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The great circle g (green) lies in a plane through the sphere's center O (black). The perpendicular line a (purple) through the center is called the axis of g, and its two intersections with the sphere, P and P ' (red), are the poles of g. Any great circle s (blue) through the poles is secondary to g. A great circle divides the sphere in two ...
While the obvious application is the diurnal motion of the stars as the celestial sphere appears to rotate about an immobile Earth (as modeled at the time), Autolycus' treatise never explicitly discusses this application: its content consists entirely of elementary theorems about the arcs of great circles and parallel small circles on an ...
A diagram illustrating great-circle distance (drawn in red) between two points on a sphere, P and Q. Two antipodal points, u and v are also shown. The great-circle distance, orthodromic distance, or spherical distance is the distance between two points on a sphere, measured along the great-circle arc between them. This arc is the shortest path ...
Orthodromic course drawn on the Earth globe. Great-circle navigation or orthodromic navigation (related to orthodromic course; from Ancient Greek ορθός (orthós) ' right angle ' and δρόμος (drómos) ' path ') is the practice of navigating a vessel (a ship or aircraft) along a great circle.
The armillary sphere survives as useful for teaching, and may be described as a skeleton celestial globe, the series of rings representing the great circles of the heavens, and revolving on an axis within a horizon. With the earth as center such a sphere is known as Ptolemaic; with the sun as center, as Copernican. [1]
A great circle separates the sphere into two equal hemispheres, each with the great circle as its boundary. If a great circle passes through a point on the sphere, it also passes through the antipodal point (the unique furthest other point on the sphere). For any pair of distinct non-antipodal points, a unique great circle passes through both.
Schematic representation of spherical harmonics on a sphere and their nodal lines. P ℓ m is equal to 0 along m great circles passing through the poles, and along ℓ-m circles of equal latitude. The function changes sign each ℓtime it crosses one of these lines. Example of a quadrupole field. This can also be constructed by moving two ...
Great circles are the largest possible circles (circumferences) of a sphere; each one divides the surface of the sphere into two equal halves. Two great circles always intersect at two polar opposite points. Common examples of great circles are lines of longitude (meridians) on a sphere, which meet at the north and south poles.