1.
Constellation
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A constellation is formally defined as a region of the celestial sphere, with boundaries laid down by the International Astronomical Union. The constellation areas mostly had their origins in Western-traditional patterns of stars from which the constellations take their names, in 1922, the International Astronomical Union officially recognized the 88 modern constellations, which cover the entire sky. They began as the 48 classical Greek constellations laid down by Ptolemy in the Almagest, Constellations in the far southern sky are late 16th- and mid 18th-century constructions. 12 of the 88 constellations compose the zodiac signs, though the positions of the constellations only loosely match the dates assigned to them in astrology. The term constellation can refer to the stars within the boundaries of that constellation. Notable groupings of stars that do not form a constellation are called asterisms, when astronomers say something is “in” a given constellation they mean it is within those official boundaries. Any given point in a coordinate system can unambiguously be assigned to a single constellation. Many astronomical naming systems give the constellation in which an object is found along with a designation in order to convey a rough idea in which part of the sky it is located. For example, the Flamsteed designation for bright stars consists of a number, the word constellation seems to come from the Late Latin term cōnstellātiō, which can be translated as set of stars, and came into use in English during the 14th century. It also denotes 88 named groups of stars in the shape of stellar-patterns, the Ancient Greek word for constellation was ἄστρον. Colloquial usage does not draw a distinction between constellation in the sense of an asterism and constellation in the sense of an area surrounding an asterism. The modern system of constellations used in astronomy employs the latter concept, the term circumpolar constellation is used for any constellation that, from a particular latitude on Earth, never sets below the horizon. From the North Pole or South Pole, all constellations south or north of the equator are circumpolar constellations. In the equatorial or temperate latitudes, the term equatorial constellation has sometimes been used for constellations that lie to the opposite the circumpolar constellations. They generally include all constellations that intersect the celestial equator or part of the zodiac, usually the only thing the stars in a constellation have in common is that they appear near each other in the sky when viewed from the Earth. In galactic space, the stars of a constellation usually lie at a variety of distances, since stars also travel on their own orbits through the Milky Way, the star patterns of the constellations change slowly over time. After tens to hundreds of thousands of years, their familiar outlines will become unrecognisable, the terms chosen for the constellation themselves, together with the appearance of a constellation, may reveal where and when its constellation makers lived. The earliest direct evidence for the constellations comes from inscribed stones and it seems that the bulk of the Mesopotamian constellations were created within a relatively short interval from around 1300 to 1000 BC
2.
Ursa Minor
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Ursa Minor, also known as the Little Bear, is a constellation in the Northern Sky. It was one of the 48 constellations listed by the 2nd-century astronomer Ptolemy, Ursa Minor has traditionally been important for navigation, particularly by mariners, because of Polaris being the North Star. Polaris, the brightest star in the constellation, is a yellow-white supergiant, Beta Ursae Minoris, also known as Kochab, is an aging star that has swollen and cooled to become an orange giant with an apparent magnitude of 2.08, only slightly fainter than Polaris. Kochab and magnitude 3 Gamma Ursae Minoris have been called the guardians of the pole star, planets have been detected orbiting four of the stars, including Kochab. The constellation also contains an isolated neutron star—Calvera—and H1504+65, the hottest white dwarf yet discovered, in the Babylonian star catalogues, Ursa Minor was known as MAR. GID. DA. AN. NA, the Wagon of Heaven, Damkianna. It appeared on a pair of tablets containing canonical star lists that were compiled around 1000 BC, the MUL. APIN, and was one of the Stars of Enlil—that is, the northern sky. The possible origin of its name was its appearing to rotate like a wheel around the celestial pole. The first mention of Ursa Minor in Greek texts was by philosopher Thales of Miletus in the 6th century BC and he pointed out that it was a more accurate guide to finding true north than Ursa Major. This knowledge had come from the Phoenicians in the eastern Mediterranean. Homer had previously referred to one bear, raising the question of what he saw the stars of Ursa Minor as. Ursa Minor and Ursa Major were related by the Greeks to the myth of Callisto and her son Arcas, in a variant of the story in which Boötes represents Arcas, Ursa Minor represents a dog. This is the tradition, which explains both the length of the tail and the obsolete alternate name of Cynosura for Polaris, the North Star. Cynosura is also described as a nurse of Zeus, honoured by the god with a place in the sky, an alternate myth tells of two bears that saved Zeus from his murderous father Kronos by hiding him on Mount Ida. Later Zeus set them in the sky, but their tails grew long from being swung by the god. Because Ursa Minor consists of seven stars, the Latin word for North is septentrio, from septem and triones, from seven oxen driving a plough and this name has also been attached to the main stars of Ursa Major. Ursa Minor has traditionally been important for navigation, particularly by mariners, Polaris is currently less than one degree away from the north celestial pole so its position in the sky is largely unaffected by the rotation of the Earth. From any point in the Northern Hemisphere the direction to Polaris is always north, in Inuit astronomy, the three brightest stars—Polaris, Kochab and Pherkad—were known as Nuutuittut never moving, though the term is more frequently used in the singular to refer to Polaris alone. The Pole Star is too high in the sky at far northern latitudes to be of use in navigation, Ursa Minor is bordered by Camelopardalis to the west, Draco to the west, and Cepheus to the east
3.
Right ascension
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Right ascension is the angular distance measured eastward along the celestial equator from the vernal equinox to the hour circle of the point in question. When combined with declination, these astronomical coordinates specify the direction of a point on the sphere in the equatorial coordinate system. Right ascension is the equivalent of terrestrial longitude. Both right ascension and longitude measure an angle from a direction on an equator. Right ascension is measured continuously in a circle from that equinox towards the east. Any units of measure could have been chosen for right ascension, but it is customarily measured in hours, minutes. Astronomers have chosen this unit to measure right ascension because they measure a stars location by timing its passage through the highest point in the sky as the Earth rotates. The highest point in the sky, called meridian, is the projection of a line onto the celestial sphere. A full circle, measured in units, contains 24 × 60 × 60 = 86 400s, or 24 × 60 = 1 440m. Because right ascensions are measured in hours, they can be used to time the positions of objects in the sky. For example, if a star with RA = 01h 30m 00s is on the meridian, sidereal hour angle, used in celestial navigation, is similar to right ascension, but increases westward rather than eastward. Usually measured in degrees, it is the complement of right ascension with respect to 24h and it is important not to confuse sidereal hour angle with the astronomical concept of hour angle, which measures angular distance of an object westward from the local meridian. The Earths axis rotates slowly westward about the poles of the ecliptic and this effect, known as precession, causes the coordinates of stationary celestial objects to change continuously, if rather slowly. Therefore, equatorial coordinates are inherently relative to the year of their observation, coordinates from different epochs must be mathematically rotated to match each other, or to match a standard epoch. The right ascension of Polaris is increasing quickly, the North Ecliptic Pole in Draco and the South Ecliptic Pole in Dorado are always at right ascension 18h and 6h respectively. The currently used standard epoch is J2000.0, which is January 1,2000 at 12,00 TT, the prefix J indicates that it is a Julian epoch. Prior to J2000.0, astronomers used the successive Besselian Epochs B1875.0, B1900.0, the concept of right ascension has been known at least as far back as Hipparchus who measured stars in equatorial coordinates in the 2nd century BC. But Hipparchus and his successors made their star catalogs in ecliptic coordinates, the easiest way to do that is to use an equatorial mount, which allows the telescope to be aligned with one of its two pivots parallel to the Earths axis
4.
