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Geodetic latitude and geocentric latitude have different definitions. Geodetic latitude is defined as the angle between the equatorial plane and the surface normal at a point on the ellipsoid, whereas geocentric latitude is defined as the angle between the equatorial plane and a radial line connecting the centre of the ellipsoid to a point on the surface (see figure).
Definition of the parametric latitude (β) on the ellipsoid. The parametric latitude or reduced latitude, β, is defined by the radius drawn from the centre of the ellipsoid to that point Q on the surrounding sphere (of radius a) which is the projection parallel to the Earth's axis of a point P on the ellipsoid at latitude ϕ.
Direction determination refers to the ways in which a cardinal direction or compass point can be determined in navigation and wayfinding. The most direct method is using a compass ( magnetic compass or gyrocompass ), but indirect methods exist, based on the Sun path (unaided or by using a watch or sundial ), the stars, and satellite navigation .
The latitude is defined as the angle between the normal to the ellipsoid and the equatorial plane. Geographical latitude and longitude are stated in the units degree, minute of arc, and second of arc. They are angles, not metric measures, and describe the direction of the local normal to the reference ellipsoid of revolution.
Vincenty relied on formulation of this method given by Rainsford, 1955. Legendre showed that an ellipsoidal geodesic can be exactly mapped to a great circle on the auxiliary sphere by mapping the geographic latitude to reduced latitude and setting the azimuth of the great circle equal to that of the geodesic.
The lines from pole to pole are lines of constant longitude, or meridians. The circles parallel to the Equator are circles of constant latitude, or parallels. The graticule shows the latitude and longitude of points on the surface. In this example, meridians are spaced at 6° intervals and parallels at 4° intervals.
The geodesic oscillates north and south of the equator; on each oscillation it completes slightly less than a full circuit around the ellipsoid resulting, in the typical case, in the geodesic filling the area bounded by the two latitude lines β = ±β 1. Two examples are given in Figs. 18 and 19.
Three line segments with the same direction. In geometry, direction, also known as spatial direction or vector direction, is the common characteristic of all rays which coincide when translated to share a common endpoint; equivalently, it is the common characteristic of vectors (such as the relative position between a pair of points) which can be made equal by scaling (by some positive scalar ...