Great circle

A (lune on the surface included between two great circles, the inclination of which is 0 radians) = 2ft"0. 

The intersection of a sphere with a plane through its center is called a great circle. 

In Fig. 1, the SBR is located at A, and B represents the nadir point. The point of interest D is located at range R from B along the great circle that goes through B and D with C representing the center of the earth (see [5]). The main parameters of an SBR setup are as shown in Fig. 1 and are listed in the table in figure 2. 

R Actual ground range from the nadir point to the point of interest along a great circle on the surface of the earth... 

Thus the number co is the arclength of the great circle arc connecting the two points. We have... 

Exercise 10.17 Suppose pr, p2 and pi are points on the unit sphere in that do not lie on one common great circle. (A great circle is the intersection of the unit sphere with a plane through the origin in ) Show that every point p on the sphere is uniquely defined by its distances from the three points pi, P2, p3. Interpret great circles in PCC ) physically i.e., give a definition in terms of experiments and probabilities. 

Let QP be a diameter of the unit sphere then, since great circles defined by Q and P are not unique, all turns TK defined by pairs of opposite points are equivalent. Since rTn can be chosen on any great circle, it commutes with any turn T. The operation of adding I, to a turn T is described as conjugation,... 

Stereographic projection provides a convenient way of displaying the angular relations between planes and directions in a crystal in two dimensions. The system involves first projecting planes and directions of interest onto a spherical surface and then mapping the spherical surface. Figure 4.1 illustrates how planes and directions are projected onto a sphere. If an infinitesimal crystal were placed at the center of a sphere and its planes extended, they would intersect the sphere as great circles and their directions would intersect the sphere as points. 

Mapping of planes and directions by placing an infinitesimal crystal at the center of a sphere and projecting planes onto the sphere to form great circles and lines to form points. 

Ibata, R., Lewis, G. F., Irwin, M., Totten, E., Quinn, T. 2001. Great Circle Tidal Streams Evidence for a Nearly Spherical Massive Dark Halo around the Milky Way, ApJ551, 294... 

This operation represents a quarter turn on a great circle or rotation of ir radians about an axis. An intermediate position is given by the spinor ... 

The orthodrome between points A and B on the surface of a geode or earth is the shortest distance between A and B on this surface the orthodrome is a segment of a great circle (e.g., a meridian) passing through both A and B. 

The celestial sphere is a fixed sphere of infinite radius, concentric with the center of the earth. The celestial North and South poles (Pjv and P ) are an extension of the earth s North and South poles to infinity. The celestial equator is the great circle whose poles are Pn and Ps. The (local) zenith point Z is the point vertically above an observer at some arbitrary point on the earth s... 

The route taken by President Gerald Ford from Washington, D.C., to Tokyo, Japan, via Fairbanks, Alaska. Panel A shows the route on a Mercator projection Panel B shows the route as a great circle. Adapted from Muehrcke and Muehrcke (1998, 526). 

A graph is a set of points (called vertices) and a set of lines (called edges) joinging these vertices, great circle... 

Figure 7.12 Gnomonic projection of point Pi on P in the Euclidean plane a. The line m maps the stippled great circle.

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