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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.
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 ...
[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.
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 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 spheres considered are usually all of identical size, and the space is usually three-dimensional Euclidean space. However, sphere packing problems can be generalised to consider unequal spheres, spaces of other dimensions (where the problem becomes circle packing in two dimensions, or hypersphere packing in higher dimensions) or to non ...
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] Listed roughly from outermost to innermost the named spheres of the Earth are:
List of Solar System objects most distant from the Sun; List of Solar System objects by size; Lists of geological features of the Solar System; List of natural satellites (moons) Lists of small Solar System bodies; Lists of comets; List of meteor showers; Minor planets. List of minor planets. List of exceptional asteroids; List of minor planet ...