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Luminosity Distance
Luminosity distance ''DL'' is defined in terms of the relationship between the absolute magnitude ''M'' and apparent magnitude ''m'' of an astronomical object. : M = m - 5 \log_\!\, which gives: : D_L = 10^ where ''DL'' is measured in parsecs. For nearby objects (say, in the Milky Way) the luminosity distance gives a good approximation to the natural notion of distance in Euclidean space. The relation is less clear for distant objects like quasars far beyond the Milky Way since the apparent magnitude is affected by spacetime curvature, redshift, and time dilation. Calculating the relation between the apparent and actual luminosity of an object requires taking all of these factors into account. The object's actual luminosity is determined using the inverse-square law and the proportions of the object's apparent distance and luminosity distance. Another way to express the luminosity distance is through the flux-luminosity relationship, : F = \frac where is flux (W·m−2), and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Absolute Magnitude
Absolute magnitude () is a measure of the luminosity of a celestial object on an inverse Logarithmic scale, logarithmic Magnitude (astronomy), astronomical magnitude scale. An object's absolute magnitude is defined to be equal to the apparent magnitude that the object would have if it were viewed from a distance of exactly , without Extinction (astronomy), extinction (or dimming) of its light due to absorption by Interstellar medium, interstellar matter and cosmic dust. By hypothetically placing all objects at a standard reference distance from the observer, their luminosities can be directly compared among each other on a magnitude scale. As with all astronomical magnitude (astronomy), magnitudes, the absolute magnitude can be specified for different wavelength ranges corresponding to specified Filter (optics), filter bands or passbands; for stars a commonly quoted absolute magnitude is the absolute visual magnitude, which uses the visual (V) band of the spectrum (in the UBV phot ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Flux
Flux describes any effect that appears to pass or travel (whether it actually moves or not) through a surface or substance. Flux is a concept in applied mathematics and vector calculus which has many applications to physics. For transport phenomena, flux is a vector quantity, describing the magnitude and direction of the flow of a substance or property. In vector calculus flux is a scalar quantity, defined as the surface integral of the perpendicular component of a vector field over a surface. Terminology The word ''flux'' comes from Latin: ''fluxus'' means "flow", and ''fluere'' is "to flow". As ''fluxion'', this term was introduced into differential calculus by Isaac Newton. The concept of heat flux was a key contribution of Joseph Fourier, in the analysis of heat transfer phenomena. His seminal treatise ''Théorie analytique de la chaleur'' (''The Analytical Theory of Heat''), defines ''fluxion'' as a central quantity and proceeds to derive the now well-known express ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Distance Modulus
The distance modulus is a way of expressing distances that is often used in astronomy. It describes distances on a logarithmic scale based on the astronomical magnitude system. Definition The distance modulus \mu=m-M is the difference between the apparent magnitude m (ideally, corrected from the effects of interstellar absorption) and the absolute magnitude M of an astronomical object. It is related to the distance d in parsecs by: :\log_(d) = 1 + \frac :\mu=5\log_(d)-5 This definition is convenient because the observed brightness of a light source is related to its distance by the inverse square law (a source twice as far away appears one quarter as bright) and because brightnesses are usually expressed not directly, but in magnitudes. Absolute magnitude M is defined as the apparent magnitude of an object when seen at a distance of 10 parsecs. Suppose a light source has luminosity L(d) when observed from a distance of d parsecs, and luminosity L(10) when observed from a dist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Distance Measure
Distance measures are used in physical cosmology to give a natural notion of the distance between two objects or events in the universe. They are often used to tie some ''observable'' quantity (such as the luminosity of a distant quasar, the redshift of a distant galaxy, or the angular size of the acoustic peaks in the cosmic microwave background (CMB) power spectrum) to another quantity that is not ''directly'' observable, but is more convenient for calculations (such as the comoving coordinates of the quasar, galaxy, etc.). The distance measures discussed here all reduce to the common notion of Euclidean distance, Euclidean distance at low redshift. In accord with our present understanding of cosmology, these measures are calculated within the context of general relativity, where the Friedmann–Lemaître–Robertson–Walker metric, Friedmann–Lemaître–Robertson–Walker solution is used to describe the universe. Overview There are a few different definitions of "distanc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Comoving Distance
In standard cosmology, comoving distance and proper distance are two closely related distance measures used by cosmologists to define distances between objects. ''Proper distance'' roughly corresponds to where a distant object would be at a specific moment of cosmological time, which can change over time due to the expansion of the universe. ''Comoving distance'' factors out the expansion of the universe, giving a distance that does not change in time due to the expansion of space (though this may change due to other, local factors, such as the motion of a galaxy within a cluster). Comoving distance and proper distance are defined to be equal at the present time. At other times, the Universe's expansion results in the proper distance changing, while the comoving distance remains constant. Comoving coordinates Although general relativity allows one to formulate the laws of physics using arbitrary coordinates, some coordinate choices are more natural or easier to work with. Com ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Etherington's Reciprocity Theorem
