Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 316 / 3 / vii

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.