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: ${\displaystyle B_{2}}$, and longitude: ${\displaystyle L_{2}}$. In a terrestrial spherical model, the equation of isoazimuth curve with initial course C passing through point S(B, L) is: ${\displaystyle \tan(B_{2})\cos(B)=\sin(B)\cos(L_{2}-L)+\sin(L_{2}-L)/\tan(C)\;}$

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:

${\displaystyle \cot(Z)/\cos(B)=\tan(Dec)/\sin(LHA)-\tan(B)/\tan(LHA)\;}$

where LHA is the local hour angle, and all points with latitude B and longitude L, they define the curve.

See also

• Great circle
• Rhumb line
• Cartography
• Navigational algorithms