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Love Number
The Love numbers (''h'', ''k'', and ''l'') are dimensionless parameters that measure the rigidity of a planetary body and the susceptibility of its shape to change in response to a tidal potential. In 1909, Augustus Edward Hough Love introduced the values ''h'' and ''k'' which characterize the overall elastic response of the Earth to the tides ― ''Earth tides'' or ''body tides''. Later, in 1912, Toshi Shida added a third Love number, ''l'', which was needed to obtain a complete overall description of the solid Earth's response to the tides.TOSHI SHIDA, On the Body Tides of the Earth, A Proposal for the International Geodetic Association, Proceedings of the Tokyo Mathematico-Physical Society. 2nd Series, 1911-1912, Volume 6, Issue 16, Pages 242-258, ISSN 2185-2693, . Definitions The Love number ''h'' is defined as the ratio of the body tide to the height of the static equilibrium tide;"Tidal Deformation of the Solid Earth: A Finite Difference Discretization", S.K.Poulsen; Nie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dimensionless Quantity
A dimensionless quantity (also known as a bare quantity, pure quantity, or scalar quantity as well as quantity of dimension one) is a quantity to which no physical dimension is assigned, with a corresponding SI unit of measurement of one (or 1), ISBN 978-92-822-2272-0. which is not explicitly shown. Dimensionless quantities are widely used in many fields, such as mathematics, physics, chemistry, engineering, and economics. Dimensionless quantities are distinct from quantities that have associated dimensions, such as time (measured in seconds). Dimensionless units are dimensionless values that serve as units of measurement for expressing other quantities, such as radians (rad) or steradians (sr) for plane angles and solid angles, respectively. For example, optical extent is defined as having units of metres multiplied by steradians. History Quantities having dimension one, ''dimensionless quantities'', regularly occur in sciences, and are formally treated within the field of d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stiffness
Stiffness is the extent to which an object resists deformation in response to an applied force. The complementary concept is flexibility or pliability: the more flexible an object is, the less stiff it is. Calculations The stiffness, k, of a body is a measure of the resistance offered by an elastic body to deformation. For an elastic body with a single degree of freedom (DOF) (for example, stretching or compression of a rod), the stiffness is defined as k = \frac where, * F is the force on the body * \delta is the displacement produced by the force along the same degree of freedom (for instance, the change in length of a stretched spring) In the International System of Units, stiffness is typically measured in newtons per meter (N/m). In Imperial units, stiffness is typically measured in pounds (lbs) per inch. Generally speaking, deflections (or motions) of an infinitesimal element (which is viewed as a point) in an elastic body can occur along multiple DOF (maximum of s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Planet
A planet is a large, rounded astronomical body that is neither a star nor its remnant. The best available theory of planet formation is the nebular hypothesis, which posits that an interstellar cloud collapses out of a nebula to create a young protostar orbited by a protoplanetary disk. Planets grow in this disk by the gradual accumulation of material driven by gravity, a process called accretion. The Solar System has at least eight planets: the terrestrial planets Mercury, Venus, Earth and Mars, and the giant planets Jupiter, Saturn, Uranus and Neptune. These planets each rotate around an axis tilted with respect to its orbital pole. All of them possess an atmosphere, although that of Mercury is tenuous, and some share such features as ice caps, seasons, volcanism, hurricanes, tectonics, and even hydrology. Apart from Venus and Mars, the Solar System planets generate magnetic fields, and all except Venus and Mercury have natural satellites. The giant planets bear plan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tidal Force
The tidal force is a gravitational effect that stretches a body along the line towards the center of mass of another body due to a gradient (difference in strength) in gravitational field from the other body; it is responsible for diverse phenomena, including tides, tidal locking, breaking apart of celestial bodies and formation of ring systems within the Roche limit, and in extreme cases, spaghettification of objects. It arises because the gravitational field exerted on one body by another is not constant across its parts: the nearest side is attracted more strongly than the farthest side. It is this difference that causes a body to get stretched. Thus, the tidal force is also known as the differential force, as well as a secondary effect of the gravitational field. In celestial mechanics, the expression ''tidal force'' can refer to a situation in which a body or material (for example, tidal water) is mainly under the gravitational influence of a second body (for example, the Eart ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Augustus Edward Hough Love
Augustus Edward Hough Love FRS (17 April 1863, Weston-super-Mare – 5 June 1940, Oxford), often known as A. E. H. Love, was a mathematician famous for his work on the mathematical theory of elasticity. He also worked on wave propagation and his work on the structure of the Earth in ''Some Problems of Geodynamics'' won for him the Adams prize in 1911 when he developed a mathematical model of surface waves known as Love waves. Love also contributed to the theory of tidal locking and introduced the parameters known as Love numbers, used in problems related to Earth tides, the tidal deformation of the solid Earth due to the gravitational attraction of the Moon and Sun. He was educated at Wolverhampton Grammar School and in 1881 won a scholarship to St John's College, Cambridge, where he was at first undecided whether to study classics or mathematics. His successful progress (he was placed Second Wrangler) vindicated his choice of mathematics, and in 1886 he was elected Fellow of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elasticity (physics)
