Gravity, Global Models
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Gravity, Global Models Nikolaos K. Pavlis Geodesy and Geophysics Basic and Applied Research, National Geospatial-Intelligence Agency (NGA), Reston, VA, USA
Synonyms Geopotential models; Global gravitational models; Potential coefficient models
Definition A Global Gravitational Model (GGM) is a mathematical approximation to the external gravitational potential of an attracting body. Gravitation is the term used to describe the potential generated by the masses of an attracting body like the Earth. Gravity is the term used for the potential of gravitation plus the centrifugal potential due to the rotation of the attracting body.
variance-covariance matrix), and a collection of mathematical expressions and algorithms that allow a user to perform: 1. Synthesis, that is, computation of the numerical values of quantities related to the gravitational potential (functionals of the gravitational field), given the position of the evaluation point. 2. Error Propagation, that is, computation of the expected errors of the computed functionals, as implied by the propagation of the errors of the parameters defining the GGM. A GGM must be able to support such computations at arbitrary points, located on or above the Earth’s surface, in a fashion that is both rigorous and efficient. In addition, a GGM should fulfill certain conditions stemming from the underlying physics. Namely, it should represent a scalar function of position that is harmonic outside the attracting masses and vanishes at infinity as the reciprocal of the distance between attracted point and attracting mass element. Moreover, the GGM should permit the computation of any functional of the field in a way that guarantees self-consistency. This means that the model should preserve the relationships (differential or integral) between the various functionals. A GGM has numerous uses, both operational and scientific (see also [Tscherning 1983]), including:
Global Gravitational Models Introduction A GGM is a mathematical approximation to the external gravitational potential of an attracting body. We will focus here on the case where the attracting body is the Earth, although many of the concepts that we discuss apply equally well to other planets and celestial bodies. In its most complete and general form, a GGM consists of a set of numerical values for certain parameters, the statistics of the errors associated with these values (as described, e.g., by their error
1. Orbit determination applications necessary for space surveillance (the detection, tracking, and orbit prediction of Earth-orbiting objects). 2. Inertial navigation applications for trajectory determination of airplanes and missiles. 3. Geoid determination. The geoid is one of the infinitely many level (or equipotential) surfaces of the gravity field of the Earth, that is, the gravity potential is constant at every point on the geoid. The geoid is the specific equipotential surface that would coincide exactly with the mean ocean surface of the Earth, if the oceans were in
© US Government 2020 H. K. Gupta (ed.), E
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