referred to as protoplanets. In February 2013 astronomers made the first direct observation of a protoplanet forming in a disk of gas, fusor Mesoplanet Planetesimal Thread on the definition of a protoplanet
22.
Naples
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Naples is the capital of the Italian region Campania and the third-largest municipality in Italy, after Rome and Milan. In 2015, around 975,260 people lived within the administrative limits. The Metropolitan City of Naples had a population of 3,115,320, Naples is the 9th-most populous urban area in the European Union with a population of between 3 million and 3.7 million. About 4.4 million people live in the Naples metropolitan area, Naples is one of the oldest continuously inhabited cities in the world. Bronze Age Greek settlements were established in the Naples area in the second millennium BC, a larger colony – initially known as Parthenope, Παρθενόπη – developed on the Island of Megaride around the ninth century BC, at the end of the Greek Dark Ages. Naples remained influential after the fall of the Western Roman Empire, thereafter, in union with Sicily, it became the capital of the Two Sicilies until the unification of Italy in 1861. Naples was the most-bombed Italian city during World War II, much of the citys 20th-century periphery was constructed under Benito Mussolinis fascist government, and during reconstruction efforts after World War II. The city has experienced significant economic growth in recent decades, and unemployment levels in the city, however, Naples still suffers from political and economic corruption, and unemployment levels remain high. Naples has the fourth-largest urban economy in Italy, after Milan, Rome and it is the worlds 103rd-richest city by purchasing power, with an estimated 2011 GDP of US$83.6 billion. The port of Naples is one of the most important in Europe, numerous major Italian companies, such as MSC Cruises Italy S. p. A, are headquartered in Naples. The city also hosts NATOs Allied Joint Force Command Naples, the SRM Institution for Economic Research, Naples is a full member of the Eurocities network of European cities. The city was selected to become the headquarters of the European institution ACP/UE and was named a City of Literature by UNESCOs Creative Cities Network, the Villa Rosebery, one of the three official residences of the President of Italy, is located in the citys Posillipo district. Naples historic city centre is the largest in Europe, covering 1,700 hectares and enclosing 27 centuries of history, Naples has long been a major cultural centre with a global sphere of influence, particularly during the Renaissance and Enlightenment eras. In the immediate vicinity of Naples are numerous culturally and historically significant sites, including the Palace of Caserta, culinarily, Naples is synonymous with pizza, which originated in the city. Neapolitan music has furthermore been highly influential, credited with the invention of the romantic guitar, according to CNN, the metro stop Toledo is the most beautiful in Europe and it won also the LEAF Award 2013 as Public building of the year. Naples is the Italian city with the highest number of accredited stars from the Michelin Guide, Naples sports scene is dominated by football and Serie A club S. S. C. Napoli, two-time Italian champions and winner of European trophies, who play at the San Paolo Stadium in the south-west of the city, the Phlegraean Fields around Naples has been inhabited since the Neolithic period. The earliest Greek settlements were established in the Naples area in the second millennium BC, sailors from the Greek island of Rhodes established a small commercial port called Parthenope on the island of Megaride in the ninth century BC
23.
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
24.
Johann Franz Encke
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Johann Franz Encke was a German astronomer. Among his activities, he worked on the calculation of the periods of comets and asteroids, measured the distance from the earth to the sun, Encke was born in Hamburg, where his father was the Pastor at the St. James Church, Hamburg. He was the youngest of eight children, and at the time his father died when he was four, thanks to the financial assistance of a teacher, he was able to be educated at the Gelehrtenschule des Johanneums. In 1814 he resumed his studies at the University but after Napoleons escape from Elba he returned to the military, having returned to Göttingen in 1816, he was at once appointed by Bernhardt von Lindenau as his assistant in the observatory of Seeberg near Gotha. That comet is now called 12P/Pons-Brooks, at this time, all the known comets had an orbital period of seventy years and more, with an aphelion far beyond the orbit of Uranus. The most famous comet of this family was Comet Halley with its period of seventy-six years. So the orbit of the discovered by Pons was a sensation, because his orbit was found to have a period of 3.3 years. Encke predicted its return for 1822, but this return was only from the southern hemisphere and was seen by Carl Ludwig Christian Rümker in Australia. The comet was identified with the one seen by Pierre Méchain in 1786. Encke sent his calculations as a note to Gauss, Olbers and his former mathematics professor published this note and Encke became famous as the discoverer of the short periodic comets. The first object of this family, the Encke comet, was named after him and so it is one of the few comets not named after the discoverer, later this comet was identified as the origin of the Taurids meteor showers. The importance of the return based on the calculation by Encke was rewarded by the Royal Astronomical Society in London by presenting their Gold Medal to him in 1824. In this year Encke married Amalie Becker, daughter of author, bookseller and publisher Rudolph Zacharias Becker and they had three sons and two daughters. In 1825 he was elected a Fellow of the Royal Society, eight masterly treatises on the comets movements were published by him in the Berliner Abhandlungen. From a fresh discussion of the transits of Venus in 1761 and 1769 he deduced a solar parallax of 8.57 arcsecond and this and the corresponding distance to the sun were long accepted as authoritative. His results were published in two tracts, entitled Die Entfernung der Sonne. Mostly on the recommendation of Bessel, Encke became director of the new observatory and secretary of the Academy of Sciences, within the following time Encke was involved in the discovery and orbital parameter determination of other short periodic comets and asteroids. In 1837, Encke described a variation in the brightness of the A Ring of Saturn
25.