Declination
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In astronomy, declination is one of the two angles that locate a point on the celestial sphere in the equatorial coordinate system, the other being hour angle. Declinations angle is measured north or south of the celestial equator, the root of the word declination means a bending away or a bending down. It comes from the root as the words incline and recline. Declination in astronomy is comparable to geographic latitude, projected onto the celestial sphere, points north of the celestial equator have positive declinations, while those south have negative declinations. Any units of measure can be used for declination, but it is customarily measured in the degrees, minutes. Declinations with magnitudes greater than 90° do not occur, because the poles are the northernmost and southernmost points of the celestial sphere, the Earths axis rotates slowly westward about the poles of the ecliptic, completing one circuit in about 26,000 years. This effect, known as precession, causes the coordinates of stationary celestial objects to change continuously, therefore, equatorial coordinates are inherently relative to the year of their observation, and astronomers specify them with reference to a particular year, known as an epoch. Coordinates from different epochs must be rotated to match each other. The currently used standard epoch is J2000.0, which is January 1,2000 at 12,00 TT, the prefix J indicates that it is a Julian epoch. Prior to J2000.0, astronomers used the successive Besselian Epochs B1875.0, B1900.0, the declinations of Solar System objects change very rapidly compared to those of stars, due to orbital motion and close proximity. This similarly occurs in the Southern Hemisphere for objects with less than −90° − φ. An extreme example is the star which has a declination near to +90°. Circumpolar stars never dip below the horizon, conversely, there are other stars that never rise above the horizon, as seen from any given point on the Earths surface. Generally, if a star whose declination is δ is circumpolar for some observer, then a star whose declination is −δ never rises above the horizon, as seen by the same observer. Likewise, if a star is circumpolar for an observer at latitude φ, neglecting atmospheric refraction, declination is always 0° at east and west points of the horizon. At the north point, it is 90° − |φ|, and at the south point, from the poles, declination is uniform around the entire horizon, approximately 0°. Non-circumpolar stars are visible only during certain days or seasons of the year, the Suns declination varies with the seasons. As seen from arctic or antarctic latitudes, the Sun is circumpolar near the summer solstice, leading to the phenomenon of it being above the horizon at midnight
5.
Apparent magnitude
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The apparent magnitude of a celestial object is a number that is a measure of its brightness as seen by an observer on Earth. The brighter an object appears, the lower its magnitude value, the Sun, at apparent magnitude of −27, is the brightest object in the sky. It is adjusted to the value it would have in the absence of the atmosphere, furthermore, the magnitude scale is logarithmic, a difference of one in magnitude corresponds to a change in brightness by a factor of 5√100, or about 2.512. The measurement of apparent magnitudes or brightnesses of celestial objects is known as photometry, apparent magnitudes are used to quantify the brightness of sources at ultraviolet, visible, and infrared wavelengths. An apparent magnitude is measured in a specific passband corresponding to some photometric system such as the UBV system. In standard astronomical notation, an apparent magnitude in the V filter band would be denoted either as mV or often simply as V, the scale used to indicate magnitude originates in the Hellenistic practice of dividing stars visible to the naked eye into six magnitudes. The brightest stars in the sky were said to be of first magnitude, whereas the faintest were of sixth magnitude. Each grade of magnitude was considered twice the brightness of the following grade and this rather crude scale for the brightness of stars was popularized by Ptolemy in his Almagest, and is generally believed to have originated with Hipparchus. This implies that a star of magnitude m is 2.512 times as bright as a star of magnitude m +1 and this figure, the fifth root of 100, became known as Pogsons Ratio. The zero point of Pogsons scale was defined by assigning Polaris a magnitude of exactly 2. However, with the advent of infrared astronomy it was revealed that Vegas radiation includes an Infrared excess presumably due to a disk consisting of dust at warm temperatures. At shorter wavelengths, there is negligible emission from dust at these temperatures, however, in order to properly extend the magnitude scale further into the infrared, this peculiarity of Vega should not affect the definition of the magnitude scale. Therefore, the scale was extrapolated to all wavelengths on the basis of the black body radiation curve for an ideal stellar surface at 11000 K uncontaminated by circumstellar radiation. On this basis the spectral irradiance for the zero magnitude point, with the modern magnitude systems, brightness over a very wide range is specified according to the logarithmic definition detailed below, using this zero reference. In practice such apparent magnitudes do not exceed 30, astronomers have developed other photometric zeropoint systems as alternatives to the Vega system. The AB magnitude zeropoint is defined such that an objects AB, the dimmer an object appears, the higher the numerical value given to its apparent magnitude, with a difference of 5 magnitudes corresponding to a brightness factor of exactly 100. Since an increase of 5 magnitudes corresponds to a decrease in brightness by a factor of exactly 100, each magnitude increase implies a decrease in brightness by the factor 5√100 ≈2.512. Inverting the above formula, a magnitude difference m1 − m2 = Δm implies a brightness factor of F2 F1 =100 Δ m 5 =100.4 Δ m ≈2.512 Δ m
6.
Stellar classification
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In astronomy, stellar classification is the classification of stars based on their spectral characteristics. Electromagnetic radiation from the star is analyzed by splitting it with a prism or diffraction grating into a spectrum exhibiting the rainbow of colors interspersed with absorption lines, each line indicates an ion of a certain chemical element, with the line strength indicating the abundance of that ion. The relative abundance of the different ions varies with the temperature of the photosphere, the spectral class of a star is a short code summarizing the ionization state, giving an objective measure of the photospheres temperature and density. Most stars are classified under the Morgan–Keenan system using the letters O, B, A, F, G, K, and M. Each letter class is subdivided using a numeric digit with 0 being hottest and 9 being coolest. The sequence has been expanded with classes for other stars and star-like objects that do not fit in the system, such as class D for white dwarfs. In the MK system, a luminosity class is added to the class using Roman numerals. This is based on the width of absorption lines in the stars spectrum. The full spectral class for the Sun is then G2V, indicating a main-sequence star with a temperature around 5,800 K, the conventional color description takes into account only the peak of the stellar spectrum. This means that the assignment of colors of the spectrum can be misleading. There are no green, indigo, or violet stars, likewise, the brown dwarfs do not literally appear brown. The modern classification system is known as the Morgan–Keenan classification, each star is assigned a spectral class from the older Harvard spectral classification and a luminosity class using Roman numerals as explained below, forming the stars spectral type. The spectral classes O through M, as well as more specialized classes discussed later, are subdivided by Arabic numerals. For example, A0 denotes the hottest stars in the A class, fractional numbers are allowed, for example, the star Mu Normae is classified as O9.7. The Sun is classified as G2, the conventional color descriptions are traditional in astronomy, and represent colors relative to the mean color of an A-class star, which is considered to be white. The apparent color descriptions are what the observer would see if trying to describe the stars under a dark sky without aid to the eye, or with binoculars. However, most stars in the sky, except the brightest ones, red supergiants are cooler and redder than dwarfs of the same spectral type, and stars with particular spectral features such as carbon stars may be far redder than any black body. O-, B-, and A-type stars are called early type
7.
