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Geopotential Spherical Harmonic Model
In geophysics and physical geodesy, a geopotential model is the theoretical analysis of measuring and calculating the effects of Earth's gravitational field (the geopotential). The Earth is not exactly spherical, mainly because of its rotation around the polar axis that makes its shape slightly oblate. However, a spherical harmonics series expansion captures the actual field with increasing fidelity. If Earth's shape were perfectly known together with the exact mass density ρ = ρ(''x'', ''y'', ''z''), it could be integrated numerically (when combined with a reciprocal distance kernel) to find an accurate model for Earth's gravitational field. However, the situation is in fact the opposite: by observing the orbits of spacecraft and the Moon, Earth's gravitational field can be determined quite accurately. The best estimate of Earth's mass is obtained by dividing the product ''GM'' as determined from the analysis of spacecraft orbit with a value for the gravitational constant ''G ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geophysics
Geophysics () is a subject of natural science concerned with the physical processes and Physical property, properties of Earth and its surrounding space environment, and the use of quantitative methods for their analysis. Geophysicists conduct investigations across a wide range of scientific disciplines. The term ''geophysics'' classically refers to solid earth applications: Earth's figure of the Earth, shape; its gravitational, Earth's magnetic field, magnetic fields, and electromagnetic fields; its structure of the Earth, internal structure and Earth#Chemical composition, composition; its geodynamics, dynamics and their surface expression in plate tectonics, the generation of magmas, volcanism and rock formation. However, modern geophysics organizations and pure scientists use a broader definition that includes the water cycle including snow and ice; geophysical fluid dynamics, fluid dynamics of the oceans and the atmosphere; atmospheric electricity, electricity and magnetism in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reference Ellipsoid
An Earth ellipsoid or Earth spheroid is a mathematical figure approximating the Earth's form, used as a reference frame for computations in geodesy, astronomy, and the geosciences. Various different ellipsoids have been used as approximations. It is a spheroid (an ellipsoid of revolution) whose minor axis (shorter diameter), which connects the geographical North Pole and South Pole, is approximately aligned with the Earth's axis of rotation. The ellipsoid is defined by the ''equatorial axis'' () and the ''polar axis'' (); their radial difference is slightly more than 21 km, or 0.335% of (which is not quite 6,400 km). Many methods exist for determination of the axes of an Earth ellipsoid, ranging from meridian arcs up to modern satellite geodesy or the analysis and interconnection of continental geodetic networks. Amongst the different set of data used in national surveys are several of special importance: the Bessel ellipsoid of 1841, the international Hayfo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geoid
The geoid ( ) is the shape that the ocean surface would take under the influence of the gravity of Earth, including gravitational attraction and Earth's rotation, if other influences such as winds and tides were absent. This surface is extended through the continents (such as might be approximated with very narrow hypothetical canals). According to Carl Friedrich Gauss, who first described it, it is the "mathematical figure of the Earth", a smooth but irregular surface whose shape results from the uneven distribution of mass within and on the surface of Earth. It can be known only through extensive gravitational measurements and calculations. Despite being an important concept for almost 200 years in the history of geodesy and geophysics, it has been defined to high precision only since advances in satellite geodesy in the late 20th century. The geoid is often expressed as a geoid undulation or geoidal height above a given reference ellipsoid, which is a slightly flattene ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
EGM96
The Earth Gravitational Models (EGM) are a series of geopotential models of the Earth published by the National Geospatial-Intelligence Agency (NGA). They are used as the geoid reference in the World Geodetic System. The NGA provides the models in two formats: as the series of numerical coefficients to the spherical harmonics which define the model, or a dataset giving the geoid height at each coordinate at a given resolution. Three model versions have been published: EGM84 with n=m=180, EGM96 with n=m=360, and EGM2008 with n=m=2160. n and m are the degree and orders of harmonic coefficients; the higher they are, the more parameters the models have, and the more precise they are. EGM2008 also contains expansions to n=2190. Developmental versions of the EGM are referred to as Preliminary Gravitational Models (PGMs). Each version of EGM has its own EPSG Geodetic Parameter Dataset code as a vertical datum. History EGM84 The first EGM, EGM84, was defined as a part of WGS8 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Goddard Space Flight Center
The Goddard Space Flight Center (GSFC) is a major NASA space research laboratory located approximately northeast of Washington, D.C., in Greenbelt, Maryland, United States. Established on May 1, 1959, as NASA's first space flight center, GSFC employs about 10,000 civil servants and contractors. Named for American rocket propulsion pioneer Robert H. Goddard, it is one of ten major NASA field centers. GSFC is partially within the former Goddard, Maryland, Goddard census-designated place; it has a Greenbelt, Maryland, Greenbelt mailing address.CENSUS 2000 BLOCK MAP: GODDARD CDP (PDF). U.S. Census Bureau. Retrieved September 1, 2018. 1990 Census map of Prince George's County [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
European Space Agency
