1.
Star
–
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
2.
Galactic coordinate system
–
It uses the right-handed convention, meaning that coordinates are positive toward the north and toward the east in the fundamental plane. Longitude measures the distance of an object eastward along the galactic equator from the galactic center. Analogous to terrestrial longitude, galactic longitude is measured in degrees. Latitude measures the distance of an object perpendicular to a plane parallel to, but ~57 light years north of. For example, the north pole has a latitude of +90°. Analogous to terrestrial latitude, galactic latitude is usually measured in degrees, the first Galactic coordinate system was used by William Herschel in 1785. 5°. Longitude 0° is the great semicircle that originates from this point along the line in position angle 123° with respect to the equatorial pole, the galactic longitude increases in the same direction as right ascension. Galactic latitude is positive towards the north pole, with a plane passing through the Sun and parallel to the galactic equator being 0°. Based on this definition, the poles and equator can be found from spherical trigonometry and can be precessed to other epochs. Radio source Sagittarius A*, which is the best physical marker of the galactic center, is located at 17h 45m 40. 0409s. Rounded to the number of digits as the table, 17h 45. 7m, −29. 01°, there is an offset of about 0. 07° from the defined coordinate center. There are two major variations of galactic coordinates, commonly used for computing space velocities of galactic objects. In these systems the xyz axes are designated UVW, but the definitions vary by author
3.
Ecliptic coordinate system
–
The ecliptic coordinate system is a celestial coordinate system commonly used for representing the positions and orbits of Solar System objects. Because most planets, and many small Solar System bodies have orbits with small inclinations to the ecliptic, using it as the fundamental plane is convenient. The systems origin can be either the center of the Sun or the center of the Earth, its direction is towards the vernal equinox. It may be implemented in spherical coordinates or rectangular coordinates, a slow motion of Earths axis, precession, causes a slow, continuous turning of the coordinate system westward about the poles of the ecliptic, completing one circuit in about 26,000 years. Superimposed on this is a motion of the ecliptic. The three most commonly used are, Mean equinox of an epoch is a fixed standard direction. Mean equinox of date is the intersection of the ecliptic of date with the mean equator, commonly used in planetary orbit calculation. True equinox of date is the intersection of the ecliptic of date with the true equator and this is the actual intersection of the two planes at any particular moment, with all motions accounted for. A position in the coordinate system is thus typically specified true equinox and ecliptic of date, mean equinox and ecliptic of J2000.0. Note that there is no mean ecliptic, as the ecliptic is not subject to small periodic oscillations, ecliptic longitude or celestial longitude measures the angular distance of an object along the ecliptic from the primary direction. Like right ascension in the coordinate system, the primary direction points from the Earth towards the Sun at the vernal equinox of the Northern Hemisphere. Because it is a system, ecliptic longitude is measured positive eastwards in the fundamental plane from 0° to 360°. Because of axial precession, the longitude of most fixed stars increases by about 50.3 arcseconds per year, or 83.8 arcminutes per century. Ecliptic latitude or celestial latitude, measures the distance of an object from the ecliptic towards the north or south ecliptic pole. For example, the ecliptic pole has a celestial latitude of +90°. Ecliptic latitude for fixed stars is not affected by precession, distance is also necessary for a complete spherical position. Different distance units are used for different objects, within the Solar System, astronomical units are used, and for objects near the Earth, Earth radii or kilometers are used. From antiquity through the 18th century, ecliptic longitude was measured using twelve zodiacal signs, each of 30° longitude
4.
Equatorial coordinate system
–
The equatorial coordinate system is a celestial coordinate system widely used to specify the positions of celestial objects. The origin at the center of the Earth means the coordinates are geocentric, a right-handed convention means that coordinates are positive toward the north and toward the east in the fundamental plane. This description of the orientation of the frame is somewhat simplified. A slow motion of Earths axis, precession, causes a slow, continuous turning of the system westward about the poles of the ecliptic. Superimposed on this is a motion of the ecliptic. In order to fix the primary direction, these motions necessitate the specification of the equinox of a particular date, known as an epoch. The three most commonly used are, Mean equinox of an epoch is a fixed standard direction. Mean equinox of date is the intersection of the ecliptic of date with the mean equator, commonly used in planetary orbit calculation. True equinox of date is the intersection of the ecliptic of date with the true equator and this is the actual intersection of the two planes at any particular moment, with all motions accounted for. A position in the coordinate system is thus typically specified true equinox and equator of date, mean equinox and equator of J2000.0. Note that there is no mean ecliptic, as the ecliptic is not subject to small periodic oscillations, a stars spherical coordinates are often expressed as a pair, right ascension and declination, without a distance coordinate. The direction of distant objects is the same for all observers. Telescopes equipped with equatorial mounts and setting circles employ the equatorial coordinate system to find objects, setting circles in conjunction with a star chart or ephemeris allow the telescope to be easily pointed at known objects on the celestial sphere. The declination symbol δ, measures the distance of an object perpendicular to the celestial equator, positive to the north. For example, the celestial pole has a declination of +90°. The origin for declination is the equator, which is the projection of the Earths equator onto the celestial sphere. Declination is analogous to terrestrial latitude, the right ascension symbol α, measures the angular distance of an object eastward along the celestial equator from the vernal equinox to the hour circle passing through the object. The vernal equinox point is one of the two where the ecliptic intersects the celestial equator, there are = 15° in one hour of right ascension, 24h of right ascension around the entire celestial equator
5.
Celestial sphere
–
In astronomy and navigation, the celestial sphere is an imaginary sphere of arbitrarily large radius, concentric with Earth. All objects in the sky can be thought of as projected upon the inside surface of the celestial sphere. The celestial sphere is a tool for spherical astronomy, allowing observers to plot positions of objects in the sky when their distances are unknown or unimportant. Because astronomical objects are at such distances, casual observation of the sky offers no information on the actual distances. All objects seem equally far away, as if fixed to the inside of a sphere of large but unknown radius, which rotates from east to west overhead while underfoot, the celestial sphere can be considered to be infinite in radius. This means any point within it, including that occupied by the observer, all parallel planes will seem to intersect the sphere in a coincident great circle. On an infinite-radius celestial sphere, all observers see the things in the same direction. For some objects, this is over-simplified, objects which are relatively near to the observer will seem to change position against the distant celestial sphere if the observer moves far enough, say, from one side of the Earth to the other. This effect, known as parallax, can be represented as an offset from a mean position. The celestial sphere can be considered to be centered at the Earths center, the Suns center, or any convenient location. Individual observers can work out their own small offsets from the mean positions, in many cases in astronomy, the offsets are insignificant. The celestial sphere can thus be thought of as a kind of astronomical shorthand, for many rough uses, this position, as seen from the Earths center, is adequate. This greatly abbreviates the amount of detail necessary in such almanacs and these concepts are important for understanding celestial coordinate systems – frameworks for measuring the positions of objects in the sky. Certain reference lines and planes on Earth, when projected onto the celestial sphere and these include the Earths equator, axis, and the Earths orbit. At their intersections with the sphere, these form the celestial equator, the north and south celestial poles. As the celestial sphere is considered infinite in radius, all observers see the celestial equator, celestial poles, from these bases, directions toward objects in the sky can be quantified by constructing celestial coordinate systems. Similar to terrestrial longitude and latitude, the coordinate system specifies positions relative to the celestial equator and celestial poles. The ecliptic coordinate system specifies positions relative to the Earths orbit, besides the equatorial and ecliptic systems, some other celestial coordinate systems, such as the galactic coordinate system, are more appropriate for particular purposes
6.
Astronomy
–
Astronomy is a natural science that studies celestial objects and phenomena. It applies mathematics, physics, and chemistry, in an effort to explain the origin of those objects and phenomena and their evolution. Objects of interest include planets, moons, stars, galaxies, and comets, while the phenomena include supernovae explosions, gamma ray bursts, more generally, all astronomical phenomena that originate outside Earths atmosphere are within the purview of astronomy. A related but distinct subject, physical cosmology, is concerned with the study of the Universe as a whole, Astronomy is the oldest of the natural sciences. The early civilizations in recorded history, such as the Babylonians, Greeks, Indians, Egyptians, Nubians, Iranians, Chinese, during the 20th century, the field of professional astronomy split into observational and theoretical branches. Observational astronomy is focused on acquiring data from observations of astronomical objects, theoretical astronomy is oriented toward the development of computer or analytical models to describe astronomical objects and phenomena. The two fields complement each other, with theoretical astronomy seeking to explain the results and observations being used to confirm theoretical results. Astronomy is one of the few sciences where amateurs can play an active role, especially in the discovery. Amateur astronomers have made and contributed to many important astronomical discoveries, Astronomy means law of the stars. Astronomy should not be confused with astrology, the system which claims that human affairs are correlated with the positions of celestial objects. Although the two share a common origin, they are now entirely distinct. Generally, either the term astronomy or astrophysics may be used to refer to this subject, however, since most modern astronomical research deals with subjects related to physics, modern astronomy could actually be called astrophysics. Few fields, such as astrometry, are purely astronomy rather than also astrophysics, some titles of the leading scientific journals in this field includeThe Astronomical Journal, The Astrophysical Journal and Astronomy and Astrophysics. In early times, astronomy only comprised the observation and predictions of the motions of objects visible to the naked eye, in some locations, early cultures assembled massive artifacts that possibly had some astronomical purpose. Before tools such as the telescope were invented, early study of the stars was conducted using the naked eye, most of early astronomy actually consisted of mapping the positions of the stars and planets, a science now referred to as astrometry. From these observations, early ideas about the motions of the planets were formed, and the nature of the Sun, Moon, the Earth was believed to be the center of the Universe with the Sun, the Moon and the stars rotating around it. This is known as the model of the Universe, or the Ptolemaic system. The Babylonians discovered that lunar eclipses recurred in a cycle known as a saros
7.
