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An example of a spherical cap in blue (and another in red) In geometry, a spherical cap or spherical dome is a portion of a sphere or of a ball cut off by a plane.It is also a spherical segment of one base, i.e., bounded by a single plane.
The magnitude of an object's solid angle in steradians is equal to the area of the segment of a unit sphere, centered at the apex, that the object covers.Giving the area of a segment of a unit sphere in steradians is analogous to giving the length of an arc of a unit circle in radians.
The division of Earth by the Equator and the prime meridian Map roughly depicting the Eastern and Western hemispheres. In geography and cartography, hemispheres of Earth are any division of the globe into two equal halves (hemispheres), typically divided into northern and southern halves by the Equator and into western and eastern halves by the Prime meridian.
The projection onto the hemisphere, giving the solid angle subtended by A j, takes care of the factors cos(θ 2) and 1/r 2; the projection onto the circle and the division by its area then takes care of the local factor cos(θ 1) and the normalisation by π.
The physics convention.Spherical coordinates (r, θ, φ) as commonly used: (ISO 80000-2:2019): radial distance r (slant distance to origin), polar angle θ (angle with respect to positive polar axis), and azimuthal angle φ (angle of rotation from the initial meridian plane).
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.
In the northern hemisphere, declination can therefore be approximately determined as the difference between the magnetic bearing and a visual bearing on Polaris. Polaris currently traces a circle 0.73° in radius around the north celestial pole, so this technique is accurate to within a degree.
The sign convention is typically that the observer latitude is 0 at the equator, positive for the Northern Hemisphere and negative for the Southern Hemisphere, and the solar declination is 0 at the vernal and autumnal equinoxes when the sun is exactly above the equator, positive during the Northern Hemisphere summer and negative during the ...