Radiation-pressure coefficient ($\beta$)

The radiation-pressure coefficient is the ratio of outward stellar radiation pressure to inward stellar gravity on a dust grain. The grain therefore feels effective gravitational parameter $(1-\beta )G{M}_{\ast }$.

If release imparts no velocity kick, a grain's initial Kepler orbit under reduced stellar attraction has $q=r_b$, $Q=r_b/(1-2\beta )$, and $e=\beta /(1-\beta )$ for $0\le \beta <1/2$. Its pericentre distance remains at the dust birth ring, while its apocentre distance grows with the radiation-pressure coefficient.

The radiation-pressure efficiency is the radiation-force cross-section of a grain divided by its geometric cross-section. It is of order unity for grains larger than the illuminating wavelength and depends strongly on size and composition in the small-particle regime.

A grain released from a circular parent orbit without a relative velocity impulse is unbound when radiation pressure reduces the effective stellar attraction sufficiently. For $\beta >1$, the effective inverse-square force is repulsive.

The zero-kick circular-parent threshold is $\beta =1/2$: below it grains are initially bound, at it their conservative release orbit is parabolic, and above it they are initially unbound. Poynting–Robertson drag can modify a marginal orbit, so the threshold is a statement about the instantaneous release orbit, not an exact capture criterion with dissipation included.