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A cometary dust tail is the extended distribution of solid grains released by a comet. Radiation pressure sorts its grains by size: high-$\beta$ grains are displaced rapidly in the anti-stellar direction, while larger low-$\beta$ grains remain closer to the projected orbit and form a more curved trail.

The Finson–Probstein model follows cometary dust after release with negligible ejection speed under stellar gravity reduced by radiation pressure. A grid of synchrones and syndynes organizes the resulting dust-tail morphology.

The same absorption and re-emission that produce radial radiation pressure also produce Poynting–Robertson drag. This velocity-dependent force removes specific orbital energy and angular momentum, destroys the exact Jacobi constant, and turns the formal equilibrium points into slowly drifting configurations. Stellar-wind drag can provide a similar correction.

The standard Shakura--Sunyaev thin disk has three qualitative radial zones. Its hot inner part is dominated by radiation pressure and electron-scattering opacity; farther out, gas pressure overtakes radiation pressure while electron scattering can remain the main opacity; in the cool outer zone, gas pressure remains dominant and free-free opacity becomes important. The transition radii vary with $M$, $\dot{M}$, and $\alpha$.

For the inner zone, hold the surface density $\Sigma$ fixed during a local thermal perturbation. Vertical hydrostatic equilibrium givesso $H\propto T_c^4/\Sigma$. The alpha disk prescription then yieldswhereas optically thick radiative diffusion with nearly constant electron-scattering opacity givesAt equilibrium $Q^{+}=Q^{-}=Q_0$. For net cooling $\dot{Q}=Q^{-}-Q^{+}$,Thus the total-pressure alpha prescription predicts thermal instability of a radiation-pressure-dominated alpha disk: a temperature increase makes heating outrun cooling. The absence of ubiquitous, large-amplitude thermal limit cycles in luminous AGN light curves indicates that this local model omits stabilizing effects, plausibly magnetic pressure and stress, vertical advection, winds, or a stress law that does not simply track total pressure.

The photogravitational restricted three-body problem adds radial radiation pressure from one or both luminous primaries. If the pressure-to-gravity ratio of primary $i$ is ${\beta }_i$, its effective attraction on the test particle is multiplied by $1-{\beta }_i$.