Natural satellite
–
A natural satellite or moon is, in the most common usage, an astronomical body that orbits a planet or minor planet. In the Solar System there are six planetary satellite systems containing 178 known natural satellites, four IAU-listed dwarf planets are also known to have natural satellites, Pluto, Haumea, Makemake, and Eris. As of January 2012, over 200 minor-planet moons have been discovered, the Earth–Moon system is unique in that the ratio of the mass of the Moon to the mass of Earth is much greater than that of any other natural-satellite–planet ratio in the Solar System. At 3,474 km across, Earths Moon is 0.27 times the diameter of Earth, the first known natural satellite was the Moon, but it was considered a planet until Copernicus introduction of heliocentrism in 1543. Until the discovery of the Galilean satellites in 1610, however, galileo chose to refer to his discoveries as Planetæ, but later discoverers chose other terms to distinguish them from the objects they orbited. The first to use of the satellite to describe orbiting bodies was the German astronomer Johannes Kepler in his pamphlet Narratio de Observatis a se quatuor Iouis satellitibus erronibus in 1610. He derived the term from the Latin word satelles, meaning guard, attendant, or companion, the term satellite thus became the normal one for referring to an object orbiting a planet, as it avoided the ambiguity of moon. In 1957, however, the launching of the artificial object Sputnik created a need for new terminology, to further avoid ambiguity, the convention is to capitalize the word Moon when referring to Earths natural satellite, but not when referring to other natural satellites. A few recent authors define moon as a satellite of a planet or minor planet, there is no established lower limit on what is considered a moon. Small asteroid moons, such as Dactyl, have also been called moonlets, the upper limit is also vague. Two orbiting bodies are described as a double body rather than primary. Asteroids such as 90 Antiope are considered double asteroids, but they have not forced a clear definition of what constitutes a moon, some authors consider the Pluto–Charon system to be a double planet. In contrast, irregular satellites are thought to be captured asteroids possibly further fragmented by collisions, most of the major natural satellites of the Solar System have regular orbits, while most of the small natural satellites have irregular orbits. The Moon and possibly Charon are exceptions among large bodies in that they are thought to have originated by the collision of two large proto-planetary objects. The material that would have placed in orbit around the central body is predicted to have reaccreted to form one or more orbiting natural satellites. As opposed to planetary-sized bodies, asteroid moons are thought to form by this process. Triton is another exception, although large and in a close, circular orbit, its motion is retrograde, most regular moons in the Solar System are tidally locked to their respective primaries, meaning that the same side of the natural satellite always faces its planet. The only known exception is Saturns natural satellite Hyperion, which rotates chaotically because of the influence of Titan
8.
Planet
–
The term planet is ancient, with ties to history, astrology, science, mythology, and religion. Several planets in the Solar System can be seen with the naked eye and these were regarded by many early cultures as divine, or as emissaries of deities. As scientific knowledge advanced, human perception of the planets changed, in 2006, the International Astronomical Union officially adopted a resolution defining planets within the Solar System. This definition is controversial because it excludes many objects of mass based on where or what they orbit. The planets were thought by Ptolemy to orbit Earth in deferent, at about the same time, by careful analysis of pre-telescopic observation data collected by Tycho Brahe, Johannes Kepler found the planets orbits were not circular but elliptical. As observational tools improved, astronomers saw that, like Earth, the planets rotated around tilted axes, and some shared such features as ice caps and seasons. Since the dawn of the Space Age, close observation by space probes has found that Earth and the planets share characteristics such as volcanism, hurricanes, tectonics. Planets are generally divided into two types, large low-density giant planets, and smaller rocky terrestrials. Under IAU definitions, there are eight planets in the Solar System, in order of increasing distance from the Sun, they are the four terrestrials, Mercury, Venus, Earth, and Mars, then the four giant planets, Jupiter, Saturn, Uranus, and Neptune. Six of the planets are orbited by one or more natural satellites, several thousands of planets around other stars have been discovered in the Milky Way. e. in the habitable zone. On December 20,2011, the Kepler Space Telescope team reported the discovery of the first Earth-sized extrasolar planets, Kepler-20e and Kepler-20f, orbiting a Sun-like star, Kepler-20. A2012 study, analyzing gravitational microlensing data, estimates an average of at least 1.6 bound planets for every star in the Milky Way, around one in five Sun-like stars is thought to have an Earth-sized planet in its habitable zone. The idea of planets has evolved over its history, from the lights of antiquity to the earthly objects of the scientific age. The concept has expanded to include not only in the Solar System. The ambiguities inherent in defining planets have led to much scientific controversy, the five classical planets, being visible to the naked eye, have been known since ancient times and have had a significant impact on mythology, religious cosmology, and ancient astronomy. In ancient times, astronomers noted how certain lights moved across the sky, as opposed to the fixed stars, ancient Greeks called these lights πλάνητες ἀστέρες or simply πλανῆται, from which todays word planet was derived. In ancient Greece, China, Babylon, and indeed all pre-modern civilizations, it was almost universally believed that Earth was the center of the Universe and that all the planets circled Earth. The first civilization known to have a theory of the planets were the Babylonians
9.
Galaxy
–
A galaxy is a gravitationally bound system of stars, stellar remnants, interstellar gas, dust, and dark matter. The word galaxy is derived from the Greek galaxias, literally milky, Galaxies range in size from dwarfs with just a few billion stars to giants with one hundred trillion stars, each orbiting its galaxys center of mass. Galaxies are categorized according to their morphology as elliptical, spiral. Many galaxies are thought to have holes at their active centers. The Milky Ways central black hole, known as Sagittarius A*, has a four million times greater than the Sun. Recent estimates of the number of galaxies in the observable universe range from 200 billion to 2 trillion or more, most of the galaxies are 1,000 to 100,000 parsecs in diameter and separated by distances on the order of millions of parsecs. The space between galaxies is filled with a gas having an average density of less than one atom per cubic meter. The majority of galaxies are organized into groups, clusters. At the largest scale, these associations are generally arranged into sheets and filaments surrounded by immense voids. In Greek mythology, Zeus places his son born by a mortal woman, the infant Heracles, on Heras breast while she is asleep so that the baby will drink her divine milk and will thus become immortal. Hera wakes up while breastfeeding and then realizes she is nursing a baby, she pushes the baby away, some of her milk spills and. In the astronomical literature, the capitalized word Galaxy is often used to refer to our galaxy, the Milky Way, to distinguish it from the other galaxies in our universe. The English term Milky Way can be traced back to a story by Chaucer c. 1380, See yonder, lo, the Galaxyë Which men clepeth the Milky Wey, For hit is whyt. However, the word Universe was later understood to mean the entirety of existence, so this expression fell into disuse and the objects instead became known as galaxies. Tens of thousands of galaxies have been catalogued, but only a few have well-established names, such as the Andromeda Galaxy, the Magellanic Clouds, the Whirlpool Galaxy, and the Sombrero Galaxy. Astronomers work with numbers from certain catalogues, such as the Messier catalogue, the NGC, the IC, the CGCG, all of the well-known galaxies appear in one or more of these catalogues but each time under a different number. For example, Messier 109 is a galaxy having the number 109 in the catalogue of Messier, but also codes NGC3992, UGC6937, CGCG 269-023, MCG +09-20-044. One of the arguments to do so is that these impressive objects deserve better than uninspired codes, for instance, Bodifee and Berger propose the informal, descriptive name Callimorphus Ursae Majoris for the well-formed barred galaxy Messier 109 in Ursa Major
10.
Coordinate system
–
The order of the coordinates is significant, and they are sometimes identified by their position in an ordered tuple and sometimes by a letter, as in the x-coordinate. The coordinates are taken to be real numbers in elementary mathematics, the use of a coordinate system allows problems in geometry to be translated into problems about numbers and vice versa, this is the basis of analytic geometry. The simplest example of a system is the identification of points on a line with real numbers using the number line. In this system, an arbitrary point O is chosen on a given line. The coordinate of a point P is defined as the distance from O to P. Each point is given a unique coordinate and each number is the coordinate of a unique point. The prototypical example of a system is the Cartesian coordinate system. In the plane, two lines are chosen and the coordinates of a point are taken to be the signed distances to the lines. In three dimensions, three perpendicular planes are chosen and the three coordinates of a point are the distances to each of the planes. This can be generalized to create n coordinates for any point in n-dimensional Euclidean space, depending on the direction and order of the coordinate axis the system may be a right-hand or a left-hand system. This is one of many coordinate systems, another common coordinate system for the plane is the polar coordinate system. A point is chosen as the pole and a ray from this point is taken as the polar axis, for a given angle θ, there is a single line through the pole whose angle with the polar axis is θ. Then there is a point on this line whose signed distance from the origin is r for given number r. For a given pair of coordinates there is a single point, for example, and are all polar coordinates for the same point. The pole is represented by for any value of θ, there are two common methods for extending the polar coordinate system to three dimensions. In the cylindrical coordinate system, a z-coordinate with the meaning as in Cartesian coordinates is added to the r and θ polar coordinates giving a triple. Spherical coordinates take this a further by converting the pair of cylindrical coordinates to polar coordinates giving a triple. A point in the plane may be represented in coordinates by a triple where x/z and y/z are the Cartesian coordinates of the point
11.
