Isoazimuthal

There are three most important curves between any two points on the earth's surface: the orthodrome, the rhumb and the isoazimuthal.

The line or curve isoazimutal, IsorZ(X,Z){displaystyle IsoZ(X,Z)}, is the geometrical place of the points on the earth's surface whose orthochromic initial course regarding a fixed point X{displaystyle X} is constant and equal to Z{displaystyle Z}.

For example, if the orthodomic initial course from S{displaystyle S} until X{displaystyle X} is 80{displaystyle 80} degrees, the associated isoazimutal line is formed by all points whose initial orthodomic course to the point X{displaystyle X} is 80 {displaystyle 80^{circ}}.

Isoazimuthal in the terrestrial sphere

Sea X{displaystyle X} a fixed point of the Earth of latitude coordinates: B2{displaystyle B_{2}}, and length: L2{displaystyle L_{2}}. In a terrestrial spherical model, the equation of the initial isoazimutal Z{displaystyle Z} that goes through the point S=(B,L){displaystyle S=(B,L)} is:

So... (B2)⋅ ⋅ # (B)=without (B)⋅ ⋅ # (L2− − L)+without (L2− − L)So... (Z){displaystyle tan(B_{2})cdot cos(B)=sin(B)cdot cos(L_{2}-L)+{frac {sin(L_{2}-L)}{tan(Z)}}}{;}.

Isoazimuthal of a star

In this case the point X{displaystyle X} is the observed star illumination pole and angle θ θ {displaystyle theta } It's his azimut. The equation of the isoazimutal curve, or spherical arc, for a coordinates star (δ δ ,GHA){displaystyle (deltaGHA)}, decline and time angle in Greenwich, observed under an azimut Z{displaystyle Z}It is given by:

cot (Z)# (B)=So... (δ δ )without (LHA)− − tan(B)So... (LHA){displaystyle {frac {cot(Z)}{cos(B)}}}={frac {tan(delta)}{sin(L!H!A)}}}}{frac {tan(B)}{tan(L!H!A)}}}{;},

where LHA{displaystyle L!H!A} is the local time angle and latitude points B{displaystyle B}, and length L{displaystyle L}They belong to the curve.