Variable star
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A variable star is a star whose brightness as seen from Earth fluctuates. Many, possibly most, stars have at least some variation in luminosity, an ancient Egyptian calendar of lucky and unlucky days composed some 3,200 years ago may be the oldest preserved historical document of the discovery of a variable star, the eclipsing binary Algol. This discovery, combined with supernovae observed in 1572 and 1604, proved that the sky was not eternally invariable as Aristotle. In this way, the discovery of variable stars contributed to the revolution of the sixteenth. The second variable star to be described was the eclipsing variable Algol, by Geminiano Montanari in 1669, chi Cygni was identified in 1686 by G. Kirch, then R Hydrae in 1704 by G. D. Maraldi. By 1786 ten variable stars were known, John Goodricke himself discovered Delta Cephei and Beta Lyrae. Since 1850 the number of variable stars has increased rapidly, especially after 1890 when it became possible to identify variable stars by means of photography. The latest edition of the General Catalogue of Variable Stars lists more than 46,000 variable stars in the Milky Way, as well as 10,000 in other galaxies, and over 10,000 suspected variables. The most common kinds of variability involve changes in brightness, but other types of variability also occur, by combining light curve data with observed spectral changes, astronomers are often able to explain why a particular star is variable. Variable stars are generally analysed using photometry, spectrophotometry and spectroscopy, measurements of their changes in brightness can be plotted to produce light curves. Peak brightnesses in the curve are known as maxima, while troughs are known as minima. By estimating the magnitude and noting the time of observation a visual lightcurve can be constructed. The American Association of Variable Star Observers collects such observations from participants around the world, from the light curve the following data are derived, are the brightness variations periodical, semiperiodical, irregular, or unique. What is the period of the brightness fluctuations, what is the shape of the light curve. From the spectrum the following data are derived, what kind of star is it, what is its temperature, is it a single star, or a binary. does the spectrum change with time. In very few cases it is possible to make pictures of a stellar disk and these may show darker spots on its surface. Combining light curves with spectral data often gives a clue as to the changes occur in a variable star. For example, evidence for a star is found in its shifting spectrum because its surface periodically moves toward and away from us
8.
Classical Cepheid variable
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Classical Cepheids are a type of Cepheid variable star. They are population I variable stars that exhibit regular radial pulsations with periods of a few days to a few weeks, HST observations of classical Cepheid variables have enabled firmer constraints on Hubbles law. Classical Cepheids have also used to clarify many characteristics of our galaxy, such as the Suns height above the galactic plane. Around 800 classical Cepheids are known in the Milky Way Galaxy, several thousand more are known in the Magellanic Clouds, with more known in other galaxies. The Hubble Space Telescope has identified classical Cepheids in NGC4603, Classical Cepheid variables are 4–20 times more massive than the Sun, and around 1,000 to 50,000 times more luminous. Spectroscopically they are bright giants or low luminosity supergiants of spectral class F6 – K2, the temperature and spectral type vary as they pulsate. Their radii are a few tens to a few hundred times that of the sun, more luminous Cepheids are cooler and larger and have longer periods. Along with the changes their radii also change during each pulsation. The brightness changes are pronounced at shorter wavelengths. Cepheid variables may pulsate in a mode, the first overtone. Pulsations in a higher than first are rare but interesting. The majority of classical Cepheids are thought to be fundamental mode pulsators, stars pulsating in an overtone are more luminous and larger than a fundamental mode pulsator with the same period. When an intermediate mass star first evolves away from the main sequence, stars more massive than about 8-12 M☉ start core helium burning before reaching the red giant branch and become red supergiants, but may still execute a blue loop through the instability strip. The duration and even existence of blue loops is very sensitive to the mass, metallicity, in some cases, stars may cross the instability strip for a fourth and fifth time when helium shell burning starts. The rate of change of the period of a Cepheid variable, along with chemical abundances detectable in the spectrum, Classical Cepheid variables were B type main sequence stars earlier than about B7, possibly late O stars, before they ran out of hydrogen in their cores. Very massive stars never cool sufficiently to reach the instability strip, at low metallicity, for example in the Magellanic Clouds, stars can retain more mass and become more luminous Cepheids with longer periods. A Cepheid light curve is typically asymmetric with a rise to maximum light followed by a slower fall to minimum. This is due to the difference between the radius and temperature variations and is considered characteristic of a fundamental mode pulsator, the most common type of type I Cepheid
9.
Astrometry
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Astrometry is the branch of astronomy that involves precise measurements of the positions and movements of stars and other celestial bodies. The information obtained by astrometric measurements provides information on the kinematics and physical origin of the Solar System and our galaxy, the history of astrometry is linked to the history of star catalogues, which gave astronomers reference points for objects in the sky so they could track their movements. This can be dated back to Hipparchus, who around 190 BC used the catalogue of his predecessors Timocharis, in doing so, he also developed the brightness scale still in use today. Hipparchus compiled a catalogue with at least 850 stars and their positions, hipparchuss successor, Ptolemy, included a catalogue of 1,022 stars in his work the Almagest, giving their location, coordinates, and brightness. Ibn Yunus observed more than 10,000 entries for the Suns position for years using a large astrolabe with a diameter of nearly 1.4 metres. In the 15th century, the Timurid astronomer Ulugh Beg compiled the Zij-i-Sultani, like the earlier catalogs of Hipparchus and Ptolemy, Ulugh Begs catalogue is estimated to have been precise to within approximately 20 minutes of arc. In the 16th century, Tycho Brahe used improved instruments, including large mural instruments, to measure star positions more accurately than previously, Taqi al-Din measured the right ascension of the stars at the Istanbul observatory of Taqi al-Din using the observational clock he invented. When telescopes became commonplace, setting circles sped measurements James Bradley first tried to measure stellar parallaxes in 1729, the stellar movement proved too insignificant for his telescope, but he instead discovered the aberration of light and the nutation of the Earths axis. His cataloguing of 3222 stars was refined in 1807 by Friedrich Bessel and he made the first measurement of stellar parallax,0.3 arcsec for the binary star 61 Cygni. Being very difficult to measure, only about 60 stellar parallaxes had been obtained by the end of the 19th century, astrographs using astronomical photographic plates sped the process in the early 20th century. Automated plate-measuring machines and more sophisticated technology of the 1960s allowed more efficient compilation of star catalogues. In the 1980s, charge-coupled devices replaced photographic plates and reduced optical uncertainties to one milliarcsecond and this technology made astrometry less expensive, opening the field to an amateur audience. In 1989, the European Space Agencys Hipparcos satellite took astrometry into orbit, operated from 1989 to 1993, Hipparcos measured large and small angles on the sky with much greater precision than any previous optical telescopes. During its 4-year run, the positions, parallaxes, and proper motions of 118,218 stars were determined with a degree of accuracy. A new Tycho catalog drew together a database of 1,058,332 to within 20-30 mas, additional catalogues were compiled for the 23,882 double/multiple stars and 11,597 variable stars also analyzed during the Hipparcos mission. Today, the catalogue most often used is USNO-B1.0, during the past 50 years,7,435 Schmidt camera plates were used to complete several sky surveys that make the data in USNO-B1.0 accurate to within 0.2 arcsec. In observational astronomy, astrometric techniques help identify stellar objects by their unique motions and it is instrumental for keeping time, in that UTC is basically the atomic time synchronized to Earths rotation by means of exact observations. Astrometry is an important step in the distance ladder because it establishes parallax distance estimates for stars in the Milky Way
10.