Three-dimensional space
–
Three-dimensional space is a geometric setting in which three values are required to determine the position of an element. This is the meaning of the term dimension. In physics and mathematics, a sequence of n numbers can be understood as a location in n-dimensional space, when n =3, the set of all such locations is called three-dimensional Euclidean space. It is commonly represented by the symbol ℝ3 and this serves as a three-parameter model of the physical universe in which all known matter exists. However, this space is one example of a large variety of spaces in three dimensions called 3-manifolds. Furthermore, in case, these three values can be labeled by any combination of three chosen from the terms width, height, depth, and breadth. In mathematics, analytic geometry describes every point in space by means of three coordinates. Three coordinate axes are given, each perpendicular to the two at the origin, the point at which they cross. They are usually labeled x, y, and z, below are images of the above-mentioned systems. Two distinct points determine a line. Three distinct points are either collinear or determine a unique plane, four distinct points can either be collinear, coplanar or determine the entire space. Two distinct lines can intersect, be parallel or be skew. Two parallel lines, or two intersecting lines, lie in a plane, so skew lines are lines that do not meet. Two distinct planes can either meet in a line or are parallel. Three distinct planes, no pair of which are parallel, can meet in a common line. In the last case, the three lines of intersection of each pair of planes are mutually parallel, a line can lie in a given plane, intersect that plane in a unique point or be parallel to the plane. In the last case, there will be lines in the plane that are parallel to the given line, a hyperplane is a subspace of one dimension less than the dimension of the full space. The hyperplanes of a space are the two-dimensional subspaces, that is
12.
Plot (graphics)
–
A plot is a graphical technique for representing a data set, usually as a graph showing the relationship between two or more variables. The plot can be drawn by hand or by a mechanical or electronic plotter, graphs are a visual representation of the relationship between variables, very useful for humans who can quickly derive an understanding which would not come from lists of values. Graphs can also be used to read off the value of an unknown variable plotted as a function of a known one, graphs of functions are used in mathematics, sciences, engineering, technology, finance, and other areas. Plots play an important role in statistics and data analysis, the procedures here can broadly be split into two parts, quantitative and graphical. Quantitative techniques are the set of procedures that yield numeric or tabular output. There are also many statistical tools generally referred to as graphical techniques, statistical graphics give insight into aspects of the underlying structure of the data. Graphs can also be used to some mathematical equations, typically by finding where two plots intersect. Arrhenius plot, This plot displays the logarithm of a rate plotted against inverse temperature, arrhenius plots are often used to analyze the effect of temperature on the rates of chemical reactions. Biplot, These are a type of graph used in statistics, a biplot allows information on both samples and variables of a data matrix to be displayed graphically. Samples are displayed as points while variables are displayed either as vectors, in the case of categorical variables, category level points may be used to represent the levels of a categorical variable. A generalised biplot displays information on both continuous and categorical variables, bland-Altman plot, In analytical chemistry and biostatistics this plot is a method of data plotting used in analysing the agreement between two different assays. It is identical to a Tukey mean-difference plot, which is what it is known as in other fields. Bode plots are used in control theory, a boxplot may also indicate which observations, if any, might be considered outliers. Carpet plot, A two-dimensional plot that illustrates the interaction between two and three independent variables and one to three dependent variables, comet plot, A two- or three-dimensional animated plot in which the data points are traced on the screen. Contour plot, A two-dimensional plot which shows the one-dimensional curves, optionally, the plotted values can be color-coded. Funnel plots, introduced by Light and Pillemer in 1994 and discussed in detail by Egger, a funnel plot is a scatterplot of treatment effect against a measure of study size. It is used primarily as an aid to detecting bias or systematic heterogeneity. Dot plot, A dot plot is a method that allows the comparison of two biological sequences and identify regions of close similarity between them
13.
Spherical coordinate system
–
It can be seen as the three-dimensional version of the polar coordinate system. The radial distance is called the radius or radial coordinate. The polar angle may be called colatitude, zenith angle, normal angle, the use of symbols and the order of the coordinates differs between sources. In both systems ρ is often used instead of r, other conventions are also used, so great care needs to be taken to check which one is being used. A number of different spherical coordinate systems following other conventions are used outside mathematics, in a geographical coordinate system positions are measured in latitude, longitude and height or altitude. There are a number of different celestial coordinate systems based on different fundamental planes, the polar angle is often replaced by the elevation angle measured from the reference plane. Elevation angle of zero is at the horizon, the spherical coordinate system generalises the two-dimensional polar coordinate system. It can also be extended to spaces and is then referred to as a hyperspherical coordinate system. To define a coordinate system, one must choose two orthogonal directions, the zenith and the azimuth reference, and an origin point in space. These choices determine a plane that contains the origin and is perpendicular to the zenith. The spherical coordinates of a point P are then defined as follows, the inclination is the angle between the zenith direction and the line segment OP. The azimuth is the angle measured from the azimuth reference direction to the orthogonal projection of the line segment OP on the reference plane. The sign of the azimuth is determined by choosing what is a sense of turning about the zenith. This choice is arbitrary, and is part of the coordinate systems definition, the elevation angle is 90 degrees minus the inclination angle. If the inclination is zero or 180 degrees, the azimuth is arbitrary, if the radius is zero, both azimuth and inclination are arbitrary. In linear algebra, the vector from the origin O to the point P is often called the vector of P. Several different conventions exist for representing the three coordinates, and for the order in which they should be written. The use of to denote radial distance, inclination, and azimuth, respectively, is common practice in physics, and is specified by ISO standard 80000-2,2009, and earlier in ISO 31-11
14.
Cartesian coordinate system
–
Each reference line is called a coordinate axis or just axis of the system, and the point where they meet is its origin, usually at ordered pair. The coordinates can also be defined as the positions of the projections of the point onto the two axis, expressed as signed distances from the origin. One can use the principle to specify the position of any point in three-dimensional space by three Cartesian coordinates, its signed distances to three mutually perpendicular planes. In general, n Cartesian coordinates specify the point in an n-dimensional Euclidean space for any dimension n and these coordinates are equal, up to sign, to distances from the point to n mutually perpendicular hyperplanes. The invention of Cartesian coordinates in the 17th century by René Descartes revolutionized mathematics by providing the first systematic link between Euclidean geometry and algebra. Using the Cartesian coordinate system, geometric shapes can be described by Cartesian equations, algebraic equations involving the coordinates of the points lying on the shape. For example, a circle of radius 2, centered at the origin of the plane, a familiar example is the concept of the graph of a function. Cartesian coordinates are also tools for most applied disciplines that deal with geometry, including astronomy, physics, engineering. They are the most common system used in computer graphics, computer-aided geometric design. Nicole Oresme, a French cleric and friend of the Dauphin of the 14th Century, used similar to Cartesian coordinates well before the time of Descartes. The adjective Cartesian refers to the French mathematician and philosopher René Descartes who published this idea in 1637 and it was independently discovered by Pierre de Fermat, who also worked in three dimensions, although Fermat did not publish the discovery. Both authors used a single axis in their treatments and have a length measured in reference to this axis. The concept of using a pair of axes was introduced later, after Descartes La Géométrie was translated into Latin in 1649 by Frans van Schooten and these commentators introduced several concepts while trying to clarify the ideas contained in Descartes work. Many other coordinate systems have developed since Descartes, such as the polar coordinates for the plane. The development of the Cartesian coordinate system would play a role in the development of the Calculus by Isaac Newton. The two-coordinate description of the plane was later generalized into the concept of vector spaces. Choosing a Cartesian coordinate system for a one-dimensional space – that is, for a straight line—involves choosing a point O of the line, a unit of length, and an orientation for the line. An orientation chooses which of the two half-lines determined by O is the positive, and which is negative, we say that the line is oriented from the negative half towards the positive half
15.
Geographic coordinate system
–
A geographic coordinate system is a coordinate system used in geography that enables every location on Earth to be specified by a set of numbers, letters or symbols. The coordinates are chosen such that one of the numbers represents a vertical position. A common choice of coordinates is latitude, longitude and elevation, to specify a location on a two-dimensional map requires a map projection. The invention of a coordinate system is generally credited to Eratosthenes of Cyrene. Ptolemy credited him with the adoption of longitude and latitude. Ptolemys 2nd-century Geography used the prime meridian but measured latitude from the equator instead. Mathematical cartography resumed in Europe following Maximus Planudes recovery of Ptolemys text a little before 1300, in 1884, the United States hosted the International Meridian Conference, attended by representatives from twenty-five nations. Twenty-two of them agreed to adopt the longitude of the Royal Observatory in Greenwich, the Dominican Republic voted against the motion, while France and Brazil abstained. France adopted Greenwich Mean Time in place of local determinations by the Paris Observatory in 1911, the latitude of a point on Earths surface is the angle between the equatorial plane and the straight line that passes through that point and through the center of the Earth. Lines joining points of the same latitude trace circles on the surface of Earth called parallels, as they are parallel to the equator, the north pole is 90° N, the south pole is 90° S. The 0° parallel of latitude is designated the equator, the plane of all geographic coordinate systems. The equator divides the globe into Northern and Southern Hemispheres, the longitude of a point on Earths surface is the angle east or west of a reference meridian to another meridian that passes through that point. All meridians are halves of great ellipses, which converge at the north and south poles, the prime meridian determines the proper Eastern and Western Hemispheres, although maps often divide these hemispheres further west in order to keep the Old World on a single side. The antipodal meridian of Greenwich is both 180°W and 180°E, the combination of these two components specifies the position of any location on the surface of Earth, without consideration of altitude or depth. The grid formed by lines of latitude and longitude is known as a graticule, the origin/zero point of this system is located in the Gulf of Guinea about 625 km south of Tema, Ghana. To completely specify a location of a feature on, in, or above Earth. Earth is not a sphere, but a shape approximating a biaxial ellipsoid. It is nearly spherical, but has an equatorial bulge making the radius at the equator about 0. 3% larger than the radius measured through the poles, the shorter axis approximately coincides with the axis of rotation
16.
