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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 ...
In spherical geometry, the basic concepts are point and great circle. However, two great circles on a plane intersect in two antipodal points, unlike coplanar lines in Elliptic geometry. In the extrinsic 3-dimensional picture, a great circle is the intersection of the sphere with any plane through the center.
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.
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 between the two points on the surface of the sphere. (By comparison, the shortest path passing through the sphere's interior is the chord between ...
Consider the great circle that contains the side BC. This great circle is defined by the intersection of a diametral plane with the surface. Draw the normal to that plane at the centre: it intersects the surface at two points and the point that is on the same side of the plane as A is (conventionally) termed the pole of A and it is denoted by A'.
The celestial equator is the great circle of the imaginary celestial sphere on the same plane as the equator of Earth. By extension, it is also a plane of reference in the equatorial coordinate system. In other words, the celestial equator is an abstract projection of the terrestrial equator into outer space. [1]
The Madison Square Garden (MSG) Sphere at the Venetian Resort in Las Vegas has LED lights that can create these large-scale projections. It has been filmed projecting the image of a gigantic ...
Circles on the sphere are, like circles in the plane, made up of all points a certain distance from a fixed point on the sphere. The intersection of a sphere and a plane is a circle, a point, or empty. [18] Great circles are the intersection of the sphere with a plane passing through the center of a sphere: others are called small circles.