In physics and materials science, elasticity is the ability of a body to resist a distorting influence and to return to its original size and shape when that influence or force is removed. Solid objects will deform when adequate loads are applied to them; if the material is elastic, the object will return to its initial shape and size after removal. This is in contrast to ''plasticity'', in which the object fails to do so and instead remains in its deformed state. The physical reasons for elastic behavior can be quite different for different materials. In metals, the atomic lattice changes size and shape when forces are applied (energy is added to the system). When forces are removed, the lattice goes back to the original lower energy state. For rubbers and other polymers, elasticity is caused by the stretching of polymer chains when forces are applied. Hooke's law states that the force required to deform elastic objects should be directly proportional to the distance of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Earth Tide
Earth tide (also known as solid Earth tide, crustal tide, body tide, bodily tide or land tide) is the displacement of the solid earth's surface caused by the gravity of the Moon and Sun. Its main component has meter-level amplitude at periods of about 12 hours and longer. The largest body tide constituents are semi- diurnal, but there are also significant diurnal, semi-annual, and fortnightly contributions. Though the gravitational force causing earth tides and ocean tides is the same, the responses are quite different. Tide raising force The larger of the periodic gravitational forces is from the Moon but that of the Sun is also important. The images here show lunar tidal force when the Moon appears directly over 30° N (or 30° S). This pattern remains fixed with the red area directed toward (or directly away from) the Moon. Red indicates upward pull, blue downward. If, for example the Moon is directly over 90° W (or 90° E), the red areas are centred on the western northern ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tide
Tides are the rise and fall of sea levels caused by the combined effects of the gravity, gravitational forces exerted by the Moon (and to a much lesser extent, the Sun) and are also caused by the Earth and Moon orbiting one another. Tide tables can be used for any given locale to find the predicted times and amplitude (or "tidal range"). The predictions are influenced by many factors including the alignment of the Sun and Moon, the #Phase and amplitude, phase and amplitude of the tide (pattern of tides in the deep ocean), the amphidromic systems of the oceans, and the shape of the coastline and near-shore bathymetry (see ''#Timing, Timing''). They are however only predictions, the actual time and height of the tide is affected by wind and atmospheric pressure. Many shorelines experience semi-diurnal tides—two nearly equal high and low tides each day. Other locations have a diurnal cycle, diurnal tide—one high and low tide each day. A "mixed tide"—two uneven magnitude ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equilibrium Tide
Tides are the rise and fall of sea levels caused by the combined effects of the gravitational forces exerted by the Moon (and to a much lesser extent, the Sun) and are also caused by the Earth and Moon orbiting one another. Tide tables can be used for any given locale to find the predicted times and amplitude (or " tidal range"). The predictions are influenced by many factors including the alignment of the Sun and Moon, the phase and amplitude of the tide (pattern of tides in the deep ocean), the amphidromic systems of the oceans, and the shape of the coastline and near-shore bathymetry (see '' Timing''). They are however only predictions, the actual time and height of the tide is affected by wind and atmospheric pressure. Many shorelines experience semi-diurnal tides—two nearly equal high and low tides each day. Other locations have a diurnal tide—one high and low tide each day. A "mixed tide"—two uneven magnitude tides a day—is a third regular category. Tides v ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gradient
In vector calculus, the gradient of a scalar-valued differentiable function of several variables is the vector field (or vector-valued function) \nabla f whose value at a point p is the "direction and rate of fastest increase". If the gradient of a function is non-zero at a point , the direction of the gradient is the direction in which the function increases most quickly from , and the magnitude of the gradient is the rate of increase in that direction, the greatest absolute directional derivative. Further, a point where the gradient is the zero vector is known as a stationary point. The gradient thus plays a fundamental role in optimization theory, where it is used to maximize a function by gradient ascent. In coordinate-free terms, the gradient of a function f(\bf) may be defined by: :df=\nabla f \cdot d\bf where ''df'' is the total infinitesimal change in ''f'' for an infinitesimal displacement d\bf, and is seen to be maximal when d\bf is in the direction of the gradi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spherical Harmonic
In mathematics and physical science, spherical harmonics are special functions defined on the surface of a sphere. They are often employed in solving partial differential equations in many scientific fields. Since the spherical harmonics form a complete set of orthogonal functions and thus an orthonormal basis, each function defined on the surface of a sphere can be written as a sum of these spherical harmonics. This is similar to periodic functions defined on a circle that can be expressed as a sum of circular functions (sines and cosines) via Fourier series. Like the sines and cosines in Fourier series, the spherical harmonics may be organized by (spatial) angular frequency, as seen in the rows of functions in the illustration on the right. Further, spherical harmonics are basis functions for irreducible representations of SO(3), the group of rotations in three dimensions, and thus play a central role in the group theoretic discussion of SO(3). Spherical harmonics originat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tides
Tides are the rise and fall of sea levels caused by the combined effects of the gravitational forces exerted by the Moon (and to a much lesser extent, the Sun) and are also caused by the Earth and Moon orbiting one another. Tide tables can be used for any given locale to find the predicted times and amplitude (or "tidal range"). The predictions are influenced by many factors including the alignment of the Sun and Moon, the phase and amplitude of the tide (pattern of tides in the deep ocean), the amphidromic systems of the oceans, and the shape of the coastline and near-shore bathymetry (see '' Timing''). They are however only predictions, the actual time and height of the tide is affected by wind and atmospheric pressure. Many shorelines experience semi-diurnal tides—two nearly equal high and low tides each day. Other locations have a diurnal tide—one high and low tide each day. A "mixed tide"—two uneven magnitude tides a day—is a third regular category. Tides va ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