Earth
–
Earth, otherwise known as the World, or the Globe, is the third planet from the Sun and the only object in the Universe known to harbor life. It is the densest planet in the Solar System and the largest of the four terrestrial planets, according to radiometric dating and other sources of evidence, Earth formed about 4.54 billion years ago. Earths gravity interacts with objects in space, especially the Sun. During one orbit around the Sun, Earth rotates about its axis over 365 times, thus, Earths axis of rotation is tilted, producing seasonal variations on the planets surface. The gravitational interaction between the Earth and Moon causes ocean tides, stabilizes the Earths orientation on its axis, Earths lithosphere is divided into several rigid tectonic plates that migrate across the surface over periods of many millions of years. About 71% of Earths surface is covered with water, mostly by its oceans, the remaining 29% is land consisting of continents and islands that together have many lakes, rivers and other sources of water that contribute to the hydrosphere. The majority of Earths polar regions are covered in ice, including the Antarctic ice sheet, Earths interior remains active with a solid iron inner core, a liquid outer core that generates the Earths magnetic field, and a convecting mantle that drives plate tectonics. Within the first billion years of Earths history, life appeared in the oceans and began to affect the Earths atmosphere and surface, some geological evidence indicates that life may have arisen as much as 4.1 billion years ago. Since then, the combination of Earths distance from the Sun, physical properties, in the history of the Earth, biodiversity has gone through long periods of expansion, occasionally punctuated by mass extinction events. Over 99% of all species that lived on Earth are extinct. Estimates of the number of species on Earth today vary widely, over 7.4 billion humans live on Earth and depend on its biosphere and minerals for their survival. Humans have developed diverse societies and cultures, politically, the world has about 200 sovereign states, the modern English word Earth developed from a wide variety of Middle English forms, which derived from an Old English noun most often spelled eorðe. It has cognates in every Germanic language, and their proto-Germanic root has been reconstructed as *erþō, originally, earth was written in lowercase, and from early Middle English, its definite sense as the globe was expressed as the earth. By early Modern English, many nouns were capitalized, and the became the Earth. More recently, the name is simply given as Earth. House styles now vary, Oxford spelling recognizes the lowercase form as the most common, another convention capitalizes Earth when appearing as a name but writes it in lowercase when preceded by the. It almost always appears in lowercase in colloquial expressions such as what on earth are you doing, the oldest material found in the Solar System is dated to 4. 5672±0.0006 billion years ago. By 4. 54±0.04 Gya the primordial Earth had formed, the formation and evolution of Solar System bodies occurred along with the Sun
17.
Sphere
–
A sphere is a perfectly round geometrical object in three-dimensional space that is the surface of a completely round ball. This distance r is the radius of the ball, and the point is the center of the mathematical ball. The longest straight line through the ball, connecting two points of the sphere, passes through the center and its length is twice the radius. While outside mathematics the terms sphere and ball are used interchangeably. The ball and the share the same radius, diameter. The surface area of a sphere is, A =4 π r 2, at any given radius r, the incremental volume equals the product of the surface area at radius r and the thickness of a shell, δ V ≈ A ⋅ δ r. The total volume is the summation of all volumes, V ≈ ∑ A ⋅ δ r. In the limit as δr approaches zero this equation becomes, V = ∫0 r A d r ′, substitute V,43 π r 3 = ∫0 r A d r ′. Differentiating both sides of equation with respect to r yields A as a function of r,4 π r 2 = A. Which is generally abbreviated as, A =4 π r 2, alternatively, the area element on the sphere is given in spherical coordinates by dA = r2 sin θ dθ dφ. In Cartesian coordinates, the element is d S = r r 2 − ∑ i ≠ k x i 2 ∏ i ≠ k d x i, ∀ k. For more generality, see area element, the total area can thus be obtained by integration, A = ∫02 π ∫0 π r 2 sin θ d θ d φ =4 π r 2. In three dimensions, the volume inside a sphere is derived to be V =43 π r 3 where r is the radius of the sphere, archimedes first derived this formula, which shows that the volume inside a sphere is 2/3 that of a circumscribed cylinder. In modern mathematics, this formula can be derived using integral calculus, at any given x, the incremental volume equals the product of the cross-sectional area of the disk at x and its thickness, δ V ≈ π y 2 ⋅ δ x. The total volume is the summation of all volumes, V ≈ ∑ π y 2 ⋅ δ x. In the limit as δx approaches zero this equation becomes, V = ∫ − r r π y 2 d x. At any given x, a right-angled triangle connects x, y and r to the origin, hence, applying the Pythagorean theorem yields, thus, substituting y with a function of x gives, V = ∫ − r r π d x. Which can now be evaluated as follows, V = π − r r = π − π =43 π r 3
18.
Great circle
–
A great circle, also known as an orthodrome or Riemannian circle, of a sphere is the intersection of the sphere and a plane that passes through the center point of the sphere. This partial case of a circle of a sphere is opposed to a circle, the intersection of the sphere. Any diameter of any great circle coincides with a diameter of the sphere, and therefore all great circles have the same circumference as each other, a great circle is the largest circle that can be drawn on any given sphere. Every circle in Euclidean 3-space is a circle of exactly one sphere. For most pairs of points on the surface of a sphere, there is a great circle through the two points. The exception is a pair of points, for which there are infinitely many great circles. The minor arc of a circle between two points is the shortest surface-path between them. In this sense, the arc is analogous to “straight lines” in Euclidean geometry. The length of the arc of a great circle is taken as the distance between two points on a surface of a sphere in Riemannian geometry. The great circles are the geodesics of the sphere, in higher dimensions, the great circles on the n-sphere are the intersection of the n-sphere with 2-planes that pass through the origin in the Euclidean space Rn+1. To prove that the arc of a great circle is the shortest path connecting two points on the surface of a sphere, one can apply calculus of variations to it. Consider the class of all paths from a point p to another point q. Introduce spherical coordinates so that p coincides with the north pole. Any curve on the sphere that does not intersect either pole, except possibly at the endpoints, can be parametrized by θ = θ, ϕ = ϕ, a ≤ t ≤ b provided we allow φ to take on arbitrary real values. The infinitesimal arc length in these coordinates is d s = r θ ′2 + ϕ ′2 sin 2 θ d t. So the length of a curve γ from p to q is a functional of the curve given by S = r ∫ a b θ ′2 + ϕ ′2 sin 2 θ d t. Note that S is at least the length of the meridian from p to q, S ≥ r ∫ a b | θ ′ | d t ≥ r | θ − θ |. Since the starting point and ending point are fixed, S is minimized if and only if φ =0, so the curve must lie on a meridian of the sphere φ = φ0 = constant
19.
Units of measurement
–
A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same quantity. Any other value of quantity can be expressed as a simple multiple of the unit of measurement. For example, length is a physical quantity, the metre is a unit of length that represents a definite predetermined length. When we say 10 metres, we actually mean 10 times the definite predetermined length called metre, the definition, agreement, and practical use of units of measurement have played a crucial role in human endeavour from early ages up to this day. Different systems of units used to be very common, now there is a global standard, the International System of Units, the modern form of the metric system. In trade, weights and measures is often a subject of regulation, to ensure fairness. The International Bureau of Weights and Measures is tasked with ensuring worldwide uniformity of measurements, metrology is the science for developing nationally and internationally accepted units of weights and measures. In physics and metrology, units are standards for measurement of quantities that need clear definitions to be useful. Reproducibility of experimental results is central to the scientific method, a standard system of units facilitates this. Scientific systems of units are a refinement of the concept of weights, science, medicine, and engineering often use larger and smaller units of measurement than those used in everyday life and indicate them more precisely. The judicious selection of the units of measurement can aid researchers in problem solving, in the social sciences, there are no standard units of measurement and the theory and practice of measurement is studied in psychometrics and the theory of conjoint measurement. A unit of measurement is a quantity of a physical property. Units of measurement were among the earliest tools invented by humans, primitive societies needed rudimentary measures for many tasks, constructing dwellings of an appropriate size and shape, fashioning clothing, or bartering food or raw materials. Weights and measures are mentioned in the Bible and it is a commandment to be honest and have fair measures. As of the 21st Century, multiple unit systems are used all over the world such as the United States Customary System, the British Customary System, however, the United States is the only industrialized country that has not yet completely converted to the Metric System. The systematic effort to develop an acceptable system of units dates back to 1790 when the French National Assembly charged the French Academy of Sciences to come up such a unit system. After this treaty was signed, a General Conference of Weights, the CGPM produced the current SI system which was adopted in 1954 at the 10th conference of weights and measures. Currently, the United States is a society which uses both the SI system and the US Customary system
20.
