Gravity Darkening
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Gravity Darkening
Gravity darkening, also referred to as gravity brightening, is an astronomical phenomenon where the poles of a star are brighter than the equator, due to rapid rotation and oblate shape. When a star is oblate, it has a larger radius at its equator than it does at its poles. As a result, the poles have a higher surface gravity, and thus higher temperature and pressure is needed to maintain hydrostatic equilibrium. Thus, the poles are "gravity brightened", and the equator "gravity darkened". The star becomes oblate (and hence gravity darkening occurs) because the centrifugal force resulting from rotation creates additional outward pressure on the star. The centrifugal force is expressed mathematically as : F_\text = m \Omega^2 \rho, where m is mass (in this case of a small volume element of the star), \Omega is the angular velocity, and \rho is the radial distance from the axis of rotation. In the case of a star, the value of \rho is largest at the equator and smallest at the poles ...
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Eso0316c
The European Organisation for Astronomical Research in the Southern Hemisphere, commonly referred to as the European Southern Observatory (ESO), is an intergovernmental research organisation made up of 16 member states for ground-based astronomy. Created in 1962, ESO has provided astronomers with state-of-the-art research facilities and access to the southern sky. The organisation employs about 730 staff members and receives annual member state contributions of approximately €162 million. Its observatories are located in northern Chile. ESO has built and operated some of the largest and most technologically advanced telescopes. These include the 3.6 m New Technology Telescope, an early pioneer in the use of active optics, and the Very Large Telescope (VLT), which consists of four individual 8.2 m telescopes and four smaller auxiliary telescopes which can all work together or separately. The Atacama Large Millimeter Array observes the universe in the millimetre and s ...
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Astronomical
Astronomy () is a natural science that studies celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and evolution. Objects of interest include planets, moons, stars, nebulae, galaxies, and comets. Relevant phenomena include supernova explosions, gamma ray bursts, quasars, blazars, pulsars, and cosmic microwave background radiation. More generally, astronomy studies everything that originates beyond Earth's atmosphere. Cosmology is a branch of astronomy that studies the universe as a whole. Astronomy is one of the oldest natural sciences. The early civilizations in recorded history made methodical observations of the night sky. These include the Babylonians, Greeks, Indians, Egyptians, Chinese, Maya, and many ancient indigenous peoples of the Americas. In the past, astronomy included disciplines as diverse as astrometry, celestial navigation, observational astronomy, and the making of calendars. Nowadays, professiona ...
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Phenomenon
A phenomenon ( : phenomena) is an observable event. The term came into its modern philosophical usage through Immanuel Kant, who contrasted it with the noumenon, which ''cannot'' be directly observed. Kant was heavily influenced by Gottfried Wilhelm Leibniz in this part of his philosophy, in which phenomenon and noumenon serve as interrelated technical terms. Far predating this, the ancient Greek Pyrrhonist philosopher Sextus Empiricus also used ''phenomenon'' and ''noumenon'' as interrelated technical terms. Common usage In popular usage, a ''phenomenon'' often refers to an extraordinary event. The term is most commonly used to refer to occurrences that at first defy explanation or baffle the observer. According to the ''Dictionary of Visual Discourse'':In ordinary language 'phenomenon/phenomena' refer to any occurrence worthy of note and investigation, typically an untoward or unusual event, person or fact that is of special significance or otherwise notable. Philosophy ...
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Star
A star is an astronomical object comprising a luminous spheroid of plasma (physics), plasma held together by its gravity. The List of nearest stars and brown dwarfs, nearest star to Earth is the Sun. Many other stars are visible to the naked eye at night sky, night, but their immense distances from Earth make them appear as fixed stars, fixed points of light. The most prominent stars have been categorised into constellations and asterism (astronomy), asterisms, and many of the brightest stars have proper names. Astronomers have assembled star catalogues that identify the known stars and provide standardized stellar designations. The observable universe contains an estimated to stars. Only about 4,000 of these stars are visible to the naked eye, all within the Milky Way galaxy. A star's life star formation, begins with the gravitational collapse of a gaseous nebula of material composed primarily of hydrogen, along with helium and trace amounts of heavier elements. Its stellar ...