Radial velocity
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The radial velocity of an object with respect to a given point is the rate of change of the distance between the object and the point. That is, the velocity is the component of the objects velocity that points in the direction of the radius connecting the object. In astronomy, the point is taken to be the observer on Earth. In astronomy, radial velocity is measured to the first order of approximation by Doppler spectroscopy. The quantity obtained by this method may be called the barycentric radial-velocity measure or spectroscopic radial velocity, by contrast, astrometric radial velocity is determined by astrometric observations. A positive radial velocity indicates the distance between the objects is or was increasing, a radial velocity indicates the distance between the source and observer is or was decreasing. In many binary stars, the orbital motion usually causes radial velocity variations of several kilometers per second, as the spectra of these stars vary due to the Doppler effect, they are called spectroscopic binaries. Radial velocity can be used to estimate the ratio of the masses of the stars and it has been suggested that planets with high eccentricities calculated by this method may in fact be two-planet systems of circular or near-circular resonant orbit. When the star moves towards us, its spectrum is blueshifted, by regularly looking at the spectrum of a star—and so, measuring its velocity—it can be determined, if it moves periodically due to the influence of a companion. From the instrumental perspective, velocities are measured relative to the telescopes motion, in the case of spectroscopic measurements corrections of the order of ±20 cm/s with respect to aberration. Proper motion Peculiar velocity Relative velocity The Radial Velocity Equation in the Search for Exoplanets
11.
Proper motion
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The components of proper motion in the equatorial coordinate system are measured in seconds of time for right ascension and seconds of arc in declination. Their combined value is computed as the proper motion, which is expressed in seconds of arc per year or per century. Knowledge of the motion, distance, and radial velocity allow approximate calculations of a stars true motion in space in respect to the Sun. Proper motion is not entirely proper, because it includes a component due to the motion of the Solar System itself, over the course of centuries, stars appear to maintain nearly fixed positions with respect to each other, so that they form the same constellations over historical time. Ursa Major or Crux, for example, looks nearly the same now as they did hundreds of years ago, however, precise long-term observations show that the constellations change shape, albeit very slowly, and that each star has an independent motion. This motion is caused by the movement of the relative to the Sun. The proper motion is a vector and is thus defined by two quantities, its position angle and its magnitude. The first quantity indicates the direction of the motion on the celestial sphere. Proper motion may alternatively be defined by the changes per year in the stars right ascension and declination. The components of motion by convention are arrived at as follows. Suppose in a year an object moves from coordinates to coordinates, then the changes of angle in seconds of arc per year are, The magnitude of the proper motion μ is given by vector addition of its components, where δ is the declination. The factor in cos δ accounts for the fact that the radius from the axis of the sphere to its surface varies as cos δ, becoming, for example, zero at the pole. Thus, the component of velocity parallel to the corresponding to a given angular change in α is smaller the further north the objects location. The change μα, which must be multiplied by cos δ to become a component of the motion, is sometimes called the proper motion in right ascension. Hence, the proper motions in right ascension and declination are made equivalent for straightforward calculations of various other stellar motions. Position angle θ is related to these components by, Motions in equatorial coordinates can be converted to motions in galactic coordinates, for the majority of stars seen in the sky, the observed proper motions are usually small and unremarkable. Such stars are either faint or are significantly distant, have changes of below 10 milliarcseconds per year. A few do have significant motions, and are usually called high-proper motion stars, Motions can also be in almost seemingly random directions
12.
Minute and second of arc
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A minute of arc, arcminute, arc minute, or minute arc is a unit of angular measurement equal to 1/60 of one degree. Since one degree is 1/360 of a turn, one minute of arc is 1/21600 of a turn, a second of arc, arcsecond, or arc second is 1/60 of an arcminute, 1/3600 of a degree, 1/1296000 of a turn, and π/648000 of a radian. To express even smaller angles, standard SI prefixes can be employed, the number of square arcminutes in a complete sphere is 4 π2 =466560000 π ≈148510660 square arcminutes. The standard symbol for marking the arcminute is the prime, though a single quote is used where only ASCII characters are permitted. One arcminute is thus written 1′ and it is also abbreviated as arcmin or amin or, less commonly, the prime with a circumflex over it. The standard symbol for the arcsecond is the prime, though a double quote is commonly used where only ASCII characters are permitted. One arcsecond is thus written 1″ and it is also abbreviated as arcsec or asec. In celestial navigation, seconds of arc are used in calculations. This notation has been carried over into marine GPS receivers, which normally display latitude and longitude in the format by default. An arcsecond is approximately the angle subtended by a U. S. dime coin at a distance of 4 kilometres, a milliarcsecond is about the size of a dime atop the Eiffel Tower as seen from New York City. A microarcsecond is about the size of a period at the end of a sentence in the Apollo mission manuals left on the Moon as seen from Earth, since antiquity the arcminute and arcsecond have been used in astronomy. The principal exception is Right ascension in equatorial coordinates, which is measured in units of hours, minutes. These small angles may also be written in milliarcseconds, or thousandths of an arcsecond, the unit of distance, the parsec, named from the parallax of one arcsecond, was developed for such parallax measurements. It is the distance at which the radius of the Earths orbit would subtend an angle of one arcsecond. The ESA astrometric space probe Gaia is hoped to measure star positions to 20 microarcseconds when it begins producing catalog positions sometime after 2016, there are about 1.3 trillion µas in a turn. Currently the best catalog positions of stars actually measured are in terms of milliarcseconds, apart from the Sun, the star with the largest angular diameter from Earth is R Doradus, a red supergiant with a diameter of 0.05 arcsecond. The dwarf planet Pluto has proven difficult to resolve because its angular diameter is about 0.1 arcsecond, space telescopes are not affected by the Earths atmosphere but are diffraction limited. For example, the Hubble space telescope can reach a size of stars down to about 0. 1″
13.
Year
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A year is the orbital period of the Earth moving in its orbit around the Sun. Due to the Earths axial tilt, the course of a year sees the passing of the seasons, marked by changes in weather, the hours of daylight, and, consequently, vegetation and soil fertility. In temperate and subpolar regions around the globe, four seasons are recognized, spring, summer, autumn. In tropical and subtropical regions several geographical sectors do not present defined seasons, but in the seasonal tropics, a calendar year is an approximation of the number of days of the Earths orbital period as counted in a given calendar. The Gregorian, or modern, calendar, presents its calendar year to be either a common year of 365 days or a year of 366 days, as do the Julian calendars. For the Gregorian calendar the average length of the year across the complete leap cycle of 400 years is 365.2425 days. The ISO standard ISO 80000-3, Annex C, supports the symbol a to represent a year of either 365 or 366 days, in English, the abbreviations y and yr are commonly used. In astronomy, the Julian year is a unit of time, it is defined as 365.25 days of exactly 86400 seconds, totalling exactly 31557600 seconds in the Julian astronomical year. The word year is used for periods loosely associated with, but not identical to, the calendar or astronomical year, such as the seasonal year, the fiscal year. Similarly, year can mean the period of any planet, for example. The term can also be used in reference to any long period or cycle, west Saxon ġēar, Anglian ġēr continues Proto-Germanic *jǣran. Cognates are German Jahr, Old High German jār, Old Norse ár and Gothic jer, all the descendants of the Proto-Indo-European noun *yeh₁rom year, season. Cognates also descended from the same Proto-Indo-European noun are Avestan yārǝ year, Greek ὥρα year, season, period of time, Old Church Slavonic jarŭ, Latin annus is from a PIE noun *h₂et-no-, which also yielded Gothic aþn year. Both *yeh₁-ro- and *h₂et-no- are based on verbal roots expressing movement, *h₁ey- and *h₂et- respectively, the Greek word for year, ἔτος, is cognate with Latin vetus old, from the PIE word *wetos- year, also preserved in this meaning in Sanskrit vat-sa- yearling and vat-sa-ras year. Derived from Latin annus are a number of English words, such as annual, annuity, anniversary, etc. per annum means each year, anno Domini means in the year of the Lord. No astronomical year has an number of days or lunar months. Financial and scientific calculations often use a 365-day calendar to simplify daily rates, in the Julian calendar, the average length of a year is 365.25 days. In a non-leap year, there are 365 days, in a year there are 366 days
14.
