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S 3: a 3-sphere is a sphere in 4-dimensional Euclidean space. Spheres for n > 2 are sometimes called hyperspheres. The n-sphere of unit radius centered at the origin is denoted S n and is often referred to as "the" n-sphere. The ordinary sphere is a 2-sphere, because it is a 2-dimensional surface which is embedded in 3-dimensional space.
Heliocentric model from Nicolaus Copernicus' De revolutionibus orbium coelestium (On the Revolutions of the Heavenly Spheres) During the 16th century Nicholas Copernicus , in reflecting on Ptolemy and Aristotle's interpretations of the Solar System, believed that all the orbits of the planets and Moon must be a perfect uniform circular motion ...
The Middle Ages broadly inherited the concept of the four elements of earth, water, air and fire arranged in concentric spheres about the earth as centre: [3] as the purest of the four elements, fire - and the sphere of fire - stood highest in the ascending sequence of the scala naturae, and closest to the superlunary world of the aether. [4]
[4] For example, if a TNO is incorrectly assumed to have a mass of 3.59 × 10 20 kg based on a radius of 350 km with a density of 2 g/cm 3 but is later discovered to have a radius of only 175 km with a density of 0.5 g/cm 3 , its true mass would be only 1.12 × 10 19 kg.
The 3-sphere is the boundary of a -ball in four-dimensional space. The ( n − 1 ) {\displaystyle (n-1)} -sphere is the boundary of an n {\displaystyle n} -ball. Given a Cartesian coordinate system , the unit n {\displaystyle n} -sphere of radius 1 {\displaystyle 1} can be defined as:
The seven heavens and the sublunar spheres, from an engraving of Albertus Magnus' Philosophia naturalis.. Plato and Aristotle helped to formulate the original theory of a sublunary sphere in antiquity, [4] the idea usually going hand in hand with geocentrism and the concept of a spherical Earth.
Mars has an atmosphere composed mostly of carbon dioxide, with surface pressure 0.6% of that of Earth, which is sufficient to support some weather phenomena. [119] During the Mars year (687 Earth days), there are large surface temperature swings on the surface between −78.5 °C (−109.3 °F) to 5.7 °C (42.3 °F).
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.