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Given the coordinates of the two points (Φ 1, L 1) and (Φ 2, L 2), the inverse problem finds the azimuths α 1, α 2 and the ellipsoidal distance s. Calculate U 1, U 2 and L, and set initial value of λ = L. Then iteratively evaluate the following equations until λ converges:
A standard Brunton compass, used commonly by geologists and surveyors to obtain a bearing in the field. In navigation, bearing or azimuth is the horizontal angle between the direction of an object and north or another object. The angle value can be specified in various angular units, such as degrees, mils, or grad. More specifically:
The inverse problem for earth sections is: given two points, and on the surface of the reference ellipsoid, find the length, , of the short arc of a spheroid section from to and also find the departure and arrival azimuths (angle from true north) of that curve, and . The figure to the right illustrates the notation used here.
Position resection and intersection are methods for determining an unknown geographic position (position finding) by measuring angles with respect to known positions.In resection, the one point with unknown coordinates is occupied and sightings are taken to the known points; in intersection, the two points with known coordinates are occupied and sightings are taken to the unknown point.
The solutions to both problems in plane geometry reduce to simple trigonometry and are valid for small areas on Earth's surface; on a sphere, solutions become significantly more complex as, for example, in the inverse problem, the azimuths differ going between the two end points along the arc of the connecting great circle.
A systematic solution for the paths of geodesics was given by Legendre (1806) and Oriani (1806) (and subsequent papers in 1808 and 1810). The full solution for the direct problem (complete with computational tables and a worked out example) is given by Bessel (1825). During the 18th century geodesics were typically referred to as "shortest lines".
As time passed, train (also called bearing), the direction to the target, also became part of rangekeeping, but tradition kept the term alive. Rangekeeping is an excellent example of the application of analog computing to a real-world mathematical modeling problem.
It was originally called the azimuth intercept method because the process involves drawing a line which intercepts the azimuth line. This name was shortened to intercept method and the intercept distance was shortened to 'intercept'. The method yields a line of position (LOP) on which the observer is situated. The intersection of two or more ...