Stellar parallax
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Stellar parallax is parallax on an interstellar scale, the apparent shift of position of any nearby star against the background of distant objects. Stellar parallax is so difficult to detect that its existence was the subject of debate in astronomy for thousands of years. It was first observed by Giuseppe Calandrelli who reported parallax in α-Lyrae in his work Osservazione e riflessione sulla parallasse annua dall’alfa della Lira, then in 1838 Friedrich Bessel made the first successful parallax measurement ever, for the star 61 Cygni, using a Fraunhofer heliometer at Königsberg Observatory. Once a stars parallax is known, its distance from Earth can be computed trigonometrically, but the more distant an object is, the smaller its parallax. Even with 21st-century techniques in astrometry, the limits of accurate measurement make distances farther away than about 100 parsecs too approximate to be useful when obtained by this technique. Relatively close on a scale, the applicability of stellar parallax leaves most astronomical distance measurements to be calculated by spectral red-shift or other methods. Stellar parallax measures are given in the units of arcseconds. The distance unit parsec is defined as the length of the leg of a right triangle adjacent to the angle of one arcsecond at one vertex, because stellar parallaxes and distances all involve such skinny right triangles, a convenient trigonometric approximation can be used to convert parallaxes to distance. The distance is simply the reciprocal of the parallax, d =1 / p, for example, Proxima Centauri, whose parallax is 0.7687, is 1 /0.7687 =1.3009 parsecs distant. Stellar parallax is so small that its apparent absence was used as an argument against heliocentrism during the early modern age. James Bradley first tried to measure stellar parallaxes in 1729, the stellar movement proved too insignificant for his telescope, but he instead discovered the aberration of light, the nutation of Earth’s axis, and catalogued 3222 stars. The parsec is defined as the distance for which the annual parallax is 1 arcsecond, annual parallax is normally measured by observing the position of a star at different times of the year as Earth moves through its orbit. Measurement of annual parallax was the first reliable way to determine the distances to the closest stars, the first successful measurements of stellar parallax were made by Friedrich Bessel in 1838 for the star 61 Cygni using a heliometer. Being very difficult to measure, only about 60 stellar parallaxes had been obtained by the end of the 19th century, astrographs using astronomical photographic plates sped the process in the early 20th century. Automated plate-measuring machines and more sophisticated technology of the 1960s allowed more efficient compilation of star catalogues. In the 1980s, charge-coupled devices replaced photographic plates and reduced optical uncertainties to one milliarcsecond, stellar parallax remains the standard for calibrating other measurement methods. The angles involved in these calculations are very small and thus difficult to measure, the nearest star to the Sun, Proxima Centauri, has a parallax of 0.7687 ±0.0003 arcsec. This angle is approximately that subtended by an object 2 centimeters in diameter located 5.3 kilometers away
15.
Distance (astronomy)
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The cosmic distance ladder is the succession of methods by which astronomers determine the distances to celestial objects. A real direct distance measurement of an object is possible only for those objects that are close enough to Earth. The techniques for determining distances to more distant objects are all based on various measured correlations between methods that work at distances and methods that work at larger distances. Several methods rely on a candle, which is an astronomical object that has a known luminosity. The ladder analogy arises because no single technique can measure distances at all ranges encountered in astronomy, instead, one method can be used to measure nearby distances, a second can be used to measure nearby to intermediate distances, and so on. Each rung of the ladder provides information that can be used to determine the distances at the next higher rung, at the base of the ladder are fundamental distance measurements, in which distances are determined directly, with no physical assumptions about the nature of the object in question. The precise measurement of stellar positions is part of the discipline of astrometry, direct distance measurements are based upon the astronomical unit, which is the distance between the Earth and the Sun. Historically, observations of transits of Venus were crucial in determining the AU, in the first half of the 20th century, observations of asteroids were also important. Keplers laws provide precise ratios of the sizes of the orbits of objects orbiting the Sun, radar is used to measure the distance between the orbits of the Earth and of a second body. From that measurement and the ratio of the two sizes, the size of Earths orbit is calculated. The Earths orbit is known with a precision of a few meters, the most important fundamental distance measurements come from trigonometric parallax. As the Earth orbits the Sun, the position of stars will appear to shift slightly against the more distant background. These shifts are angles in a triangle, with 2 AU making the base leg of the triangle. The amount of shift is small, measuring 1 arcsecond for an object at the 1 parsec distance of the nearest stars. Astronomers usually express distances in units of parsecs, light-years are used in popular media, because parallax becomes smaller for a greater stellar distance, useful distances can be measured only for stars whose parallax is larger than a few times the precision of the measurement. Parallax measurements typically have an accuracy measured in milliarcseconds, the Hubble telescope WFC3 now has the potential to provide a precision of 20 to 40 microarcseconds, enabling reliable distance measurements up to 5,000 parsecs for small numbers of stars. By the early 2020s, the GAIA space mission will provide similarly accurate distances to all bright stars. Stars have a velocity relative to the Sun that causes proper motion, for a group of stars with the same spectral class and a similar magnitude range, a mean parallax can be derived from statistical analysis of the proper motions relative to their radial velocities
16.
Parsec
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The parsec is a unit of length used to measure large distances to objects outside the Solar System. One parsec is the distance at which one astronomical unit subtends an angle of one arcsecond, a parsec is equal to about 3.26 light-years in length. The nearest star, Proxima Centauri, is about 1.3 parsecs from the Sun, most of the stars visible to the unaided eye in the nighttime sky are within 500 parsecs of the Sun. The parsec unit was likely first suggested in 1913 by the British astronomer Herbert Hall Turner, named from an abbreviation of the parallax of one arcsecond, it was defined so as to make calculations of astronomical distances quick and easy for astronomers from only their raw observational data. Partly for this reason, it is still the unit preferred in astronomy and astrophysics, though the light-year remains prominent in science texts. This corresponds to the definition of the parsec found in many contemporary astronomical references. Derivation, create a triangle with one leg being from the Earth to the Sun. As that point in space away, the angle between the Sun and Earth decreases. A parsec is the length of that leg when the angle between the Sun and Earth is one arc-second. One of the oldest methods used by astronomers to calculate the distance to a star is to record the difference in angle between two measurements of the position of the star in the sky. The first measurement is taken from the Earth on one side of the Sun, and the second is approximately half a year later. The distance between the two positions of the Earth when the two measurements were taken is twice the distance between the Earth and the Sun. The difference in angle between the two measurements is twice the angle, which is formed by lines from the Sun. Then the distance to the star could be calculated using trigonometry. 5-parsec distance of 61 Cygni, the parallax of a star is defined as half of the angular distance that a star appears to move relative to the celestial sphere as Earth orbits the Sun. Equivalently, it is the angle, from that stars perspective. The star, the Sun and the Earth form the corners of a right triangle in space, the right angle is the corner at the Sun. Therefore, given a measurement of the angle, along with the rules of trigonometry. A parsec is defined as the length of the adjacent to the vertex occupied by a star whose parallax angle is one arcsecond
17.
