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<p><b>New page</b></p><div>The '''isoazimuth''' is the [[locus (mathematics)|locus]] of the points on the Earth's surface whose initial [[Great-circle distance|orthodromic course]] with respect to a fixed point is constant.<ref>Flexner, W. W.. 1943. “Azimuth Line of Position”. The American Mathematical Monthly 50 (8). Mathematical Association of America: 475–84. doi:10.2307/2304185. [https://www.jstor.org/stable/2304185?seq=1#page_scan_tab_contents Accessed 2016-01-24].</ref><br />
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That is, if the initial [[Great-circle distance|orthodromic course]] Z from the starting point ''S'' to the fixed point ''X'' is 80 [[Degree (angle)|degrees]], the associated isoazimuth is formed by all points whose initial [[Great-circle distance|orthodromic course]] with respect to point ''X'' is 80° (with respect to true north). The isoazimuth is written using the notation ''isoz(X, Z)''{{According to whom|date=May 2020}} .<br />
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The isoazimuth is of use when [[navigation|navigating]] with respect to an object of known location, such as a radio beacon. A straight line called the ''azimuth line of position'' is drawn on a map, and on most common map projections this is a close enough approximation to the isoazimuth. On the [[Littrow projection]], the correspondence is exact. This line is then crossed with an astronomical observation called a [[Sumner line]], and the result gives an estimate of the navigator's position.<br />
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== Isoazimutal on the spherical Earth ==<br />
Let ''X'' be a fixed point on the Earth of coordinates latitude: <math>B_2</math>, and longitude: <math>L_2</math>. In a terrestrial spherical model, the equation of isoazimuth curve with initial course ''C'' passing through point S(''B'', ''L'') is:<br />
'''<math>\tan(B_2)\cos(B) = \sin(B) \cos(L_2-L)+\sin(L_2-L)/\tan(C)\;</math>'''<br />
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== Isoazimutal of a star ==<br />
In this case the ''X'' point is the illuminating pole of the observed star, and the angle ''Z'' is its [[azimuth]]. The equation of the ''isoazimuthal'' <ref>Le segment capable sphérique. Navigation Nº.116 Vol.XXIX, Institut français de navigation, octubre/1981.</ref> curve for a star with coordinates (''Dec, GHA''), - [[Declination]] and [[Greenwich hour angle]] -, observed under an azimuth ''Z'' is given by:<br />
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: '''<math>\cot(Z)/\cos(B) = \tan(Dec)/\sin(LHA)-\tan(B)/\tan(LHA)\;</math>'''<br />
where ''LHA'' is the [[local hour angle]], and all points with latitude ''B'' and longitude ''L'', they define the curve.<br />
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==See also ==<br />
* [[Great circle]]<br />
* [[Rhumb line]]<br />
* [[Cartography]]<br />
* [[Navigational algorithms]]<br />
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== References ==<br />
{{reflist}}<br />
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== External links ==<br />
* Navigational Algorithms http://sites.google.com/site/navigationalalgorithms/<br />
* Institut français de navigation https://web.archive.org/web/20140103212146/http://www.ifnavigation.org/<br />
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[[Category:Cartography]]<br />
[[Category:Navigation]]<br />
[[Category:Celestial navigation]]</div>wikipedia>Mauls