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Magnitude (mathematics), Magnitude
Magnitude may refer to: Mathematics *Euclidean vector, a quantity defined by both its magnitude and its direction *Magnitude (mathematics), the relative size of an object *Norm (mathematics), a term for the size or length of a vector *Order of magnitude, the class of scale having a fixed value ratio to the preceding class *Scalar (mathematics), a quantity defined only by its magnitude Astronomy *Absolute magnitude, the brightness of a celestial object corrected to a standard luminosity distance *Apparent magnitude, the calibrated apparent brightness of a celestial object *Instrumental magnitude, the uncalibrated apparent magnitude of a celestial object *Magnitude (astronomy), a measure of brightness and brightness differences used in astronomy *Magnitude of eclipse or geometric magnitude, the size of the eclipsed part of the Sun during a solar eclipse or the Moon during a lunar eclipse * Photographic magnitude, the brightness of a celestial object corrected for photographic sen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euclidean Vector
In mathematics, physics, and engineering, a Euclidean vector or simply a vector (sometimes called a geometric vector or spatial vector) is a geometric object that has magnitude (or length) and direction. Vectors can be added to other vectors according to vector algebra. A Euclidean vector is frequently represented by a '' directed line segment'', or graphically as an arrow connecting an ''initial point'' ''A'' with a ''terminal point'' ''B'', and denoted by \overrightarrow . A vector is what is needed to "carry" the point ''A'' to the point ''B''; the Latin word ''vector'' means "carrier". It was first used by 18th century astronomers investigating planetary revolution around the Sun. The magnitude of the vector is the distance between the two points, and the direction refers to the direction of displacement from ''A'' to ''B''. Many algebraic operations on real numbers such as addition, subtraction, multiplication, and negation have close analogues for vectors, operations whic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Magnitude Of Eclipse
The magnitude of eclipse is the fraction of the angular diameter of a celestial body being eclipsed. This applies to all celestial eclipses. The magnitude of a partial or annular solar eclipse is always between 0.0 and 1.0, while the magnitude of a total solar eclipse is always greater than or equal to 1.0. This measure is strictly a ratio of diameters and should not be confused with the covered fraction of the apparent area (disk) of the eclipsed body. Neither should it be confused with the astronomical magnitude scale of apparent brightness. Effect of the magnitude on a solar eclipse The apparent sizes of the Moon and Sun are both approximately 0.5°, or 30', but both vary because the distance between Earth and Moon varies. (The distance between Earth and Sun also varies, but the effect is slight in comparison.) In an annular solar eclipse, the magnitude of the eclipse is the ratio between the apparent angular diameters of the Moon and that of the Sun during the maximu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Surface-wave Magnitude
The surface wave magnitude (M_s) scale is one of the magnitude scales used in seismology to describe the size of an earthquake. It is based on measurements of Rayleigh surface waves that travel along the uppermost layers of the Earth. This magnitude scale is related to the local magnitude scale proposed by Charles Francis Richter in 1935, with modifications from both Richter and Beno Gutenberg throughout the 1940s and 1950s. It is currently used in People's Republic of China as a national standard (GB 17740-1999) for categorising earthquakes. Recorded magnitudes of earthquakes through the mid 20th century, commonly attributed to Richter, could be either M_s or M_L. Definition The formula to calculate surface wave magnitude is: :M_s = \log_\left(\frac\right)_ + \sigma(\Delta)\,, where A is the maximum particle displacement in surface waves (vector sum of the two horizontal displacements) in μm, T is the corresponding period in s (usually 20 2 seconds), Δ is the epi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Richter Magnitude Scale
The Richter scale —also called the Richter magnitude scale, Richter's magnitude scale, and the Gutenberg–Richter scale—is a measure of the strength of earthquakes, developed by Charles Francis Richter and presented in his landmark 1935 paper, where he called it the "magnitude scale". This was later revised and renamed the local magnitude scale, denoted as ML or . Because of various shortcomings of the original scale, most seismological authorities now use other similar scales such as the moment magnitude scale () to report earthquake magnitudes, but much of the news media still erroneously refers to these as "Richter" magnitudes. All magnitude scales retain the logarithmic character of the original and are scaled to have roughly comparable numeric values (typically in the middle of the scale). Due to the variance in earthquakes, it is essential to understand the Richter scale uses logarithms simply to make the measurements manageable (i.e., a magnitude 3 quake factors ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Moment Magnitude Scale
The moment magnitude scale (MMS; denoted explicitly with or Mw, and generally implied with use of a single M for magnitude) is a measure of an earthquake's magnitude ("size" or strength) based on its seismic moment. It was defined in a 1979 paper by Thomas C. Hanks and Hiroo Kanamori. Similar to the local magnitude scale, local magnitude/Richter scale () defined by Charles Francis Richter in 1935, it uses a logarithmic scale; small earthquakes have approximately the same magnitudes on both scales. Despite the difference, news media often says "Richter scale" when referring to the moment magnitude scale. Moment magnitude () is considered the authoritative magnitude scale for ranking earthquakes by size. It is more directly related to the energy of an earthquake than other scales, and does not saturate—that is, it does not underestimate magnitudes as other scales do in certain conditions. It has become the standard scale used by seismological authorities like the U.S. Geological ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Seismic Magnitude Scales
