Angular separation ($\theta$)

The angle between two lines of sight. If their unit vectors are ${\mathbf{n}}_1$ and ${\mathbf{n}}_2$, the dot product gives $\cos \theta ={\mathbf{n}}_1\cdot {\mathbf{n}}_2$. This definition concerns viewing directions, so two stars can have a small angular separation while having very different Euclidean distances from the observer.

For a small transverse physical separation $s$ at a common Euclidean distance $D$, the small-angle approximation gives $\theta \simeq s/D$ in radians. Thus a separation of one astronomical unit at one parsec subtends approximately one arcsecond. At cosmological distances the appropriate scale factor is the angular diameter distance, rather than an arbitrary notion of distance.