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
18.
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
19.
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
20.
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
21.
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
22.
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
23.
Amplitude
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The amplitude of a periodic variable is a measure of its change over a single period. There are various definitions of amplitude, which are all functions of the magnitude of the difference between the extreme values. In older texts the phase is called the amplitude. Peak-to-peak amplitude is the change between peak and trough, with appropriate circuitry, peak-to-peak amplitudes of electric oscillations can be measured by meters or by viewing the waveform on an oscilloscope. Peak-to-peak is a measurement on an oscilloscope, the peaks of the waveform being easily identified and measured against the graticule. This remains a common way of specifying amplitude, but sometimes other measures of amplitude are more appropriate. In audio system measurements, telecommunications and other areas where the measurand is a signal that swings above and below a value but is not sinusoidal. If the reference is zero, this is the absolute value of the signal, if the reference is a mean value. Semi-amplitude means half the peak-to-peak amplitude, some scientists use amplitude or peak amplitude to mean semi-amplitude, that is, half the peak-to-peak amplitude. It is the most widely used measure of orbital wobble in astronomy, the RMS of the AC waveform. For complicated waveforms, especially non-repeating signals like noise, the RMS amplitude is used because it is both unambiguous and has physical significance. For example, the power transmitted by an acoustic or electromagnetic wave or by an electrical signal is proportional to the square of the RMS amplitude. For alternating current electric power, the practice is to specify RMS values of a sinusoidal waveform. One property of root mean square voltages and currents is that they produce the same heating effect as direct current in a given resistance, the peak-to-peak value is used, for example, when choosing rectifiers for power supplies, or when estimating the maximum voltage that insulation must withstand. Some common voltmeters are calibrated for RMS amplitude, but respond to the value of a rectified waveform. Many digital voltmeters and all moving coil meters are in this category, the RMS calibration is only correct for a sine wave input since the ratio between peak, average and RMS values is dependent on waveform. If the wave shape being measured is greatly different from a sine wave, true RMS-responding meters were used in radio frequency measurements, where instruments measured the heating effect in a resistor to measure current. The advent of microprocessor controlled meters capable of calculating RMS by sampling the waveform has made true RMS measurement commonplace
24.
Solar mass
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The solar mass is a standard unit of mass in astronomy, equal to approximately 1.99 ×1030 kilograms. It is used to indicate the masses of stars, as well as clusters, nebulae. It is equal to the mass of the Sun, about two kilograms, M☉ = ×1030 kg The above mass is about 332946 times the mass of Earth. Because Earth follows an orbit around the Sun, its solar mass can be computed from the equation for the orbital period of a small body orbiting a central mass. The value he obtained differs by only 1% from the modern value, the diurnal parallax of the Sun was accurately measured during the transits of Venus in 1761 and 1769, yielding a value of 9″. From the value of the parallax, one can determine the distance to the Sun from the geometry of Earth. The first person to estimate the mass of the Sun was Isaac Newton, in his work Principia, he estimated that the ratio of the mass of Earth to the Sun was about 1/28700. Later he determined that his value was based upon a faulty value for the solar parallax and he corrected his estimated ratio to 1/169282 in the third edition of the Principia. The current value for the parallax is smaller still, yielding an estimated mass ratio of 1/332946. As a unit of measurement, the solar mass came into use before the AU, the mass of the Sun has been decreasing since the time it formed. This occurs through two processes in nearly equal amounts, first, in the Suns core, hydrogen is converted into helium through nuclear fusion, in particular the p–p chain, and this reaction converts some mass into energy in the form of gamma ray photons. Most of this energy eventually radiates away from the Sun, second, high-energy protons and electrons in the atmosphere of the Sun are ejected directly into outer space as a solar wind. The original mass of the Sun at the time it reached the main sequence remains uncertain, the early Sun had much higher mass-loss rates than at present, and it may have lost anywhere from 1–7% of its natal mass over the course of its main-sequence lifetime. The Sun gains a small amount of mass through the impact of asteroids. However, as the Sun already contains 99. 86% of the Solar Systems total mass, M☉ G / c2 ≈1.48 km M☉ G / c3 ≈4.93 μs I. -J. A Bright Young Sun Consistent with Helioseismology and Warm Temperatures on Ancient Earth and Mars
25.
Solar luminosity
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The solar luminosity, L☉, is a unit of radiant flux conventionally used by astronomers to measure the luminosity of stars. It is defined in terms of the Suns output, one solar luminosity is 3. 828×1026 W. This does not include the solar luminosity, which would add 0.023 L☉. The Sun is a variable star, and its luminosity therefore fluctuates. The major fluctuation is the solar cycle that causes a periodic variation of about ±0. 1%. Other variations over the last 200–300 years are thought to be smaller than this. Solar luminosity is related to solar irradiance, Solar irradiance is responsible for the orbital forcing that causes the Milankovitch cycles, which determine Earthly glacial cycles. The mean irradiance at the top of the Earths atmosphere is known as the solar constant. Solar mass Solar radius Nuclear fusion Triple-alpha process Sackmann, I. -J, a Bright Young Sun Consistent with Helioseismology and Warm Temperatures on Ancient Earth and Mars, Astrophys. J.583, 1024–39, arXiv, astro-ph/0210128, Bibcode, 2003ApJ.583. 1024S, doi,10. 1086/345408 Foukal, P. Fröhlich, spruit, H. Wigley, T. M. L. Variations in solar luminosity and their effect on the Earths climate, Nature,443, 161–66, Bibcode, 2006Natur.443. 161F, doi,10. 1038/nature05072, PMID16971941 Pelletier, variations in Solar Luminosity from Timescales of Minutes to Months, Astrophys. J.463, L41–L45, arXiv, astro-ph/9510026, Bibcode, 1996ApJ. 463L. 41P, doi,10. 1086/310049 Stoykova, D. A. Shopov, ford, D. Georgiev, L. N. et al
26.