The Etherington's distance-duality equation is the relationship between the luminosity distance of standard candles and the angular diameter distance. The equation is as follows: d_L=(1+z)^2 d_A, where z is the redshift, d_L is the luminosity distance and d_A the angular-diameter distance. History and derivations When Ivor Etherington introduced this equation in 1933, he mentioned that this equation was proposed by Tolman as a way to test a cosmological model. Ellis proposed a proof of this equation in the context of Riemannian geometry. A quote from Ellis: "The core of the reciprocity theorem is the fact that many geometric properties are invariant when the roles of the source and observer in astronomical observations are transposed". This statement is fundamental in the derivation of the reciprocity theorem. Validation from astronomical observations The Etherington's distance-duality equation has been validated from astronomical observations based on the X-ray surface bright ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Angular Diameter Distance
In astronomy, angular diameter distance is a distance defined in terms of an object's physical size, x, and its angular size, \theta, as viewed from Earth: d_A= \frac Cosmology dependence The angular diameter distance depends on the assumed cosmology of the universe. The angular diameter distance to an object at redshift, z , is expressed in terms of the comoving distance, r as: d_A = \frac where S_k(r) is the FLRW coordinate defined as: S_k(r) = \begin \sin \left( \sqrt H_0 r \right)/\left(H_0\sqrt\right) & \Omega_k 0 \end where \Omega_k is the curvature density and H_0 is the value of the Hubble parameter today. In the currently favoured geometric model of our Universe, the "angular diameter distance" of an object is a good approximation to the "real distance", i.e. the proper distance when the light left the object. Angular size redshift relation The angular size redshift relation describes the relation between the angular size observed on the sky of an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Luminosity
Luminosity is an absolute measure of radiated electromagnetic power (light), the radiant power emitted by a light-emitting object over time. In astronomy, luminosity is the total amount of electromagnetic energy emitted per unit of time by a star, galaxy, or other astronomical object. In SI units, luminosity is measured in joules per second, or watts. In astronomy, values for luminosity are often given in the terms of the luminosity of the Sun, ''L''⊙. Luminosity can also be given in terms of the astronomical magnitude system: the absolute bolometric magnitude (''M''bol) of an object is a logarithmic measure of its total energy emission rate, while absolute magnitude is a logarithmic measure of the luminosity within some specific wavelength range or filter band. In contrast, the term ''brightness'' in astronomy is generally used to refer to an object's apparent brightness: that is, how bright an object appears to an observer. Apparent brightness depends on both the lumin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Time Dilation
In physics and relativity, time dilation is the difference in the elapsed time as measured by two clocks. It is either due to a relative velocity between them ( special relativistic "kinetic" time dilation) or to a difference in gravitational potential between their locations ( general relativistic gravitational time dilation). When unspecified, "time dilation" usually refers to the effect due to velocity. After compensating for varying signal delays due to the changing distance between an observer and a moving clock (i.e. Doppler effect), the observer will measure the moving clock as ticking slower than a clock that is at rest in the observer's own reference frame. In addition, a clock that is close to a massive body (and which therefore is at lower gravitational potential) will record less elapsed time than a clock situated further from the said massive body (and which is at a higher gravitational potential). These predictions of the theory of relativity have been repeatedl ... [...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] |
Redshift
In physics, a redshift is an increase in the wavelength, and corresponding decrease in the frequency and photon energy, of electromagnetic radiation (such as light). The opposite change, a decrease in wavelength and simultaneous increase in frequency and energy, is known as a negative redshift, or blueshift. The terms derive from the colours red and blue which form the extremes of the visible light spectrum. In astronomy and cosmology, the three main causes of electromagnetic redshift are # The radiation travels between objects which are moving apart (" relativistic" redshift, an example of the relativistic Doppler effect) #The radiation travels towards an object in a weaker gravitational potential, i.e. towards an object in less strongly curved (flatter) spacetime (gravitational redshift) #The radiation travels through expanding space (cosmological redshift). The observation that all sufficiently distant light sources show redshift corresponding to their distance from Earth ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Curvature
In mathematics, curvature is any of several strongly related concepts in geometry. Intuitively, the curvature is the amount by which a curve deviates from being a straight line, or a surface deviates from being a plane. For curves, the canonical example is that of a circle, which has a curvature equal to the reciprocal of its radius. Smaller circles bend more sharply, and hence have higher curvature. The curvature ''at a point'' of a differentiable curve is the curvature of its osculating circle, that is the circle that best approximates the curve near this point. The curvature of a straight line is zero. In contrast to the tangent, which is a vector quantity, the curvature at a point is typically a scalar quantity, that is, it is expressed by a single real number. For surfaces (and, more generally for higher-dimensional manifolds), that are embedded in a Euclidean space, the concept of curvature is more complex, as it depends on the choice of a direction on the surface or man ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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