The European Space Agency (ESA) is a 23-member International organization, international organization devoted to space exploration. With its headquarters in Paris and a staff of around 2,547 people globally as of 2023, ESA was founded in 1975 in the context of European integration. Its 2025 annual budget was €7.7 billion. The ESA Human and Robotic Exploration programme includes human spaceflight (mainly through participation in the International Space Station programme); as well as the launch and operation of missions to Mars and Moon. Further activities include science missions to Jupiter, Mercury, the Sun, Earth observation, Asteroid impact avoidance and Telecommunications missions, designing launch vehicles; and maintaining Europe's Spaceport, the Guiana Space Centre at Kourou (French Guiana). Further programmes include space safety, satellite navigation, applications and commercialisation. The main European launch vehicle Ariane 6 is operated through Arianespace ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
European Space Research Organisation
The European Space Research Organisation (ESRO) was an international organisation founded by 10 European nations with the intention of jointly pursuing scientific research in space. It was founded in 1964. As an organisation ESRO was based on a previously existing international scientific institution, CERN. The ESRO convention, the organisations founding document outlines it as an entity exclusively devoted to scientific pursuits. This was the case for most of its lifetime but in the final years before the formation of ESA, the European Space Agency, ESRO began a programme in the field of telecommunications. Consequently, ESA is not a mainly pure science focused entity but concentrates on telecommunications, earth observation and other application motivated activities. ESRO was merged with European Launcher Development Organisation, ELDO in 1975 to form the European Space Agency. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
NASA
The National Aeronautics and Space Administration (NASA ) is an independent agencies of the United States government, independent agency of the federal government of the United States, US federal government responsible for the United States's civil list of government space agencies, space program, aeronautics research and outer space, space research. National Aeronautics and Space Act, Established in 1958, it succeeded the National Advisory Committee for Aeronautics (NACA) to give the American space development effort a distinct civilian orientation, emphasizing peaceful applications in space science. It has since led most of America's space exploration programs, including Project Mercury, Project Gemini, the 1968–1972 Apollo program missions, the Skylab space station, and the Space Shuttle. Currently, NASA supports the International Space Station (ISS) along with the Commercial Crew Program and oversees the development of the Orion (spacecraft), Orion spacecraft and the Sp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Recursion (mathematics)
In mathematics, a recurrence relation is an equation according to which the nth term of a sequence of numbers is equal to some combination of the previous terms. Often, only k previous terms of the sequence appear in the equation, for a parameter k that is independent of n; this number k is called the ''order'' of the relation. If the values of the first k numbers in the sequence have been given, the rest of the sequence can be calculated by repeatedly applying the equation. In ''linear recurrences'', the th term is equated to a linear function of the k previous terms. A famous example is the recurrence for the Fibonacci numbers, F_n=F_+F_ where the order k is two and the linear function merely adds the two previous terms. This example is a linear recurrence with constant coefficients, because the coefficients of the linear function (1 and 1) are constants that do not depend on n. For these recurrences, one can express the general term of the sequence as a closed-form expression o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gradient
In vector calculus, the gradient of a scalar-valued differentiable function f of several variables is the vector field (or vector-valued function) \nabla f whose value at a point p gives the direction and the rate of fastest increase. The gradient transforms like a vector under change of basis of the space of variables of f. If the gradient of a function is non-zero at a point p, the direction of the gradient is the direction in which the function increases most quickly from p, 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 minimize a function by gradient descent. In coordinate-free terms, the gradient of a function f(\mathbf) may be defined by: df=\nabla f \cdot d\mathbf where df is the total infinitesimal change in f for a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equations Of Motion
In physics, equations of motion are equations that describe the behavior of a physical system in terms of its motion as a function of time. More specifically, the equations of motion describe the behavior of a physical system as a set of mathematical functions in terms of dynamic variables. These variables are usually spatial coordinates and time, but may include momentum components. The most general choice are generalized coordinates which can be any convenient variables characteristic of the physical system. The functions are defined in a Euclidean space in classical mechanics, but are replaced by curved spaces in relativity. If the dynamics of a system is known, the equations are the solutions for the differential equations describing the motion of the dynamics. Types There are two main descriptions of motion: dynamics and kinematics. Dynamics is general, since the momenta, forces and energy of the particles are taken into account. In this instance, sometimes the term ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Numerical Methods For Ordinary Differential Equations
Numerical methods for ordinary differential equations are methods used to find Numerical analysis, numerical approximations to the solutions of ordinary differential equations (ODEs). Their use is also known as "numerical integration", although this term can also refer to the computation of integrals. Many differential equations cannot be solved exactly. For practical purposes, however – such as in engineering – a numeric approximation to the solution is often sufficient. The algorithms studied here can be used to compute such an approximation. An alternative method is to use techniques from calculus to obtain a series expansion of the solution. Ordinary differential equations occur in many scientific disciplines, including physics, chemistry, biology, and economics. In addition, some methods in numerical partial differential equations convert the partial differential equation into an ordinary differential equation, which must then be solved. The problem A firs ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