Seismic magnitude scales are used to describe the overall strength or "size" of an earthquake. These are distinguished from seismic intensity scales that categorize the intensity or severity of ground shaking (quaking) caused by an earthquake at a given location. Magnitudes are usually determined from measurements of an earthquake's seismic waves as recorded on a seismogram. Magnitude scales vary on what aspect of the seismic waves are measured and how they are measured. Different magnitude scales are necessary because of differences in earthquakes, the information available, and the purposes for which the magnitudes are used. Earthquake magnitude and ground-shaking intensity The Earth's crust is stressed by tectonic forces. When this stress becomes great enough to rupture the crust, or to overcome the friction that prevents one block of crust from slipping past another, energy is released, some of it in the form of various kinds of seismic waves that cause ground-shaking, o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Visual Magnitude
Apparent magnitude () is a measure of the brightness of a star or other astronomical object observed from Earth. An object's apparent magnitude depends on its intrinsic luminosity, its distance from Earth, and any extinction of the object's light caused by interstellar dust along the line of sight to the observer. The word ''magnitude'' in astronomy, unless stated otherwise, usually refers to a celestial object's apparent magnitude. The magnitude scale dates back to the ancient Roman astronomer Claudius Ptolemy, whose star catalog listed stars from 1st magnitude (brightest) to 6th magnitude (dimmest). The modern scale was mathematically defined in a way to closely match this historical system. The scale is reverse logarithmic: the brighter an object is, the lower its magnitude number. A difference of 1.0 in magnitude corresponds to a brightness ratio of \sqrt /math>, or about 2.512. For example, a star of magnitude 2.0 is 2.512 times as bright as a star of magnitude 3.0, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Photographic Magnitude
Photographic magnitude ( or ) is a measure of the relative brightness of a star or other astronomical object as imaged on a photographic film emulsion with a camera attached to a telescope. An object's apparent photographic magnitude depends on its intrinsic luminosity, its distance and any extinction of light by interstellar matter existing along the line of sight to the observer. Photographic observations have now been superseded by electronic photometry such as CCD charge-couple device cameras that convert the incoming light into an electric current by the photoelectric effect. Determination of magnitude is made using a photometer. Method Prior to photographic methods to determine magnitude, the brightness of celestial objects was determined by visual photometric methods. This was simply achieved with the human eye by compared the brightness of an astronomical object with other nearby objects of known or fixed magnitude : especially regarding stars, planets and other pl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Magnitude (astronomy)
In astronomy, magnitude is a unitless measure of the brightness Brightness is an attribute of visual perception in which a source appears to be radiating or reflecting light. In other words, brightness is the perception elicited by the luminance of a visual target. The perception is not linear to luminance, ... of an astronomical object, object in a defined passband, often in the visible spectrum, visible or infrared spectrum, but sometimes across all wavelengths. An imprecise but systematic determination of the magnitude of objects was introduced in ancient times by Hipparchus. The scale is Logarithmic scale, logarithmic and defined such that a magnitude 1 star is exactly 100 times brighter than a magnitude 6 star. Thus each step of one magnitude is \sqrt[5] \approx 2.512 times brighter than the magnitude 1 higher. The brighter an object appears, the lower the value of its magnitude, with the brightest objects reaching negative values. Astronomers use two different defini ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Magnitude (mathematics)
In mathematics, the magnitude or size of a mathematical object is a property which determines whether the object is larger or smaller than other objects of the same kind. More formally, an object's magnitude is the displayed result of an order theory, ordering (or ranking)—of the class (mathematics), class of objects to which it belongs. In physics, magnitude can be defined as quantity or distance. History The Greeks distinguished between several types of magnitude, including: *Positive fractions *Line segments (ordered by length) *Geometric shape, Plane figures (ordered by area) *Solid geometry, Solids (ordered by volume) *Angle, Angles (ordered by angular magnitude) They proved that the first two could not be the same, or even isomorphic systems of magnitude. They did not consider negative number, negative magnitudes to be meaningful, and ''magnitude'' is still primarily used in contexts in which zero is either the smallest size or less than all possible sizes. Numbers Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Instrumental Magnitude
Instrumental magnitude refers to an uncalibrated apparent magnitude, and, like its counterpart, it refers to the brightness of an astronomical object seen from an observer on Earth, but unlike its counterpart, it is only useful in relative comparisons to other astronomical objects in the same image (assuming the photometric calibration does not spatially vary across the image; in the case of images from the Palomar Transient Factory, the absolute photometric calibration involves a zero point that varies over the image by up to 0.16 magnitudes to make a required illumination correction). Instrumental magnitude is defined in various ways, and so when working with instrumental magnitudes, it is important to know how they are defined. The most basic definition of instrumental magnitude, m, is given by :m = -2.5 \log_(f) where f is the intensity of the source object in known physical units. For example, in the paper by Mighell, it was assumed that the data are in units of electron num ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Apparent Magnitude
Apparent magnitude () is a measure of the brightness of a star or other astronomical object observed from Earth. An object's apparent magnitude depends on its intrinsic luminosity, its distance from Earth, and any extinction of the object's light caused by interstellar dust along the line of sight to the observer. The word ''magnitude'' in astronomy, unless stated otherwise, usually refers to a celestial object's apparent magnitude. The magnitude scale dates back to the ancient Roman astronomer Claudius Ptolemy, whose star catalog listed stars from 1st magnitude (brightest) to 6th magnitude (dimmest). The modern scale was mathematically defined in a way to closely match this historical system. The scale is reverse logarithmic: the brighter an object is, the lower its magnitude number. A difference of 1.0 in magnitude corresponds to a brightness ratio of \sqrt /math>, or about 2.512. For example, a star of magnitude 2.0 is 2.512 times as bright as a star of magnitude 3.0, 6. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
