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For an ovoid and a hyperplane , which contains at least two points of , the subset is an ovoid (or an oval, if d = 3) within the hyperplane . For finite projective spaces of dimension d ≥ 3 (i.e., the point set is finite, the space is pappian [ 1 ] ), the following result is true:
The ellipsoid is a mathematically defined regular surface with specific dimensions. The geoid, on the other hand, coincides with that surface to which the oceans would conform over the entire Earth if free to adjust to the combined effect of the Earth's mass attraction (gravitation) and the centrifugal force of the Earth's rotation.
The undulation of the geoid N is closely related to the disturbing potential T according to Bruns' formula (named after Heinrich Bruns): N = T / γ , {\displaystyle N=T/\gamma \,,} where γ {\displaystyle \gamma } is the force of normal gravity , computed from the normal field potential U {\displaystyle U} .
Geophysics emerged as a separate discipline only in the 19th century, from the intersection of physical geography, geology, astronomy, meteorology, and physics. [ 46 ] [ 47 ] The first known use of the word geophysics was in German ("Geophysik") by Julius Fröbel in 1834. [ 48 ]
the mass–energy equivalence formula which gives the energy in terms of the momentum and the rest mass of a particle. The equation for the mass shell is also often written in terms of the four-momentum ; in Einstein notation with metric signature (+,−,−,−) and units where the speed of light c = 1 {\displaystyle c=1} , as p μ p μ ≡ p ...
Classical mechanics is the branch of physics used to describe the motion of macroscopic objects. [1] It is the most familiar of the theories of physics. The concepts it covers, such as mass, acceleration, and force, are commonly used and known. [2] The subject is based upon a three-dimensional Euclidean space with fixed axes, called a frame of ...
Many equations in relativistic physics appear simpler when expressed in geometric units, because all occurrences of G and of c drop out. For example, the Schwarzschild radius of a nonrotating uncharged black hole with mass m becomes r = 2m. For this reason, many books and papers on relativistic physics use geometric units.
A surface mass on a surface given by the equation f (x, y, z) = 0 may be represented by a density distribution g(x, y, z) δ(f (x, y, z)), where / | | is the mass per unit area. The mathematical modelling can be done by potential theory , by numerical methods (e.g. a great number of mass points ), or by theoretical equilibrium figures.