Astronomy:Isoazimuth
The isoazimuth is the locus of the points on the Earth's surface whose initial orthodromic course with respect to a fixed point is constant.[1] That is, if the initial orthodromic course Z from the starting point S to the fixed point X is 80 degrees, the associated isoazimuth is formed by all points whose initial 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?] .
The isoazimuth is of use when 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.
Isoazimutal on the spherical Earth
Let X be a fixed point on the Earth of coordinates latitude: [math]\displaystyle{ B_2 }[/math], and longitude: [math]\displaystyle{ L_2 }[/math]. In a terrestrial spherical model, the equation of isoazimuth curve with initial course C passing through point S(B, L) is: [math]\displaystyle{ \tan(B_2)\cos(B) = \sin(B) \cos(L_2-L)+\sin(L_2-L)/\tan(C)\; }[/math]
Isoazimutal of a star
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 [2] curve for a star with coordinates (Dec, GHA), - Declination and Greenwich hour angle -, observed under an azimuth Z is given by:
- [math]\displaystyle{ \cot(Z)/\cos(B) = \tan(Dec)/\sin(LHA)-\tan(B)/\tan(LHA)\; }[/math]
where LHA is the local hour angle, and all points with latitude B and longitude L, they define the curve.
See also
References
- ↑ Flexner, W. W.. 1943. “Azimuth Line of Position”. The American Mathematical Monthly 50 (8). Mathematical Association of America: 475–84. doi:10.2307/2304185. Accessed 2016-01-24.
- ↑ Le segment capable sphérique. Navigation Nº.116 Vol.XXIX, Institut français de navigation, octubre/1981.
External links
- Navigational Algorithms http://sites.google.com/site/navigationalalgorithms/
- Institut français de navigation https://web.archive.org/web/20140103212146/http://www.ifnavigation.org/
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