Equator
–
The Equator usually refers to an imaginary line on the Earths surface equidistant from the North Pole and South Pole, dividing the Earth into the Northern Hemisphere and Southern Hemisphere. The Equator is about 40,075 kilometres long, some 78. 7% lies across water and 21. 3% over land, other planets and astronomical bodies have equators similarly defined. Generally, an equator is the intersection of the surface of a sphere with the plane that is perpendicular to the spheres axis of rotation. The latitude of the Earths equator is by definition 0° of arc, the equator is the only line of latitude which is also a great circle — that is, one whose plane passes through the center of the globe. The plane of Earths equator when projected outwards to the celestial sphere defines the celestial equator, in the cycle of Earths seasons, the plane of the equator passes through the Sun twice per year, at the March and September equinoxes. To an observer on the Earth, the Sun appears to travel North or South over the equator at these times, light rays from the center of the Sun are perpendicular to the surface of the Earth at the point of solar noon on the Equator. Locations on the Equator experience the quickest sunrises and sunsets because the sun moves nearly perpendicular to the horizon for most of the year. The Earth bulges slightly at the Equator, the diameter of the Earth is 12,750 kilometres. Because the Earth spins to the east, spacecraft must also launch to the east to take advantage of this Earth-boost of speed, seasons result from the yearly revolution of the Earth around the Sun and the tilt of the Earths axis relative to the plane of revolution. During the year the northern and southern hemispheres are inclined toward or away from the sun according to Earths position in its orbit, the hemisphere inclined toward the sun receives more sunlight and is in summer, while the other hemisphere receives less sun and is in winter. At the equinoxes, the Earths axis is not tilted toward the sun, instead it is perpendicular to the sun meaning that the day is about 12 hours long, as is the night, across the whole of the Earth. Near the Equator there is distinction between summer, winter, autumn, or spring. The temperatures are usually high year-round—with the exception of high mountains in South America, the temperature at the Equator can plummet during rainstorms. In many tropical regions people identify two seasons, the wet season and the dry season, but many places close to the Equator are on the oceans or rainy throughout the year, the seasons can vary depending on elevation and proximity to an ocean. The Equator lies mostly on the three largest oceans, the Pacific Ocean, the Atlantic Ocean, and the Indian Ocean. The highest point on the Equator is at the elevation of 4,690 metres, at 0°0′0″N 77°59′31″W and this is slightly above the snow line, and is the only place on the Equator where snow lies on the ground. At the Equator the snow line is around 1,000 metres lower than on Mount Everest, the Equator traverses the land of 11 countries, it also passes through two island nations, though without making a landfall in either. Starting at the Prime Meridian and heading eastwards, the Equator passes through, Despite its name, however, its island of Annobón is 155 km south of the Equator, and the rest of the country lies to the north
21.
Horizontal coordinate system
–
The horizontal coordinate system is a celestial coordinate system that uses the observers local horizon as the fundamental plane. It is expressed in terms of angle and azimuth. This coordinate system divides the sky into the upper hemisphere where objects are visible, the great circle separating the hemispheres is called the celestial horizon. The celestial horizon is defined as the circle on the celestial sphere whose plane is normal to the local gravity vector. In practice, the horizon can be defined as the tangent to a still liquid surface such as a pool of mercury. The pole of the upper hemisphere is called the zenith, the pole of the lower hemisphere is called the nadir. There are two independent horizontal angular coordinates, Altitude, sometimes referred to as elevation, is the angle between the object and the local horizon. For visible objects it is an angle between 0 degrees to 90 degrees, alternatively, zenith distance may be used instead of altitude. More details on the computation of azimuth and zenith angle can be found at Solar azimuth angle, the horizontal coordinate system is fixed to the Earth, not the stars. Therefore, the altitude and azimuth of an object in the sky changes with time, horizontal coordinates are very useful for determining the rise and set times of an object in the sky. When an objects altitude is 0°, it is on the horizon, if at that moment its altitude is increasing, it is rising, but if its altitude is decreasing, it is setting. However, all objects on the sphere are subject to diurnal motion. One can determine whether altitude is increasing or decreasing by instead considering the azimuth of the celestial object, if the azimuth is between 180° and 360°, it is setting. There are the special cases, As seen from the north pole all directions are south. Viewed from either pole, a star has constant altitude, the Sun, Moon, and planets can rise or set over the span of a year when viewed from the poles because their declinations are constantly changing. As seen from the equator, objects on the poles stay at fixed points on the horizon. Note that the above considerations are strictly speaking true for the horizon only. That is, the horizon as it would appear for an observer at sea level on a perfectly smooth Earth without an atmosphere
22.
Horizon
–
At many locations, the true horizon is obscured by trees, buildings, mountains, etc. and the resulting intersection of earth and sky is called the visible horizon. When looking at a sea from a shore, the part of the sea closest to the horizon is called the offing. The word horizon derives from the Greek ὁρίζων κύκλος horizōn kyklos, separating circle, from the verb ὁρίζω horizō, to divide, to separate, a pilot can also retain his or her spatial orientation by referring to the horizon. For observers near sea level the difference between this geometrical horizon and the horizon is imperceptible to the naked eye. In astronomy the horizon is the plane through the eyes of the observer. It is the plane of the horizontal coordinate system, the locus of points that have an altitude of zero degrees. While similar in ways to the horizon, in this context a horizon may be considered to be a plane in space. One typically sees further along the Earths curved surface than a simple geometric calculation allows for because of refraction error, the reverse happens if the ground is hotter than the air above it, as often happens in deserts, producing mirages. Examples, For an observer standing on the ground with h =1.70 metres, for an observer standing on the ground with h =2 metres, the horizon is at a distance of 5 kilometres. For an observer standing on a hill or tower of 100 metres in height, for an observer standing at the top of the Burj Khalifa, the horizon is at a distance of 103 kilometres. For an observer atop Mount Everest, the horizon is at a distance of 336 kilometres, with d in miles and h in feet, d ≈1.5 h ≈1.22 h. Examples, assuming no refraction, For an observer on the ground with eye level at h =5 ft 7 in, for an observer standing on a hill or tower 100 feet in height, the horizon is at a distance of 12.2 miles. For an observer on the summit of Aconcagua, the horizon to the west is at a distance of 184 miles. The secant-tangent theorem states that O C2 = O A × O B, the equation can also be derived using the Pythagorean theorem. Since the line of sight is a tangent to the Earth and this sets up a right triangle, with the sum of the radius and the height as the hypotenuse. Another relationship involves the distance s along the surface of the Earth to the horizon, with γ in radians, s = R γ. Solving for s gives s = R cos −1 R R + h, the distances d and s are nearly the same when the height of the object is negligible compared to the radius. If the observer is close to the surface of the earth, then it is valid to disregard h in the term, and the formula becomes d =2 R h
23.
Zenith
–
The zenith is an imaginary point directly above a particular location, on the imaginary celestial sphere. Above means in the direction opposite to the apparent gravitational force at that location. The opposite direction, i. e. the direction in which gravity pulls, is toward the nadir, the zenith is the highest point on the celestial sphere. It was reduced to samt and miswritten as senit/cenit, as the m was misread as an ni, through the Old French cenith, zenith first appeared in the 17th century. The term zenith is sometimes used to refer to the highest point, way or level reached by a celestial body during its apparent orbit around a given point of observation. This sense of the word is used to describe the location of the Sun, but to an astronomer the sun does not have its own zenith. In a scientific context, the zenith is the direction of reference for measuring the zenith angle, in astronomy, the altitude in the horizontal coordinate system and the zenith angle are complementary angles, with the horizon perpendicular to the zenith. The astronomical meridian is also determined by the zenith, and is defined as a circle on the sphere that passes through the zenith, nadir. A zenith telescope is a type of telescope designed to point straight up at or near the zenith, the NASA Orbital Debris Observatory and the Large Zenith Telescope are both zenith telescopes since the use of liquid mirrors meant these telescopes could only point straight up. Azimuth Geodesy History of geodesy Keyhole problem Midheaven Subsolar point Vertical deflection Horizontal coordinate system Glickman, Todd S. Glossary of meteorology
24.
Nadir
–
The nadir, is the direction pointing directly below a particular location, that is, it is one of two vertical directions at a specified location, orthogonal to a horizontal flat surface there. Since the concept of being below is itself somewhat vague, scientists define the nadir in more rigorous terms. Specifically, in astronomy, geophysics and related sciences, the nadir at a point is the local vertical direction pointing in the direction of the force of gravity at that location. The direction opposite of the nadir is the zenith, the word is also used figuratively to mean the lowest point of a persons spirits, or the quality of an activity or profession. The term nadir can also be used to represent the lowest point reached by a body during its apparent orbit around a given point of observation. This can be used to describe the location of the Sun, the sun is said to be at the nadir at a location when it is at the zenith at the locations antipode and the sun is 90 degrees below the horizon. In oncology, the nadir is used to represent the lowest level of a blood cell count while a patient is undergoing chemotherapy. A diagnosis of neutropenic nadir after chemotherapy typically lasts 7–10 days
25.
