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A cometary dust tail is a superposition of synchrones and syndynes, rather than a material line emitted in one fixed direction. For grains larger than the stellar wavelength, $\beta \propto D^{-1}$: small grains have large $\beta$, are displaced rapidly in the anti-stellar direction, and make a relatively straight broad tail. Large grains have small $\beta$, remain closer to the comet's Kepler orbit, and make a more strongly curved dust trail. The observed position angle consequently depends on grain size, release time, orbital phase, and projection onto the plane of the sky.

Put the star at the origin, take $\hat{\mathbf{z}}$ along the line of sight toward the observer, and let $\hat{\mathbf{x}}$ point North in the plane of the sky. The $\hat{\mathbf{y}}$ direction is then $90^{\circ }$ anticlockwise from North. Draw the ascending node on the sky plane at position angle $\Omega$, tilt the circular Kepler orbit through the orbital inclination $I$ about that nodal line, and place the planet an angle $f$ along the orbit from the ascending node. The direction of increasing $f$ must cross the sky plane toward $+\hat{\mathbf{z}}$ at $f=0$.

A convenient orthonormal basis in the orbital plane isHere ${\mathbf{e}}_1$ points along the nodal line and ${\mathbf{e}}_2$ fixes the required sense of motion. The planet lies at $\mathbf{r}=a(\cos f{\mathbf{e}}_1+\sin f{\mathbf{e}}_2)$; this relation also specifies all the labels required in the sketch.