Lightcurve
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In astronomy, a light curve is a graph of light intensity of a celestial object or region, as a function of time. The light is usually in a particular frequency interval or band, the study of the light curve, together with other observations, can yield considerable information about the physical process that produces it or constrain the physical theories about it. Light waves can also be used in botany to determine a plants reactions to light intensities, in astronomy, light curves from a supernova are used to determine what type of supernova it is. If the supernovas light curve has a maximum and slopes down gradually. If the supernovas light curve has a sharp maximum, slopes down quickly. In planetary science, a curve can be used to derive the rotation period of a minor planet, moon. Thus, astronomers measure the amount of produced by an object as a function of time. The time separation of peaks in the curve gives an estimate of the rotational period of the object. The difference between the maximum and minimum brightnesses can be due to the shape of the object, or to bright, for example, an asymmetrical asteroids light curve generally has more pronounced peaks, while a more spherical objects light curve will be flatter. The Asteroid Lightcurve Database of the Collaborative Asteroid Lightcurve Link uses a code to assess the quality of a period solution for minor planet light curves. Its quality code parameter U ranges from 0 to 3, U =0 → Result later proven incorrect U =1 → Result based on fragmentary light curve, U =2 → Result based on less than full coverage. Period may be wrong by 30 percent or ambiguous, U =3 → Secure result within the precision given. A trailing plus sign or minus sign is used to indicate a slightly better or worse quality than the unsigned value. In botany, a light curve shows the response of leaf tissue or algal communities to varying light intensities. Since photosynthesis is limited by ambient carbon dioxide levels, light curves are often repeated at several different constant carbon dioxide concentrations. The AAVSO online light curve generator can plot light curves for thousands of variable stars Lightcurves, An Introduction by NASAs Imagine the Universe
26.
Perturbation (astronomy)
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In astronomy, perturbation is the complex motion of a massive body subject to forces other than the gravitational attraction of a single other massive body. The other forces can include a body, resistance, as from an atmosphere. The study of perturbations began with the first attempts to predict planetary motions in the sky, in ancient times the causes were a mystery. Newton, at the time he formulated his laws of motion and of gravitation, applied them to the first analysis of perturbations, the complex motions of gravitational perturbations can be broken down. The hypothetical motion that the body follows under the effect of one other body only is typically a conic section. This is called a problem, or an unperturbed Keplerian orbit. The differences between that and the motion of the body are perturbations due to the additional gravitational effects of the remaining body or bodies. If there is one other significant body then the perturbed motion is a three-body problem. A general analytical solution exists for the problem, when more than two bodies are considered analytic solutions exist only for special cases. Even the two-body problem becomes insoluble if one of the bodies is irregular in shape, most systems that involve multiple gravitational attractions present one primary body which is dominant in its effects. The gravitational effects of the bodies can be treated as perturbations of the hypothetical unperturbed motion of the planet or satellite around its primary body. In methods of general perturbations, general differential equations, either of motion or of change in the elements, are solved analytically, usually by series expansions. The result is expressed in terms of algebraic and trigonometric functions of the orbital elements of the body in question. This can be applied generally to many different sets of conditions, historically, general perturbations were investigated first. The classical methods are known as variation of the elements, variation of parameters or variation of the constants of integration, in these methods, it is considered that the body is always moving in a conic section, however the conic section is constantly changing due to the perturbations. General perturbations is applicable if the perturbing forces are about one order of magnitude smaller, or less. In the Solar System, this is usually the case, Jupiter, general perturbation methods are preferred for some types of problems, as the source of certain observed motions are readily found. In effect, the positions and velocities are perturbed directly, special perturbations can be applied to any problem in celestial mechanics, as it is not limited to cases where the perturbing forces are small
27.