Azimuth
–
An azimuth is an angular measurement in a spherical coordinate system. An example is the position of a star in the sky, the star is the point of interest, the reference plane is the horizon or the surface of the sea, and the reference vector points north. The azimuth is the angle between the vector and the perpendicular projection of the star down onto the horizon. Azimuth is usually measured in degrees, the concept is used in navigation, astronomy, engineering, mapping, mining and artillery. In land navigation, azimuth is usually denoted alpha, α, azimuth has also been more generally defined as a horizontal angle measured clockwise from any fixed reference plane or easily established base direction line. Today, the plane for an azimuth is typically true north, measured as a 0° azimuth. Moving clockwise on a 360 degree circle, east has azimuth 90°, south 180°, there are exceptions, some navigation systems use south as the reference vector. Any direction can be the vector, as long as it is clearly defined. Quite commonly, azimuths or compass bearings are stated in a system in which either north or south can be the zero, the reference direction, stated first, is always north or south, and the turning direction, stated last, is east or west. The directions are chosen so that the angle, stated between them, is positive, between zero and 90 degrees. If the bearing happens to be exactly in the direction of one of the cardinal points and this is the reason why the X and Y axis in the above formula are swapped. If the azimuth becomes negative, one can always add 360°, the formula in radians would be slightly easier, α = atan2 Caveat, Most computer libraries reverse the order of the atan2 parameters. We are standing at latitude φ1, longitude zero, we want to find the azimuth from our viewpoint to Point 2 at latitude φ2, longitude L. The difference is usually small, if Point 2 is not more than 100 km away. Various websites will calculate geodetic azimuth, e. g. GeoScience Australia site, formulas for calculating geodetic azimuth are linked in the distance article. Normal-section azimuth is simpler to calculate, Bomford says Cunninghams formula is exact for any distance, replace φ2 with declination and longitude difference with hour angle, and change the sign. There is a variety of azimuthal map projections. They all have the property that directions from a point are preserved
26.
North
–
North is one of the four cardinal directions or compass points. It is the opposite of south and is perpendicular to east and west, North is a noun, adjective, or adverb indicating direction or geography. The word north is related to the Old High German nord, the Latin word borealis comes from the Greek boreas north wind, north, which, according to Ovid, was personified as the son of the river-god Strymon, the father of Calais and Zetes. Septentrionalis is from septentriones, the seven plow oxen, a name of Ursa Maior, the Greek ἀρκτικός is named for the same constellation, and is the source of the English word Arctic. For example, in Lezgian, kefer can mean both disbelief and north, since to the north of the Muslim Lezgian homeland there are areas formerly inhabited by non-Muslim Caucasian, in many languages of Mesoamerica, north also means up. The direction north is associated with colder climates because most of the worlds land at high latitudes is located in the Northern Hemisphere. By convention, the top side of a map is often north, to go north using a compass for navigation, set a bearing or azimuth of 0° or 360°. North is specifically the direction that, in Western culture, is treated as the fundamental direction, on any rotating non-astronomical object, north denotes the side appearing to rotate counter-clockwise when viewed from afar along the axis of rotation. Magnetic north is of interest because it is the direction indicated as north on a properly functioning magnetic compass, the difference between it and true north is called the magnetic declination. But simple generalizations on the subject should be treated as unsound, maps intended for usage in orienteering by compass will clearly indicate the local declination for easy correction to true north. Maps may also indicate grid north, which is a term referring to the direction northwards along the grid lines of a map projection. The visible rotation of the sky around the visible celestial pole provides a vivid metaphor of that direction corresponding to up. Thus the choice of the north as corresponding to up in the hemisphere, or of south in that role in the southern, is, prior to worldwide communication, anything. On the contrary, it is of interest that Chinese and Islamic culture even considered south as the top end for maps. Up is a metaphor for north, the notion that north should always be up and east at the right was established by the Greek astronomer Ptolemy. While the choice of north over south as prime direction reflects quite arbitrary historical factors and their folk definitions are, respectively, where the sun rises and where it sets. The true folk-astronomical definitions of east and west are the directions, an angle from the prime direction. Being the default direction on the compass, north is referred to frequently in Western popular culture, some examples include, The phrase north of X is often used by Americans to mean more than X or greater than X, i. e
27.
South
–
South is a noun, adjective, or adverb indicating direction or geography. It is one of the four directions or compass points. South is the polar opposite of north and is perpendicular to east and west, the word south comes from Old English sūþ, from earlier Proto-Germanic *sunþaz, possibly related to the same Proto-Indo-European root that the word sun derived from. By convention, the side of a map is south. To go south using a compass for navigation, set a bearing or azimuth of 180°, alternatively, in the Northern Hemisphere outside the tropics, the Sun will be roughly in the south at midday. True south is the direction towards the end of the axis about which the earth rotates. The South Pole is located in Antarctica, magnetic south is the direction towards the south magnetic pole, some distance away from the south geographic pole. Roald Amundsen, from Norway, was the first to reach the South Pole, on 14 December 1911, the Global South refers to the socially and economically less-developed southern half of the globe. 95% of the Global North has enough food and shelter, in the South, on the other hand, only 5% of the population has enough food and shelter. It lacks appropriate technology, it has no political stability, the economies are disarticulated, in the card game bridge, one of the players is known for scoring purposes as South. South partners with North and plays against East and West, in Greek religion, Notos, was the south wind and bringer of the storms of late summer and autumn. The dictionary definition of south at Wiktionary
28.
Sun
–
The Sun is the star at the center of the Solar System. It is a perfect sphere of hot plasma, with internal convective motion that generates a magnetic field via a dynamo process. It is by far the most important source of energy for life on Earth. Its diameter is about 109 times that of Earth, and its mass is about 330,000 times that of Earth, accounting for about 99. 86% of the total mass of the Solar System. About three quarters of the Suns mass consists of hydrogen, the rest is mostly helium, with smaller quantities of heavier elements, including oxygen, carbon, neon. The Sun is a G-type main-sequence star based on its spectral class and it formed approximately 4.6 billion years ago from the gravitational collapse of matter within a region of a large molecular cloud. Most of this matter gathered in the center, whereas the rest flattened into a disk that became the Solar System. The central mass became so hot and dense that it eventually initiated nuclear fusion in its core and it is thought that almost all stars form by this process. The Sun is roughly middle-aged, it has not changed dramatically for more than four billion years and it is calculated that the Sun will become sufficiently large enough to engulf the current orbits of Mercury, Venus, and probably Earth. The enormous effect of the Sun on Earth has been recognized since prehistoric times, the synodic rotation of Earth and its orbit around the Sun are the basis of the solar calendar, which is the predominant calendar in use today. The English proper name Sun developed from Old English sunne and may be related to south, all Germanic terms for the Sun stem from Proto-Germanic *sunnōn. The English weekday name Sunday stems from Old English and is ultimately a result of a Germanic interpretation of Latin dies solis, the Latin name for the Sun, Sol, is not common in general English language use, the adjectival form is the related word solar. The term sol is used by planetary astronomers to refer to the duration of a solar day on another planet. A mean Earth solar day is approximately 24 hours, whereas a mean Martian sol is 24 hours,39 minutes, and 35.244 seconds. From at least the 4th Dynasty of Ancient Egypt, the Sun was worshipped as the god Ra, portrayed as a falcon-headed divinity surmounted by the solar disk, and surrounded by a serpent. In the New Empire period, the Sun became identified with the dung beetle, in the form of the Sun disc Aten, the Sun had a brief resurgence during the Amarna Period when it again became the preeminent, if not only, divinity for the Pharaoh Akhenaton. The Sun is viewed as a goddess in Germanic paganism, Sól/Sunna, in ancient Roman culture, Sunday was the day of the Sun god. It was adopted as the Sabbath day by Christians who did not have a Jewish background, the symbol of light was a pagan device adopted by Christians, and perhaps the most important one that did not come from Jewish traditions
29.
Celestial equator
–
The celestial equator is a great circle on the imaginary celestial sphere, in the same plane as the Earths equator. In other words, it is a projection of the terrestrial equator out into space, as a result of the Earths axial tilt, the celestial equator is inclined by 23. 4° with respect to the ecliptic plane. An observer standing on the Earths equator visualizes the celestial equator as a semicircle passing directly overhead through the zenith, as the observer moves north, the celestial equator tilts towards the opposite horizon. Celestial objects near the equator are visible worldwide, but they culminate the highest in the sky in the tropics. The celestial equator currently passes through these constellations, Celestial bodies other than Earth also have similarly defined celestial equators, Celestial pole Celestial sphere Declination Equatorial coordinate system
30.
Celestial pole
–
The north and south celestial poles are the two imaginary points in the sky where the Earths axis of rotation, indefinitely extended, intersects the celestial sphere. The north and south celestial poles appear permanently directly overhead to an observer at the Earths North Pole and South Pole respectively. As the Earth spins on its axis, the two celestial poles remain fixed in the sky, and all other points appear to rotate around them, completing one circuit per day. The celestial poles are also the poles of the equatorial coordinate system, meaning they have declinations of +90 degrees. The celestial poles do not remain permanently fixed against the background of the stars, because of a phenomenon known as the precession of the equinoxes, the poles trace out circles on the celestial sphere, with a period of about 25,700 years. The Earths axis is subject to other complex motions which cause the celestial poles to shift slightly over cycles of varying lengths, see nutation, polar motion. Finally, over long periods the positions of the stars themselves change. An analogous concept applies to other planets, a planets celestial poles are the points in the sky where the projection of the axis of rotation intersects the celestial sphere. These points vary because different planets axes are oriented differently, Celestial bodies other than Earth also have similarly defined celestial poles. The north celestial pole currently is within a degree of the bright star Polaris, Polaris can, of course, only be seen from locations in the northern hemisphere. Polaris is near the pole for only a small fraction of the 25. It will remain a good approximation for about 1,000 years, to find Polaris, face north and locate the Big Dipper and Little Dipper asterisms. Looking at the cup part of the Big Dipper, imagine that the two stars at the edge of the cup form a line pointing upward out of the cup. This line points directly at the star at the tip of the Little Dippers handle and that star is Polaris, the North Star. The south celestial pole is only from the southern hemisphere. It lies in the dim constellation Octans, the Octant, sigma Octantis is identified as the south pole star, over a degree away from the pole, but with a magnitude of 5.5 it is barely visible on a clear night. The south celestial pole can be located from the Southern Cross, draw an imaginary line from γ Crucis to α Crucis—the two stars at the extreme ends of the long axis of the cross—and follow this line through the sky. This point is 5 or 6 degrees from the celestial pole
31.
