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Darwin–Radau Equation
In astrophysics, the Darwin–Radau equation (named after Rodolphe Radau and Charles Galton Darwin) gives an approximate relation between the moment of inertia factor of a planetary body and its rotational speed and shape. The moment of inertia factor is directly related to the largest principal moment of inertia, ''C''. It is assumed that the rotating body is in hydrostatic equilibrium and is an ellipsoid of revolution. The Darwin–Radau equation states : \frac = \frac = \frac \left( 1 - \frac \sqrt \right) where ''M'' and ''Re'' represent the mass and mean equatorial radius of the body. Here λ is the d'Alembert parameter and the Radau parameter η is defined as : \eta = \frac - 2 where ''q'' is the geodynamical constant : q = \frac and ε is the geometrical flattening : \epsilon = \frac where ''Rp'' is the mean polar radius and ''Re'' is the mean equatorial radius. For Earth Earth is the third planet from the Sun and the only astronomical object kn ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Astrophysics
Astrophysics is a science that employs the methods and principles of physics and chemistry in the study of astronomical objects and phenomena. As one of the founders of the discipline said, Astrophysics "seeks to ascertain the nature of the heavenly bodies, rather than their positions or motions in space–''what'' they are, rather than ''where'' they are." Among the subjects studied are the Sun, other stars, galaxies, extrasolar planets, the interstellar medium and the cosmic microwave background. Emissions from these objects are examined across all parts of the electromagnetic spectrum, and the properties examined include luminosity, density, temperature, and chemical composition. Because astrophysics is a very broad subject, ''astrophysicists'' apply concepts and methods from many disciplines of physics, including classical mechanics, electromagnetism, statistical mechanics, thermodynamics, quantum mechanics, relativity, nuclear and particle physics, and atomic and m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rodolphe Radau
Jean Charles Rodolphe Radau (22 January 1835 – 21 December 1911) was an astronomer and mathematician who worked in Paris at the ''Revue des deux Mondes'' for most of his life. He was the co-founder of the Bulletin Astronomique. Radau was born in Angerburg, Province of Prussia (now Węgorzewo in Poland), and after studying in Königsberg and working on the Three-body problem, he moved to Paris to collaborate with other scientists. In 1871 he was given the Ph.D. in honor of his work in mathematics. Radau won the Prix Damoiseau of the French Academy of Sciences in 1892 working on planetary perturbations in the motion of the Moon. This work was of such a high quality that he was elected to the Academy in 1897. A crater on Mars is named in Radau's honor. His publications include the ''Wonders of Acoustics'' (1867 Events January–March * January 1 – The Covington–Cincinnati Suspension Bridge opens between Cincinnati, Ohio, and Covington, Kentucky, in the U ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Charles Galton Darwin
Sir Charles Galton Darwin (19 December 1887 – 31 December 1962) was an English physicist who served as director of the National Physical Laboratory (NPL) during the Second World War. He was a son of the mathematician George Howard Darwin and a grandson of Charles Darwin. Early life Darwin was born at Newnham Grange in Cambridge, England into a scientific dynasty. He was a son of mathematician Sir George Howard Darwin and a grandson of Charles Darwin. His mother was Lady Darwin, Maud du Puy of Philadelphia, Pennsylvania. Darwin's elder sister was the artist Gwen Raverat, and his younger sister Margaret married Geoffrey Keynes, the brother of the economist John Maynard Keynes. His younger brother William Robert Darwin was a London stockbroker. Darwin was educated at Marlborough College (1901–1906) and then studied mathematics at Trinity College, Cambridge, graduating BA in 1910, later promoted to MA by seniority. Career He secured a post-graduate position at the Victoria ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Moment Of Inertia Factor
In planetary sciences, the moment of inertia factor or normalized polar moment of inertia is a dimensionless quantity that characterizes the radial distribution of mass inside a planet or satellite. Since a moment of inertia must have dimensions of mass times length squared, the moment of inertia factor is the coefficient that multiplies these. Definition For a planetary body with principal moments of inertia A [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Moment Of Inertia
The moment of inertia, otherwise known as the mass moment of inertia, angular mass, second moment of mass, or most accurately, rotational inertia, of a rigid body is a quantity that determines the torque needed for a desired angular acceleration about a rotational axis, akin to how mass determines the force needed for a desired acceleration. It depends on the body's mass distribution and the axis chosen, with larger moments requiring more torque to change the body's rate of rotation. It is an extensive (additive) property: for a point mass the moment of inertia is simply the mass times the square of the perpendicular distance to the axis of rotation. The moment of inertia of a rigid composite system is the sum of the moments of inertia of its component subsystems (all taken about the same axis). Its simplest definition is the second moment of mass with respect to distance from an axis. For bodies constrained to rotate in a plane, only their moment of inertia about an axis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ellipsoid Of Revolution
