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The sphere is normally chosen to model the Earth when the extent of the mapped region exceeds a few hundred kilometers in length in both dimensions. For maps of smaller regions, an ellipsoidal model must be chosen if greater accuracy is required. [1] The ellipsoidal form of the polar ellipsoidal projection uses conformal latitude. There are ...
The intersection of the parallels with the outer circle can be used as a de facto protractor for plotting a point's longitude as the angle in the polar projection. The Schmidt net's horizontal axis can then be used as a scalar measuring device to convert the point's latitude (relative to the pole) into a radial distance from the centre of the ...
In blue, the point (4, 210°). In mathematics, the polar coordinate system specifies a given point in a plane by using a distance and an angle as its two coordinates. These are the point's distance from a reference point called the pole, and; the point's direction from the pole relative to the direction of the polar axis, a ray drawn from the pole.
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Polar regions receive less intense solar radiation than the other parts of Earth because the Sun's energy arrives at an oblique angle, spreading over a larger area, being less concentrated, and also travels a longer distance through the Earth's atmosphere in which it may be absorbed, scattered or reflected, which is the same thing that causes ...
Even with these restrictions, if the polar angle (inclination) is 0° or 180°—elevation is −90° or +90°—then the azimuth angle is arbitrary; and if r is zero, both azimuth and polar angles are arbitrary. To define the coordinates as unique, the user can assert the convention that (in these cases) the arbitrary coordinates are set to zero.
A useful application for this type of projection is a polar projection which shows all meridians (lines of longitude) as straight, with distances from the pole represented correctly. The flag of the United Nations contains an example of a polar azimuthal equidistant projection.
On the other hand, the geodesic between these points is a great circle arc through the pole subtending an angle of 60° at the center: the length of this arc is one sixth of the great circle circumference, about 6,672 km. The difference is 3,338 km so the ruler distance measured from the map is quite misleading even after correcting for the ...
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