Vinkelafstand

Vinkelafstand, also known as angular distance or angular separation, is the angular separation between two lines of sight from a common observer. It describes how far apart two directions appear on the sky or within a surveying frame. The term is used in Danish, Norwegian, and related languages and corresponds to the general concept of angular distance in astronomy and surveying.

Mathematically, if the two directions are represented by unit vectors u and v, the angle θ between them satisfies cos θ = u · v. In astronomy, directions are often given in celestial coordinates (right ascension α and declination δ). The separation is θ = arccos( sin δ1 sin δ2 + cos δ1 cos δ2 cos(Δα) ), where Δα = α2 − α1. For small separations, θ ≈ sqrt( (Δα cos δ)^2 + (Δδ)^2 ), with α and δ converted to radians. Angular distance is invariant under the actual distances to the objects.

Applications and interpretation: vinkelafstand is used to quantify how far apart two stars are on the celestial sphere, the angular separation between objects in images, and the angle between lines of sight in surveying and navigation. It is independent of the objects’ distances; to obtain a physical separation, distance information is required. For objects at similar distances, the linear separation s ≈ d · θ, with θ in radians and d the common distance. If distances differ, a full 3D treatment is necessary.

Etymology and distinctions: the term combines the Danish/Norwegian words for angle (vinkel) and distance (afstand). It should not be confused with angular size, which measures how large a single object appears rather than the separation between two objects.