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Hydrostatic Equilibrium
In fluid mechanics, hydrostatic equilibrium (hydrostatic balance, hydrostasy) is the condition of a fluid or plastic solid at rest, which occurs when external forces, such as gravity, are balanced by a pressure-gradient force. In the planetary physics of Earth, the pressure-gradient force prevents gravity from collapsing the planetary atmosphere into a thin, dense shell, whereas gravity prevents the pressure-gradient force from diffusing the atmosphere into outer space. Hydrostatic equilibrium is the distinguishing criterion between dwarf planets and small solar system bodies, and features in astrophysics and planetary geology. Said qualification of equilibrium indicates that the shape of the object is symmetrically ellipsoid, where any irregular surface features are consequent to a relatively thin solid crust. In addition to the Sun, there are a dozen or so equilibrium objects confirmed to exist in the Solar System. Mathematical consideration For a hydrostatic fluid on Ear ...
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Centrifugal Force
In Newtonian mechanics, the centrifugal force is an inertial force (also called a "fictitious" or "pseudo" force) that appears to act on all objects when viewed in a rotating frame of reference. It is directed away from an axis which is parallel to the axis of rotation and passing through the coordinate system's origin. If the axis of rotation passes through the coordinate system's origin, the centrifugal force is directed radially outwards from that axis. The magnitude of centrifugal force ''F'' on an object of mass ''m'' at the distance ''r'' from the origin of a frame of reference rotating with angular velocity is: F = m\omega^2 r The concept of centrifugal force can be applied in rotating devices, such as centrifuges, centrifugal pumps, centrifugal governors, and centrifugal clutches, and in centrifugal railways, planetary orbits and banked curves, when they are analyzed in a rotating coordinate system. Confusingly, the term has sometimes also been used for the reactiv ...
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Angular Velocity
In physics, angular velocity or rotational velocity ( or ), also known as angular frequency vector,(UP1) is a pseudovector representation of how fast the angular position or orientation of an object changes with time (i.e. how quickly an object rotates or revolves relative to a point or axis). The magnitude of the pseudovector represents the ''angular speed'', the rate at which the object rotates or revolves, and its direction is normal to the instantaneous plane of rotation or angular displacement. The orientation of angular velocity is conventionally specified by the right-hand rule.(EM1) There are two types of angular velocity. * Orbital angular velocity refers to how fast a point object revolves about a fixed origin, i.e. the time rate of change of its angular position relative to the origin. * Spin angular velocity refers to how fast a rigid body rotates with respect to its center of rotation and is independent of the choice of origin, in contrast to orbital angular ve ...
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Von Zeipel's Theorem
In astrophysics, the von Zeipel theorem states that the radiative flux F in a uniformly rotating star is proportional to the local effective gravity g_\text. The theorem is named after Swedish astronomer Edvard Hugo von Zeipel. The theorem is: : F = -\frac g_\text, where the luminosity L and mass M_* are evaluated on a surface of constant pressure P. The effective temperature T_\text can then be found at a given colatitude \theta from the local effective gravity: : T_\text(\theta) \sim g_\text^(\theta). This relation ignores the effect of convection in the envelope, so it primarily applies to early-type stars. According to the theory of rotating stars, if the rotational velocity of a star depends only on the radius, it cannot simultaneously be in thermal and hydrostatic equilibrium. This is called the von Zeipel paradox. The paradox is resolved, however, if the rotational velocity also depends on height, or there is a meridional circulation. A similar situation may arise in a ...
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Effective Temperature
The effective temperature of a body such as a star or planet is the temperature of a black body that would emit the same total amount of electromagnetic radiation. Effective temperature is often used as an estimate of a body's surface temperature when the body's emissivity curve (as a function of wavelength) is not known. When the star's or planet's net emissivity in the relevant wavelength band is less than unity (less than that of a black body), the actual temperature of the body will be higher than the effective temperature. The net emissivity may be low due to surface or atmospheric properties, including greenhouse effect. Star The effective temperature of a star is the temperature of a black body with the same luminosity per ''surface area'' () as the star and is defined according to the Stefan–Boltzmann law . Notice that the total (bolometric) luminosity of a star is then , where is the stellar radius. The definition of the stellar radius is obviously not straightf ...
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