Co-width

As Colatitude or co-width in astronomy, Geodesy and spherical trigonometry which is complementary angle of geographic or astronomical width referred to:

Width = B → K width = 90 ° - B

The introduction of the term, which corresponds to the angular distance of a location from the North Pole , simplifies the spelling of many formulas and can in some cases also prevent sign errors.

Astronomical triangle with the 3 sides (width 90 ° -B, pole distance 90 ° declination, zenith distance 90 ° height) and the 3 angles ( azimuth Az, hour angle t, parallactic angle q). In the northeast the star moves steeply upwards (see also largest digression ).

The astronomical triangle ( pole - zenith - star , see picture) always contains the angle 90 ° -B as one of its 3 sides, i.e. the co-width. Since the two other sides are also complementary angles, analogous terms are often used for them:

• Zenith star: 90 ° - elevation angle = zenith distance
• Pole star: 90 ° - declination = pole distance .

Use in geometry

The co-width is used in spherical coordinates under the symbol θ or ϑ. The square of an infinitesimal line element is thus through in these coordinates

(ds) ² = (dr) ² + r² (dϑ) ² + r²sin² (ϑ) (dφ) ²

given, where φ stands for the (in the case of the earth, geographical or astronomical) longitude.