A spheroid, also known as an ellipsoid of revolution or rotational ellipsoid, is a quadric surface obtained by rotating an ellipse about one of its principal axes; in other words, an ellipsoid with two equal semi-diameters. A spheroid has circular symmetry. If the ellipse is rotated about its major axis, the result is a ''prolate spheroid'', elongated like a rugby ball. The American football is similar but has a pointier end than a spheroid could. If the ellipse is rotated about its minor axis, the result is an ''oblate spheroid'', flattened like a lentil or a plain M&M. If the generating ellipse is a circle, the result is a sphere. Due to the combined effects of gravity and rotation, the figure of the Earth (and of all planets) is not quite a sphere, but instead is slightly flattened in the direction of its axis of rotation. For that reason, in cartography and geodesy the Earth is often approximated by an oblate spheroid, known as the reference ellipsoid, instead o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Astronomy And Astrophysics
''Astronomy & Astrophysics'' is a monthly peer-reviewed scientific journal covering theoretical, observational, and instrumental astronomy and astrophysics. The journal is run by a Board of Directors representing 27 sponsoring countries plus a representative of the European Southern Observatory. The journal is published by EDP Sciences and the editor-in-chief is . History Origins ''Astronomy and Astrophysics'' (A&A) was created as an answer to the publishing scenario found in Europe in the 1960s. At that time, multiple journals were being published in several countries around the continent. These journals usually had a limited number of subscribers, and published articles in languages other than English, resulting in a small number of citations compared to American and British journals. Starting in 1963, conversations between astronomers from European countries assessed the need for a common astronomical journal. On 8 April 1968, leading astronomers from Belgium, Denmark, Fran ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jean Le Rond D'Alembert
Jean-Baptiste le Rond d'Alembert (; ; 16 November 1717 – 29 October 1783) was a French mathematician, mechanician, physicist, philosopher, and music theorist. Until 1759 he was, together with Denis Diderot, a co-editor of the ''Encyclopédie''. D'Alembert's formula for obtaining solutions to the wave equation is named after him. The wave equation is sometimes referred to as d'Alembert's equation, and the fundamental theorem of algebra is named after d'Alembert in French. Early years Born in Paris, d'Alembert was the natural son of the writer Claudine Guérin de Tencin and the chevalier Louis-Camus Destouches, an artillery officer. Destouches was abroad at the time of d'Alembert's birth. Days after birth his mother left him on the steps of the church. According to custom, he was named after the patron saint of the church. D'Alembert was placed in an orphanage for foundling children, but his father found him and placed him with the wife of a glazier, Madame Rousseau, with who ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geodynamical Constant
Geodynamics is a subfield of geophysics dealing with dynamics of the Earth. It applies physics, chemistry and mathematics to the understanding of how mantle convection leads to plate tectonics and geologic phenomena such as seafloor spreading, mountain building, volcanoes, earthquakes, faulting. It also attempts to probe the internal activity by measuring magnetic fields, gravity, and seismic waves, as well as the mineralogy of rocks and their isotopic composition. Methods of geodynamics are also applied to exploration of other planets. Overview Geodynamics is generally concerned with processes that move materials throughout the Earth. In the Earth's interior, movement happens when rocks melt or deform and flow in response to a stress field.Turcotte, D. L. and G. Schubert (2014). "Geodynamics." This deformation may be brittle, elastic, or plastic, depending on the magnitude of the stress and the material's physical properties, especially the stress relaxation time scale. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Flattening
Flattening is a measure of the compression of a circle or sphere along a diameter to form an ellipse or an ellipsoid of revolution (spheroid) respectively. Other terms used are ellipticity, or oblateness. The usual notation for flattening is and its definition in terms of the semi-axes of the resulting ellipse or ellipsoid is :: \mathrm = f =\frac . The ''compression factor'' is \frac\,\! in each case; for the ellipse, this is also its aspect ratio. Definitions There are three variants of flattening; when it is necessary to avoid confusion, the main flattening is called the first flattening.Torge, W. (2001). ''Geodesy'' (3rd edition). de Gruyter. and online web textsOsborne, P. (2008). The Mercator Projections'' Chapter 5.Rapp, Richard H. (1991). ''Geometric Geodesy, Part I''. Dept. of Geodetic Science and Surveying, Ohio State Univ., Columbus, Ohio/ref> In the following, is the larger dimension (e.g. semimajor axis), whereas is the smaller (semiminor axis). All flatt ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Earth
Earth is the third planet from the Sun and the only astronomical object known to harbor life. While large volumes of water can be found throughout the Solar System, only Earth sustains liquid surface water. About 71% of Earth's surface is made up of the ocean, dwarfing Earth's polar ice, lakes, and rivers. The remaining 29% of Earth's surface is land, consisting of continents and islands. Earth's surface layer is formed of several slowly moving tectonic plates, which interact to produce mountain ranges, volcanoes, and earthquakes. Earth's liquid outer core generates the magnetic field that shapes the magnetosphere of the Earth, deflecting destructive solar winds. The atmosphere of the Earth consists mostly of nitrogen and oxygen. Greenhouse gases in the atmosphere like carbon dioxide (CO2) trap a part of the energy from the Sun close to the surface. Water vapor is widely present in the atmosphere and forms clouds that cover most of the planet. More solar e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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