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The geoid is often expressed as a geoid undulation or geoidal height above a given reference ellipsoid, which is a slightly flattened sphere whose equatorial bulge is caused by the planet's rotation. Generally the geoidal height rises where the Earth's material is locally more dense and exerts greater gravitational force than the surrounding areas.
Unsolved problems relating to the structure and function of non-human organs, processes and biomolecules include: Korarchaeota (archaea). The metabolic processes of this phylum of archaea are so far unclear. Glycogen body. The function of this structure in the spinal cord of birds is not known. Arthropod head problem. A long-standing zoological ...
As can be seen from Fig. 1, these problems involve solving the triangle NAB given one angle, α 1 for the direct problem and λ 12 = λ 2 − λ 1 for the inverse problem, and its two adjacent sides. For a sphere the solutions to these problems are simple exercises in spherical trigonometry , whose solution is given by formulas for solving a ...
The geometrical separation between it and the reference ellipsoid is called the geoidal undulation, or more usually the geoid-ellipsoid separation, N. It varies globally between ±110 m. A reference ellipsoid, customarily chosen to be the same size (volume) as the geoid, is described by its semi-major axis (equatorial radius) a and flattening f.
The solutions to both problems in plane geometry reduce to simple trigonometry and are valid for small areas on Earth's surface; on a sphere, solutions become significantly more complex as, for example, in the inverse problem, the azimuths differ going between the two end points along the arc of the connecting great circle.
It is then possible to compute the geoid height by subtracting the measured altitude from the ellipsoidal height. This allows direct measurement of the geoid, since the ocean surface closely follows the geoid. [3]: 64 The difference between the ocean surface and the actual geoid gives ocean surface topography.
Dynamic topography is the reason why the geoid is high over regions of low-density mantle. If the mantle were static, these low-density regions would be geoid lows. However, these low-density regions move upwards in a mobile, convecting mantle, elevating density interfaces such as the core-mantle boundary , 440 and 670 kilometer discontinuities ...
For example, at a radius of 6600 km (about 200 km above Earth's surface) J 3 /(J 2 r) is about 0.002; i.e., the correction to the "J 2 force" from the "J 3 term" is in the order of 2 permille. The negative value of J 3 implies that for a point mass in Earth's equatorial plane the gravitational force is tilted slightly towards the south due to ...