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The density at the center is the same as in the PREM, but the surface density is chosen so that the mass of the sphere equals the mass of the real Earth. See also: Shell theorem An approximate value for gravity at a distance r from the center of the Earth can be obtained by assuming that the Earth's density is spherically symmetric.
The surface of a sphere can be completely described by two dimensions, since no matter how rough the surface may appear to be, it is still only a surface, which is the two-dimensional outside border of a volume. Even the surface of the Earth, which is fractal in complexity, is still only a two-dimensional boundary along the outside of a volume. [3]
Dividing the result by length of curve or chord has also been tried. In 2002 several Italian scientists [4] proposed one more method. At first, the curve is divided into several (N) parts with constant sign of curvature (using hysteresis to decrease sensitivity to noise). Then the arc-chord ratio for each part is found and the tortuosity is ...
Vertical deflections are principally used in four matters: For precise calculation of survey networks.The geodetic theodolites and levelling instruments are oriented with respect to the true vertical, but its deflection exceeds the geodetic measuring accuracy by a factor of 5 to 50.
Jacobi constant, a Zero Velocity Surface and Curve (also Hill's curve) [1] A zero-velocity surface is a concept that relates to the N-body problem of gravity. It represents a surface a body of given energy cannot cross, since it would have zero velocity on the surface. It was first introduced by George William Hill. [2]
So when water molecules (water vapor) are added to a given volume of air, the dry air molecules must decrease by the same number, to keep the pressure from increasing or temperature from decreasing. Hence the mass per unit volume of the gas (its density) decreases. The density of humid air may be calculated by treating it as a mixture of ideal ...
The curve can also be shown in non-dimensional or standardized form by scaling elevation and area by the maximum values. The non-dimensional hypsometric curve provides a hydrologist or a geomorphologist with a way to assess the similarity of watersheds — and is one of several characteristics used for doing so. The hypsometric integral is a ...
Lateral earth stress theory is used to estimate the amount of stress soil can exert perpendicular to gravity. This is the stress exerted on retaining walls. A lateral earth stress coefficient, K, is defined as the ratio of lateral (horizontal) effective stress to vertical effective stress for cohesionless soils (K=σ' h /σ' v). There are three ...