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As an example, the distance squared between the points (0,0,0,0) and (1,1,1,0) is 3 in both the Euclidean and Minkowskian 4-spaces, while the distance squared between (0,0,0,0) and (1,1,1,1) is 4 in Euclidean space and 2 in Minkowski space; increasing b 4 decreases the metric distance. This leads to many of the well-known apparent "paradoxes ...
Visualization of a celestial sphere. In astronomy and navigation, the celestial sphere is an abstract sphere that has an arbitrarily large radius and is concentric to Earth.All objects in the sky can be conceived as being projected upon the inner surface of the celestial sphere, which may be centered on Earth or the observer.
Curved into eyelike spheres, the material reflects X-rays and is packed into telescopes.These crustaceans have inspired other inventions as well, such as microchips and the Lobster Eye X-ray ...
In Greek antiquity the ideas of celestial spheres and rings first appeared in the cosmology of Anaximander in the early 6th century BC. [7] In his cosmology both the Sun and Moon are circular open vents in tubular rings of fire enclosed in tubes of condensed air; these rings constitute the rims of rotating chariot-like wheels pivoting on the Earth at their centre.
For Plato, the celestial regions were made "mostly out of fire" [1] [2] on account of fire's mobility. [3] Later Platonists, such as Plotinus, maintained that although fire moves naturally upward in a straight line toward its natural place at the periphery of the universe, when it arrived there, it would either rest or move naturally in a ...
When many sizes of spheres (or a distribution) are available, the problem quickly becomes intractable, but some studies of binary hard spheres (two sizes) are available. When the second sphere is much smaller than the first, it is possible to arrange the large spheres in a close-packed arrangement, and then arrange the small spheres within the ...
Examples of astronomical objects include planetary systems, star clusters, nebulae, and galaxies, while asteroids, moons, planets, and stars are astronomical bodies. A comet may be identified as both a body and an object: It is a body when referring to the frozen nucleus of ice and dust, and an object when describing the entire comet with its ...
Many of the subsystems are characterized as "spheres", coinciding with the shape of the planet. The four spheres (for which most of the other spheres are a subtype of) are the atmosphere, the biosphere, the hydrosphere and the geosphere. Earth's ecosphere lies it self within the heliosphere (the Sun's astrosphere). [4]