Declination
–
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
32.
Right ascension
–
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
33.
Hour angle
–
In astronomy and celestial navigation, the hour angle is one of the coordinates used in the equatorial coordinate system to give the direction of a point on the celestial sphere. The hour angle of a point is the angle between two planes, one containing the Earths axis and the zenith, and the containing the Earths axis. The angle may be expressed as negative east of the plane and positive west of the meridian plane. The angle may be measured in degrees or in time, with 24h = 360° exactly, in astronomy, hour angle is defined as the angular distance on the celestial sphere measured westward along the celestial equator from the meridian to the hour circle passing through a point. It may be given in degrees, time, or rotations depending on the application, in celestial navigation, the convention is to measure in degrees westward from the prime meridian, from the local meridian or from the first point of Aries. The hour angle is paired with the declination to fully specify the location of a point on the sphere in the equatorial coordinate system. These angles can be measured in time or in degrees — one or the other, negative hour angles indicate the time until the next transit across the meridian, an hour angle of zero means the object is on the meridian. Observing the sun from earth, the hour angle is an expression of time, expressed in angular measurement, usually degrees. At solar noon the hour angle is 0.000 degree, with the time before solar noon expressed as negative degrees, for example, at 10,30 AM local apparent time the hour angle is -22. 5°. The cosine of the angle is used to calculate the solar zenith angle. The sidereal hour angle of a body on the sphere is its angular distance west of the vernal equinox generally measured in degrees. The SHA of a star changes slowly, and the SHA of a planet doesnt change very quickly, SHA is often used in celestial navigation and navigational astronomy. Sidereal hour angle + right ascension = 360° Clock position
34.
Ecliptic
–
The ecliptic is the apparent path of the Sun on the celestial sphere, and is the basis for the ecliptic coordinate system. It also refers to the plane of this path, which is coplanar with the orbit of Earth around the Sun, the motions as described above are simplifications. Due to the movement of Earth around the Earth–Moon center of mass, due to further perturbations by the other planets of the Solar System, the Earth–Moon barycenter wobbles slightly around a mean position in a complex fashion. The ecliptic is actually the apparent path of the Sun throughout the course of a year, because Earth takes one year to orbit the Sun, the apparent position of the Sun also takes the same length of time to make a complete circuit of the ecliptic. With slightly more than 365 days in one year, the Sun moves a little less than 1° eastward every day, again, this is a simplification, based on a hypothetical Earth that orbits at uniform speed around the Sun. The actual speed with which Earth orbits the Sun varies slightly during the year, for example, the Sun is north of the celestial equator for about 185 days of each year, and south of it for about 180 days. The variation of orbital speed accounts for part of the equation of time, if the equator is projected outward to the celestial sphere, forming the celestial equator, it crosses the ecliptic at two points known as the equinoxes. The Sun, in its apparent motion along the ecliptic, crosses the equator at these points, one from south to north. The crossing from south to north is known as the equinox, also known as the first point of Aries. The crossing from north to south is the equinox or descending node. Likewise, the ecliptic itself is not fixed, the gravitational perturbations of the other bodies of the Solar System cause a much smaller motion of the plane of Earths orbit, and hence of the ecliptic, known as planetary precession. The combined action of two motions is called general precession, and changes the position of the equinoxes by about 50 arc seconds per year. Once again, this is a simplification, periodic motions of the Moon and apparent periodic motions of the Sun cause short-term small-amplitude periodic oscillations of Earths axis, and hence the celestial equator, known as nutation. Obliquity of the ecliptic is the used by astronomers for the inclination of Earths equator with respect to the ecliptic. It is about 23. 4° and is currently decreasing 0.013 degrees per hundred years due to planetary perturbations, the angular value of the obliquity is found by observation of the motions of Earth and other planets over many years. From 1984, the Jet Propulsion Laboratorys DE series of computer-generated ephemerides took over as the ephemeris of the Astronomical Almanac. Obliquity based on DE200, which analyzed observations from 1911 to 1979, was calculated, jPLs fundamental ephemerides have been continually updated. J. Laskar computed an expression to order T10 good to 0″. 04/1000 years over 10,000 years, all of these expressions are for the mean obliquity, that is, without the nutation of the equator included
35.
Orbital pole
–
An orbital pole is either end of an imaginary line running through the center of an orbit perpendicular to the orbital plane, projected onto the celestial sphere. It is similar in concept to a pole but based on the planets orbit instead of the planets rotation. The orbital pole of the earth is referred to as the Ecliptic pole, the ecliptic poles are the points on the celestial sphere where it meets the imaginary line perpendicular to the ecliptic plane, in which the Earth travels on its orbit around the Sun. There are two poles, Due to precession, the celestial pole moves in a circle around the ecliptic poles once every 25,800 years. It is not possible to have a pole at the zenith in a dark sky. By definition, the poles are located 90 degrees from the Suns position. Therefore, whenever either ecliptic pole is directly overhead, the Sun must be on the horizon, the ecliptic poles can be at the zenith on the Arctic and Antarctic Circles
36.
Ecliptic latitude
–
The ecliptic coordinate system is a celestial coordinate system commonly used for representing the positions and orbits of Solar System objects. Because most planets, and many small Solar System bodies have orbits with small inclinations to the ecliptic, using it as the fundamental plane is convenient. The systems origin can be either the center of the Sun or the center of the Earth, its direction is towards the vernal equinox. It may be implemented in spherical coordinates or rectangular coordinates, a slow motion of Earths axis, precession, causes a slow, continuous turning of the coordinate system westward about the poles of the ecliptic, completing one circuit in about 26,000 years. Superimposed on this is a motion of the ecliptic. The three most commonly used are, Mean equinox of an epoch is a fixed standard direction. Mean equinox of date is the intersection of the ecliptic of date with the mean equator, commonly used in planetary orbit calculation. True equinox of date is the intersection of the ecliptic of date with the true equator and this is the actual intersection of the two planes at any particular moment, with all motions accounted for. A position in the coordinate system is thus typically specified true equinox and ecliptic of date, mean equinox and ecliptic of J2000.0. Note that there is no mean ecliptic, as the ecliptic is not subject to small periodic oscillations, ecliptic longitude or celestial longitude measures the angular distance of an object along the ecliptic from the primary direction. Like right ascension in the coordinate system, the primary direction points from the Earth towards the Sun at the vernal equinox of the Northern Hemisphere. Because it is a system, ecliptic longitude is measured positive eastwards in the fundamental plane from 0° to 360°. Because of axial precession, the longitude of most fixed stars increases by about 50.3 arcseconds per year, or 83.8 arcminutes per century. Ecliptic latitude or celestial latitude, measures the distance of an object from the ecliptic towards the north or south ecliptic pole. For example, the ecliptic pole has a celestial latitude of +90°. Ecliptic latitude for fixed stars is not affected by precession, distance is also necessary for a complete spherical position. Different distance units are used for different objects, within the Solar System, astronomical units are used, and for objects near the Earth, Earth radii or kilometers are used. From antiquity through the 18th century, ecliptic longitude was measured using twelve zodiacal signs, each of 30° longitude
37.
Ecliptic longitude
–
The ecliptic coordinate system is a celestial coordinate system commonly used for representing the positions and orbits of Solar System objects. Because most planets, and many small Solar System bodies have orbits with small inclinations to the ecliptic, using it as the fundamental plane is convenient. The systems origin can be either the center of the Sun or the center of the Earth, its direction is towards the vernal equinox. It may be implemented in spherical coordinates or rectangular coordinates, a slow motion of Earths axis, precession, causes a slow, continuous turning of the coordinate system westward about the poles of the ecliptic, completing one circuit in about 26,000 years. Superimposed on this is a motion of the ecliptic. The three most commonly used are, Mean equinox of an epoch is a fixed standard direction. Mean equinox of date is the intersection of the ecliptic of date with the mean equator, commonly used in planetary orbit calculation. True equinox of date is the intersection of the ecliptic of date with the true equator and this is the actual intersection of the two planes at any particular moment, with all motions accounted for. A position in the coordinate system is thus typically specified true equinox and ecliptic of date, mean equinox and ecliptic of J2000.0. Note that there is no mean ecliptic, as the ecliptic is not subject to small periodic oscillations, ecliptic longitude or celestial longitude measures the angular distance of an object along the ecliptic from the primary direction. Like right ascension in the coordinate system, the primary direction points from the Earth towards the Sun at the vernal equinox of the Northern Hemisphere. Because it is a system, ecliptic longitude is measured positive eastwards in the fundamental plane from 0° to 360°. Because of axial precession, the longitude of most fixed stars increases by about 50.3 arcseconds per year, or 83.8 arcminutes per century. Ecliptic latitude or celestial latitude, measures the distance of an object from the ecliptic towards the north or south ecliptic pole. For example, the ecliptic pole has a celestial latitude of +90°. Ecliptic latitude for fixed stars is not affected by precession, distance is also necessary for a complete spherical position. Different distance units are used for different objects, within the Solar System, astronomical units are used, and for objects near the Earth, Earth radii or kilometers are used. From antiquity through the 18th century, ecliptic longitude was measured using twelve zodiacal signs, each of 30° longitude
38.
