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The star is the point of interest, the reference plane is the local area (e.g. a circular area with a 5 km radius at sea level) around an observer on Earth's surface, and the reference vector points to true north. The azimuth is the angle between the north vector and the star's vector on the horizontal plane. [2]
The azimuth (or azimuthal angle) is the signed angle measured from the azimuth reference direction to the orthogonal projection of the radial line segment OP on the reference plane. The sign of the azimuth is determined by designating the rotation that is the positive sense of turning about the zenith. This choice is arbitrary, and is part of ...
The bearing angle value will always be less than 90 degrees. [1] For example, if Point B is located exactly southeast of Point A, the bearing from Point A to Point B is "S 45° E". [3] For example, if the bearing between Point A and Point B is S 45° E, the azimuth between Point A and Point B is 135°. [1] [3] Azimuths and bearings.
Vincenty's formulae are two related iterative methods used in geodesy to calculate the distance between two points on the surface of a spheroid, developed by Thaddeus Vincenty (1975a). They are based on the assumption that the figure of the Earth is an oblate spheroid, and hence are more accurate than methods that assume a spherical Earth, such ...
To find the way-points, that is the positions of selected points on the great circle between P 1 and P 2, we first extrapolate the great circle back to its node A, the point at which the great circle crosses the equator in the northward direction: let the longitude of this point be λ 0 — see Fig 1. The azimuth at this point, α 0, is given by
A line through three-dimensional space between points of interest on a spherical Earth is the chord of the great circle between the points. The central angle between the two points can be determined from the chord length. The great circle distance is proportional to the central angle.
The haversine formula determines the great-circle distance between two points on a sphere given their longitudes and latitudes. Important in navigation , it is a special case of a more general formula in spherical trigonometry , the law of haversines , that relates the sides and angles of spherical triangles.
Similar equations are coded into a Fortran 90 routine in Ref. [3] and are used to calculate the solar zenith angle and solar azimuth angle as observed from the surface of the Earth. Start by calculating n, the number of days (positive or negative, including fractional days) since Greenwich noon, Terrestrial Time, on 1 January 2000 .