Effective temperature
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The effective temperature of a body such as a star or planet is the temperature of a black body that would emit the same total amount of electromagnetic radiation. Effective temperature is used as an estimate of a bodys surface temperature when the bodys emissivity curve is not known. When the stars or planets net emissivity in the relevant wavelength band is less than unity, the net emissivity may be low due to surface or atmospheric properties, including greenhouse effect. Notice that the luminosity of a star is then L =4 π R2 σ T e f f 4. The definition of the radius is obviously not straightforward. More rigorously the effective temperature corresponds to the temperature at the radius that is defined by a value of the Rosseland optical depth within the stellar atmosphere. The effective temperature and the bolometric luminosity are the two fundamental physical parameters needed to place a star on the Hertzsprung–Russell diagram, both effective temperature and bolometric luminosity depend on the chemical composition of a star. The effective temperature of our Sun is around 5780 kelvin, stars have a decreasing temperature gradient, going from their central core up to the atmosphere. The core temperature of the temperature at the centre of the sun where nuclear reactions take place—is estimated to be 15,000,000 K. The effective temperature of a star indicates the amount of heat that the star radiates per unit of surface area, from the warmest surfaces to the coolest is the sequence of star types known as O, B, A, F, G, K, and M. The effective temperature of a planet can be calculated by equating the power received by the planet with the emitted by a blackbody of temperature T. Take the case of a planet at a distance D from the star and we also allow the planet to reflect some of the incoming radiation by incorporating a parameter called the albedo. An albedo of 1 means that all the radiation is reflected, the effective temperature for Jupiter from this calculation is 112 K and 51 Pegasi b is 1258 K. A better estimate of effective temperature for some planets, such as Jupiter, the actual temperature depends on albedo and atmosphere effects. The actual temperature from spectroscopic analysis for HD209458 b is 1130 K, the internal heating within Jupiter raises the effective temperature to about 152 K. The surface temperature of a planet can be estimated by modifying the effective-temperature calculation to account for emissivity and this area intercepts some of the power which is spread over the surface of a sphere of radius D. We also allow the planet to some of the incoming radiation by incorporating a parameter a called the albedo. An albedo of 1 means that all the radiation is reflected, there is also a factor ε, which is the emissivity and represents atmospheric effects
27.
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
28.
Metallicity
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In astronomy and physical cosmology, the metallicity or Z is the fraction of mass of a star or other kind of astronomical object that is not in hydrogen or helium. Most of the matter in the universe is in the form of hydrogen and helium, so astronomers use the word metals as a convenient short term for all elements except hydrogen. This usage is distinct from the physical definition of a solid metal. In cosmological terms, the universe is chemically evolving, according to the Big Bang Theory, the early universe first consisted of hydrogen and helium, with trace amounts of lithium and beryllium, but no heavier elements. It is believed that older generations of stars generally have lower metallicities than those of younger generations and these became commonly known as Population I and Population II stars. A third stellar population was introduced in 1978, known as Population III stars and these extremely metal-poor stars were theorised to have been the first-born stars created in the universe. Measurements have demonstrated the connection between a stars metallicity and gas giant planets, like Jupiter and Saturn, the more metals in a star and thus its planetary system and proplyd, the more likely the system may have gas giant planets and rocky planets. Current models show that the metallicity along with the planetary system temperature and distance from the star are key to planet. Metallicity also affects a stars color temperature, metal poor stars are bluer and metal rich stars are redder. The Sun, with 8 planets and 5 planetesimals, is used as the reference, other stars are noted with a positive or negative value. A star with a =0.0 has the iron abundance as the Sun. A star with =−1.0 has one tenth heavy elements of found in the Sun. At =+1, the element abundance is 10 times the Suns value. The survey of population of stars shows that older stars have less metallicity. Stellar composition, as determined by spectroscopy, is simply defined by the parameters X, Y and Z. Here X is the percentage of hydrogen, Y is the fractional percentage of helium. It is simply defined as, X + Y + Z =1.00 In most stars, nebulae and other sources, hydrogen. The hydrogen mass fraction is generally expressed as X ≡ m H M where M is the mass of the system
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Stellar rotation
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Stellar rotation is the angular motion of a star about its axis. The rate of rotation can be measured from the spectrum of the star, the rotation of a star produces an equatorial bulge due to centrifugal force. As stars are not solid bodies, they can also undergo differential rotation, thus the equator of the star can rotate at a different angular velocity than the higher latitudes. These differences in the rate of rotation within a star may have a significant role in the generation of a magnetic field. The magnetic field of a star interacts with the stellar wind, as the wind moves away from the star its rate of angular velocity slows. The magnetic field of the star interacts with the wind, which applies a drag to the stellar rotation, as a result, angular momentum is transferred from the star to the wind, and over time this gradually slows the stars rate of rotation. Unless a star is being observed from the direction of its pole, the component of movement that is in the direction of the observer is called the radial velocity. For the portion of the surface with a radial velocity component toward the observer, likewise the region that has a component moving away from the observer is shifted to a lower frequency. When the absorption lines of a star are observed, this shift at each end of the causes the line to broaden. However, this broadening must be separated from other effects that can increase the line width. The component of the radial velocity observed through line broadening depends on the inclination of the pole to the line of sight. The derived value is given as v e ⋅ sin i, however, i is not always known, so the result gives a minimum value for the stars rotational velocity. That is, if i is not a right angle, then the velocity is greater than v e ⋅ sin i. This is sometimes referred to as the rotational velocity. For giant stars, the atmospheric microturbulence can result in line broadening that is larger than effects of rotational. However, an approach can be employed that makes use of gravitational microlensing events. These occur when an object passes in front of the more distant star and functions like a lens. The more detailed information gathered by this means allows the effects of microturbulence to be distinguished from rotation, if a star displays magnetic surface activity such as starspots, then these features can be tracked to estimate the rotation rate
30.
Projected rotational velocity
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Stellar rotation is the angular motion of a star about its axis. The rate of rotation can be measured from the spectrum of the star, the rotation of a star produces an equatorial bulge due to centrifugal force. As stars are not solid bodies, they can also undergo differential rotation, thus the equator of the star can rotate at a different angular velocity than the higher latitudes. These differences in the rate of rotation within a star may have a significant role in the generation of a magnetic field. The magnetic field of a star interacts with the stellar wind, as the wind moves away from the star its rate of angular velocity slows. The magnetic field of the star interacts with the wind, which applies a drag to the stellar rotation, as a result, angular momentum is transferred from the star to the wind, and over time this gradually slows the stars rate of rotation. Unless a star is being observed from the direction of its pole, the component of movement that is in the direction of the observer is called the radial velocity. For the portion of the surface with a radial velocity component toward the observer, likewise the region that has a component moving away from the observer is shifted to a lower frequency. When the absorption lines of a star are observed, this shift at each end of the causes the line to broaden. However, this broadening must be separated from other effects that can increase the line width. The component of the radial velocity observed through line broadening depends on the inclination of the pole to the line of sight. The derived value is given as v e ⋅ sin i, however, i is not always known, so the result gives a minimum value for the stars rotational velocity. That is, if i is not a right angle, then the velocity is greater than v e ⋅ sin i. This is sometimes referred to as the rotational velocity. For giant stars, the atmospheric microturbulence can result in line broadening that is larger than effects of rotational. However, an approach can be employed that makes use of gravitational microlensing events. These occur when an object passes in front of the more distant star and functions like a lens. The more detailed information gathered by this means allows the effects of microturbulence to be distinguished from rotation, if a star displays magnetic surface activity such as starspots, then these features can be tracked to estimate the rotation rate
31.