IRAS
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The Infrared Astronomical Satellite was the first-ever space telescope to perform a survey of the entire night sky at infrared wavelengths. Launched on 25 January 1983, its mission lasted ten months, the telescope was a joint project of the United States, the Netherlands, and the United Kingdom. Over 250,000 infrared sources were observed at 12,25,60, support for the processing and analysis of data from IRAS was contributed from the Infrared Processing and Analysis Center at the California Institute of Technology. Currently, the Infrared Science Archive at IPAC holds the IRAS archive, the success of early infrared space astronomy led to further missions, such as the Infrared Space Observatory and the Hubble Space Telescopes NICMOS instrument. IRAS was the first observatory to perform a survey at infrared wavelengths. It mapped 96% of the sky four times, at 12,25,60 and 100 micrometers and it discovered about 350,000 sources, many of which are still awaiting identification. About 75,000 of those are believed to be starburst galaxies, many other sources are normal stars with disks of dust around them, possibly the early stage of planetary system formation. New discoveries included a dust disk around Vega and the first images of the Milky Ways core, IRASs life, like that of most infrared satellites that followed, was limited by its cooling system. To effectively work in the domain, a telescope must be cooled to cryogenic temperatures. In IRASs case,73 kilograms of superfluid helium kept the telescope at a temperature of 2 K, the on-board supply of liquid helium was depleted after 10 months on 21 November 1983, causing the telescope temperature to rise, preventing further observations. The spacecraft continues to orbit the Earth, IRAS was designed to catalog fixed sources, so it scanned the same region of sky several times. Jack Meadows led a team at Leicester University, including John Davies and Simon Green and this led to the discovery of three asteroids, including 3200 Phaethon, six comets, and a huge dust trail associated with comet 10P/Tempel. The comets included 126P/IRAS, 161P/Hartley–IRAS, and comet IRAS–Araki–Alcock, which made an approach to the Earth in 1983. Out of the six comets IRAS found, four were long period, further analysis revealed that, of several unidentified objects, nine were distant galaxies and the tenth was intergalactic cirrus. None were found to be Solar System bodies, during its mission, IRAS detected odd infrared signatures around several stars. This led to the systems being targeted by the Hubble Space Telescopes NICMOS instrument between 1999 and 2006, but nothing was detected, in 2014, using new image processing techniques on the Hubble data, researchers discovered planetary disks around these stars. A next generation of infrared space telescopes began when NASAs Wide-field Infrared Survey Explorer launched on 14 December 2009 aboard a Delta II rocket from Vandenberg Air Force Base. A. Neugebauer, G. Habing, H. J. Clegg, P. E. Chester, Infrared Astronomical Satellite, Catalogs and Atlases
28.
Infrared
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It extends from the nominal red edge of the visible spectrum at 700 nanometers, to 1000000 nm. Most of the radiation emitted by objects near room temperature is infrared. Like all EMR, IR carries radiant energy, and behaves both like a wave and like its quantum particle, the photon, slightly more than half of the total energy from the Sun was eventually found to arrive on Earth in the form of infrared. The balance between absorbed and emitted infrared radiation has an effect on Earths climate. Infrared radiation is emitted or absorbed by molecules when they change their rotational-vibrational movements and it excites vibrational modes in a molecule through a change in the dipole moment, making it a useful frequency range for study of these energy states for molecules of the proper symmetry. Infrared spectroscopy examines absorption and transmission of photons in the infrared range, Infrared radiation is used in industrial, scientific, and medical applications. Night-vision devices using active near-infrared illumination allow people or animals to be observed without the observer being detected, Infrared thermal-imaging cameras are used to detect heat loss in insulated systems, to observe changing blood flow in the skin, and to detect overheating of electrical apparatuses. Thermal-infrared imaging is used extensively for military and civilian purposes, military applications include target acquisition, surveillance, night vision, homing, and tracking. Humans at normal body temperature radiate chiefly at wavelengths around 10 μm, Infrared radiation extends from the nominal red edge of the visible spectrum at 700 nanometers to 1 mm. This range of wavelengths corresponds to a range of approximately 430 THz down to 300 GHz. Below infrared is the portion of the electromagnetic spectrum. Sunlight, at a temperature of 5,780 kelvins, is composed of near thermal-spectrum radiation that is slightly more than half infrared. At zenith, sunlight provides an irradiance of just over 1 kilowatt per square meter at sea level, of this energy,527 watts is infrared radiation,445 watts is visible light, and 32 watts is ultraviolet radiation. Nearly all the radiation in sunlight is near infrared, shorter than 4 micrometers. On the surface of Earth, at far lower temperatures than the surface of the Sun, almost all thermal radiation consists of infrared in mid-infrared region, much longer than in sunlight. Of these natural thermal radiation processes only lightning and natural fires are hot enough to produce much visible energy, thermal infrared radiation also has a maximum emission wavelength, which is inversely proportional to the absolute temperature of object, in accordance with Wiens displacement law. Therefore, the band is often subdivided into smaller sections. Due to the nature of the blackbody radiation curves, typical hot objects, such as exhaust pipes, the three regions are used for observation of different temperature ranges, and hence different environments in space
29.
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
30.
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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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
, a semicircle topped by a star, represents a butterfly's wing, symbol of the soul (psyche is the Greek word for 'soul'), and a star.[6] In 1851, German astronomer J. F. Encke suggested using a circled number, and 16 Psyche was the first new asteroid to be discovered that was designated using this scheme when American astronomer James Ferguson published his observations in 1852.[7].png)
. Bibcode:2017AJ....153...31T. doi:10.3847/1538-3881/153/1/31.