Galactic plane
–
The galactic plane is the plane in which the majority of a disk-shaped galaxys mass lies. The directions perpendicular to the galactic plane point to the galactic poles. Most often, in usage, the terms galactic plane and galactic poles are used to refer specifically to the plane and poles of the Milky Way. Some galaxies are irregular and do not have any well-defined disk, even in the case of a barred spiral galaxy like the Milky Way, defining the galactic plane is slightly imprecise and arbitrary since the stars are not perfectly coplanar. 282s, Dec 27° 07′42. 01″. This position is in Coma Berenices, near the bright star Arcturus, likewise, the zero of longitude of galactic coordinates was also defined in 1959 to be at position angle 123° from the north celestial pole. Thus the zero point on the galactic equator was at 17h 42m 26. 603s, −28° 55′00. 445″ or 17h 45m 37. 224s, −28° 56′10. 23″. The galactic center is located at position angle 31. 72° or 31. 40° east of north, galactic coordinate system Reid, M. J. Brunthaler, A. The Proper Motion of Sagittarius A*, the Mass of Sagittarius A*, The Astrophysical Journal,616, 872–884, arXiv, astro-ph/0408107, Bibcode, 2004ApJ.616. 872R, doi,10. 1086/424960. See appendix for the numbers listed above
39.
Galactic pole
–
It uses the right-handed convention, meaning that coordinates are positive toward the north and toward the east in the fundamental plane. Longitude measures the distance of an object eastward along the galactic equator from the galactic center. Analogous to terrestrial longitude, galactic longitude is measured in degrees. Latitude measures the distance of an object perpendicular to a plane parallel to, but ~57 light years north of. For example, the north pole has a latitude of +90°. Analogous to terrestrial latitude, galactic latitude is usually measured in degrees, the first Galactic coordinate system was used by William Herschel in 1785. 5°. Longitude 0° is the great semicircle that originates from this point along the line in position angle 123° with respect to the equatorial pole, the galactic longitude increases in the same direction as right ascension. Galactic latitude is positive towards the north pole, with a plane passing through the Sun and parallel to the galactic equator being 0°. Based on this definition, the poles and equator can be found from spherical trigonometry and can be precessed to other epochs. Radio source Sagittarius A*, which is the best physical marker of the galactic center, is located at 17h 45m 40. 0409s. Rounded to the number of digits as the table, 17h 45. 7m, −29. 01°, there is an offset of about 0. 07° from the defined coordinate center. There are two major variations of galactic coordinates, commonly used for computing space velocities of galactic objects. In these systems the xyz axes are designated UVW, but the definitions vary by author
40.
Galactic Center
–
The Galactic Center is the rotational center of the Milky Way. The estimates for its range from 7.6 to 8.7 kiloparsecs from Earth in the direction of the constellations Sagittarius, Ophiuchus. There is strong evidence consistent with the existence of a black hole at the Galactic Center of the Milky Way. Because of interstellar dust along the line of sight, the Galactic Center cannot be studied at visible, the available information about the Galactic Center comes from observations at gamma ray, hard X-ray, infrared, sub-millimetre and radio wavelengths. In the early 1940s Walter Baade at Mount Wilson Observatory took advantage of wartime conditions in nearby Los Angeles to conduct a search for the center with the 100 inch Hooker Telescope. This gap has been known as Baades Window ever since, by 1954 they had built an 80 feet fixed dish antenna and used it to make a detailed study of an extended, extremely powerful belt of radio emission that was detected in Sagittarius. In 1958 the International Astronomical Union decided to adopt the position of Sagittarius A as the true zero co-ordinate point for the system of latitude and longitude. In the equatorial system the location is, RA 17h 45m 40. 04s. The exact distance between the Solar System and the Galactic Center is not certain, although estimates since 2000 have remained within the range 7. 2–8.8 kpc. The nature of the Milky Ways bar, which extends across the Galactic Center, is also debated, with estimates for its half-length. Certain authors advocate that the Milky Way features two bars, one nestled within the other. The bar is delineated by red-clump stars, however, RR Lyr variables do not trace a prominent Galactic bar. The bar may be surrounded by a called the 5-kpc ring that contains a large fraction of the molecular hydrogen present in the Milky Way. Viewed from the Andromeda Galaxy, it would be the brightest feature of the Milky Way, accretion of gas onto the black hole, probably involving a disk around it, would release energy to power the radio source, itself much larger than the black hole. The latter is too small to see with present instruments, a study in 2008 which linked radio telescopes in Hawaii, Arizona and California measured the diameter of Sagittarius A* to be 44 million kilometers. For comparison, the radius of Earths orbit around the Sun is about 150 million kilometers, thus the diameter of the radio source is slightly less than the distance from Mercury to the Sun.3 million solar masses. On 5 January 2015, NASA reported observing an X-ray flare 400 times brighter than usual, the central cubic parsec around Sagittarius A* contains around 10 million stars. Although most of them are old red giant stars, the Galactic Center is also rich in massive stars, more than 100 OB and Wolf–Rayet stars have been identified there so far
41.
Sidereal day
–
Sidereal time /saɪˈdɪəriəl/ is a time-keeping system that astronomers use to locate celestial objects. Using sidereal time it is possible to point a telescope to the proper coordinates in the night sky. Briefly, sidereal time is a scale that is based on Earths rate of rotation measured relative to the fixed stars rather than the Sun. From a given point, a star found at one location in the sky will be found at the same location on another night at the same sidereal time. This is similar to how the time kept by a sundial can be used to find the location of the Sun, just as the Sun and Moon appear to rise in the east and set in the west due to the rotation of Earth, so do the stars. Both solar time and sidereal time make use of the regularity of Earths rotation about its polar axis, a mean sidereal day is 23 hours,56 minutes,4.0916 seconds, the time it takes Earth to make one rotation relative to the vernal equinox. The longer true sidereal period is called a day by the International Earth Rotation. It is also referred to as the period of rotation. Maps of the stars in the night sky use declination and right ascension as coordinates and these correspond to latitude and longitude respectively. In the sky, the meridian is the north to south line that goes through the point directly overhead. Solar time is measured by the apparent diurnal motion of the Sun, a mean solar day is the average time between local solar noons. Earth makes one rotation around its axis in a sidereal day, so after a sidereal day has passed, Earth still needs to rotate slightly more before the Sun reaches local noon according to solar time. A mean solar day is, therefore, nearly 4 minutes longer than a sidereal day, the stars are so far away that Earths movement along its orbit makes nearly no difference to their apparent direction, and so they return to their highest point in a sidereal day. Another way to see this difference is to notice that, relative to the stars, therefore, there is one fewer solar day per year than there are sidereal days. This makes a sidereal day approximately 365. 24/366.24 times the length of the 24-hour solar day, Earths rotation is not a simple rotation around an axis that would always remain parallel to itself. Earths rotational axis itself rotates about an axis, orthogonal to Earths orbit. This phenomenon is called the precession of the equinoxes, because of this precession, the stars appear to move around Earth in a manner more complicated than a simple constant rotation. In this reference frame, Earths rotation is close to constant and it is also in this reference frame that the tropical year, the year related to Earths seasons, represents one orbit of Earth around the Sun
42.
Center of mass
–
The distribution of mass is balanced around the center of mass and the average of the weighted position coordinates of the distributed mass defines its coordinates. Calculations in mechanics are simplified when formulated with respect to the center of mass. It is a point where entire mass of an object may be assumed to be concentrated to visualise its motion. In other words, the center of mass is the equivalent of a given object for application of Newtons laws of motion. In the case of a rigid body, the center of mass is fixed in relation to the body. The center of mass may be located outside the body, as is sometimes the case for hollow or open-shaped objects. In the case of a distribution of separate bodies, such as the planets of the Solar System, in orbital mechanics, the equations of motion of planets are formulated as point masses located at the centers of mass. The center of mass frame is a frame in which the center of mass of a system is at rest with respect to the origin of the coordinate system. The concept of center of mass in the form of the center of gravity was first introduced by the ancient Greek physicist, mathematician, and engineer Archimedes of Syracuse. He worked with simplified assumptions about gravity that amount to a uniform field, in work on floating bodies he demonstrated that the orientation of a floating object is the one that makes its center of mass as low as possible. He developed mathematical techniques for finding the centers of mass of objects of uniform density of various well-defined shapes, Newtons second law is reformulated with respect to the center of mass in Eulers first law. The center of mass is the point at the center of a distribution of mass in space that has the property that the weighted position vectors relative to this point sum to zero. In analogy to statistics, the center of mass is the location of a distribution of mass in space. Solving this equation for R yields the formula R =1 M ∑ i =1 n m i r i, solve this equation for the coordinates R to obtain R =1 M ∭ Q ρ r d V, where M is the total mass in the volume. If a continuous mass distribution has density, which means ρ is constant. The center of mass is not generally the point at which a plane separates the distribution of mass into two equal halves, in analogy with statistics, the median is not the same as the mean. The coordinates R of the center of mass of a system, P1 and P2, with masses m1. The percentages of mass at each point can be viewed as projective coordinates of the point R on this line, another way of interpreting the process here is the mechanical balancing of moments about an arbitrary point