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A mass distribution can be modeled as a measure. This allows point masses, line masses, surface masses, as well as masses given by a volume density function. Alternatively the latter can be generalized to a distribution. For example, a point mass is represented by a delta function defined in 3-dimensional space.
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]
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 ...
Stand density index (SDI; also known as Reineke's Stand Density Index [1] after its founder) is a measure of the stocking of a stand of trees based on the number of trees per unit area and diameter at breast height (DBH) of the tree of average basal area, also known as the quadratic mean diameter.
D 50: Mass-median-diameter (MMD). The log-normal distribution mass median diameter. The MMD is considered to be the average particle diameter by mass. σ g: Geometric standard deviation. This value is determined mathematically by the equation: σ g = D 84.13 /D 50 = D 50 /D 15.87. The value of σ g determines the slope of the least-squares ...
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.
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]
The X/Y plane coincides with Earth's equatorial plane, with the +X axis pointing toward the vernal equinox and the Y axis completing a right-handed set. The ECI reference frame is not truly inertial because of the slow, 26,000 year precession of Earth's axis , so the reference frames defined by Earth's orientation at a standard astronomical ...