Stellar evolution
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Stellar evolution is the process by which a star changes over the course of time. The table shows the lifetimes of stars as a function of their masses, all stars are born from collapsing clouds of gas and dust, often called nebulae or molecular clouds. Over the course of millions of years, these protostars settle down into a state of equilibrium, nuclear fusion powers a star for most of its life. Initially the energy is generated by the fusion of hydrogen atoms at the core of the main-sequence star, later, as the preponderance of atoms at the core becomes helium, stars like the Sun begin to fuse hydrogen along a spherical shell surrounding the core. This process causes the star to gradually grow in size, passing through the subgiant stage until it reaches the red giant phase. Once a star like the Sun has exhausted its fuel, its core collapses into a dense white dwarf. Stars with around ten or more times the mass of the Sun can explode in a supernova as their inert iron cores collapse into a dense neutron star or black hole. Stellar evolution is not studied by observing the life of a star, as most stellar changes occur too slowly to be detected. Instead, astrophysicists come to understand how stars evolve by observing numerous stars at various points in their lifetime, in June 2015, astronomers reported evidence for Population III stars in the Cosmos Redshift 7 galaxy at z =6.60. Stellar evolution starts with the collapse of a giant molecular cloud. Typical giant molecular clouds are roughly 100 light-years across and contain up to 6,000,000 solar masses, as it collapses, a giant molecular cloud breaks into smaller and smaller pieces. In each of these fragments, the collapsing gas releases gravitational potential energy as heat, as its temperature and pressure increase, a fragment condenses into a rotating sphere of superhot gas known as a protostar. A protostar continues to grow by accretion of gas and dust from the molecular cloud, further development is determined by its mass. Protostars are encompassed in dust, and are more readily visible at infrared wavelengths. Observations from the Wide-field Infrared Survey Explorer have been important for unveiling numerous Galactic protostars. Protostars with masses less than roughly 0.08 M☉ never reach high enough for nuclear fusion of hydrogen to begin. These are known as brown dwarfs, the International Astronomical Union defines brown dwarfs as stars massive enough to fuse deuterium at some point in their lives. Objects smaller than 13 MJ are classified as sub-brown dwarfs, both types, deuterium-burning and not, shine dimly and die away slowly, cooling gradually over hundreds of millions of years
32.
Star
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A star is a luminous sphere of plasma held together by its own gravity. The nearest star to Earth is the Sun, many other stars are visible to the naked eye from Earth during the night, appearing as a multitude of fixed luminous points in the sky due to their immense distance from Earth. Historically, the most prominent stars were grouped into constellations and asterisms, astronomers have assembled star catalogues that identify the known stars and provide standardized stellar designations. However, most of the stars in the Universe, including all stars outside our galaxy, indeed, most are invisible from Earth even through the most powerful telescopes. Almost all naturally occurring elements heavier than helium are created by stellar nucleosynthesis during the stars lifetime, near the end of its life, a star can also contain degenerate matter. Astronomers can determine the mass, age, metallicity, and many properties of a star by observing its motion through space, its luminosity. The total mass of a star is the factor that determines its evolution. Other characteristics of a star, including diameter and temperature, change over its life, while the environment affects its rotation. A plot of the temperature of stars against their luminosities produces a plot known as a Hertzsprung–Russell diagram. Plotting a particular star on that allows the age and evolutionary state of that star to be determined. A stars life begins with the collapse of a gaseous nebula of material composed primarily of hydrogen, along with helium. When the stellar core is sufficiently dense, hydrogen becomes steadily converted into helium through nuclear fusion, the remainder of the stars interior carries energy away from the core through a combination of radiative and convective heat transfer processes. The stars internal pressure prevents it from collapsing further under its own gravity, a star with mass greater than 0.4 times the Suns will expand to become a red giant when the hydrogen fuel in its core is exhausted. In some cases, it will fuse heavier elements at the core or in shells around the core, as the star expands it throws a part of its mass, enriched with those heavier elements, into the interstellar environment, to be recycled later as new stars. Meanwhile, the core becomes a remnant, a white dwarf. Binary and multi-star systems consist of two or more stars that are bound and generally move around each other in stable orbits. When two such stars have a close orbit, their gravitational interaction can have a significant impact on their evolution. Stars can form part of a much larger gravitationally bound structure, historically, stars have been important to civilizations throughout the world
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Star catalogue
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A star catalogue or star catalog, is an astronomical catalogue that lists stars. In astronomy, many stars are referred to simply by catalogue numbers, there are a great many different star catalogues which have been produced for different purposes over the years, and this article covers only some of the more frequently quoted ones. Star catalogues were compiled by many different ancient peoples, including the Babylonians, Greeks, Chinese, Persians, most modern catalogues are available in electronic format and can be freely downloaded from space agencies data center. Completeness and accuracy is described by the weakest apparent magnitude V, from their existing records, it is known that the ancient Egyptians recorded the names of only a few identifiable constellations and a list of thirty-six decans that were used as a star clock. They are better known by their Assyrian-era name Three Stars Each and these star catalogues, written on clay tablets, listed thirty-six stars, twelve for Anu along the celestial equator, twelve for Ea south of that, and twelve for Enlil to the north. In Ancient Greece, the astronomer and mathematician Eudoxus laid down a set of the classical constellations around 370 BC. His catalogue Phaenomena, rewritten by Aratus of Soli between 275 and 250 BC as a poem, became one of the most consulted astronomical texts in antiquity. It contains descriptions of the positions of the stars, the shapes of the constellations, approximately in the 3rd century BC, the Greek astronomers Timocharis of Alexandria and Aristillus created another star catalogue. Hipparchus completed his star catalogue in 129 BC, which he compared to Timocharis and this led him to determine the first value of the precession of the equinoxes. In the 2nd century, Ptolemy of Roman Egypt published a star catalogue as part of his Almagest, ptolemys catalogue was based almost entirely on an earlier one by Hipparchus. It remained the star catalogue in the Western and Arab worlds for over eight centuries. The earliest known inscriptions for Chinese star names were written on oracle bones, sources dating from the Zhou Dynasty which provide star names include the Zuo Zhuan, the Shi Jing, and the Canon of Yao in the Book of Documents. The Lüshi Chunqiu written by the Qin statesman Lü Buwei provides most of the names for the twenty-eight mansions, an earlier lacquerware chest found in the Tomb of Marquis Yi of Zeng contains a complete list of the names of the twenty-eight mansions. Star catalogues are traditionally attributed to Shi Shen and Gan De, the Shi Shen astronomy is attributed to Shi Shen, and the Astronomic star observation to Gan De. It was not until the Han Dynasty that astronomers started to observe and record names for all the stars that were apparent in the night sky, not just those around the ecliptic. A star catalogue is featured in one of the chapters of the late 2nd-century-BC history work Records of the Grand Historian by Sima Qian and contains the schools of Shi Shen and Gan Des work. For his Spiritual Constitution of the Universe of 120 AD, the astronomer Zhang Heng compiled a star catalogue comprising 124 constellations, Chinese constellation names were later adopted by the Koreans and Japanese. A large number of star catalogues were published by Muslim astronomers in the medieval Islamic world and these were mainly Zij treatises, including Arzachels Tables of Toledo, the Maragheh observatorys Zij-i Ilkhani and Ulugh Begs Zij-i-Sultani
. Bibcode:2008AJ....136.1137E. doi:10.1088/0004-6256/136/3/1137.
