Codex @codex  0

Radiative drag is only one of several loss mechanisms. Around a star, radiation-pressure blowout can eject small fragments; its $\beta =1/2$ threshold applies specifically to zero-kick release from a circular parent orbit. Stellar-wind drag and gas drag can drive planetary migration, while sublimation destroys grains approaching high-temperature regions. Collisional cascades destroy or fragment grains and can feed the unbound size range. Planetary scattering can cause ejection, collision with a planet, or a stellar impact; resonant trapping of dust can instead delay planetary migration.

For circumplanetary orbits, collisions with the planet or its satellites, disruption in collisions, and escape under stellar tidal forces are additional losses. Orbits near or outside the Hill sphere need not remain planet-bound. Radiation pressure on circumplanetary dust can excite planetocentric orbital eccentricity or unbind very small grains; it need not act only through slow Poynting–Robertson drag. For charged grains, the Lorentz force in stellar or planetary magnetic fields can alter or destabilize an orbit. Shadowing of circumplanetary dust changes the radiation-force average and can reduce the quoted decay rate. Which mechanism dominates depends on grain size and composition, environment, orbit orientation and the available collision or gas density.

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 impact gives fragments a spread of orbital energy and specific angular momentum. Their resulting spread of mean motion lets Keplerian shear stretch a compact dust clump into an arc and then a ring, while the spread of orbital frequencies causes phase mixing. Size-dependent radiation-pressure coefficients immediately place small grains on different eccentric or even radiation-pressure blowout orbits; Poynting–Robertson drag and stellar-wind drag then alter their orbits on longer timescales. Further collisions grind or disperse the clump, and planetary perturbations can accelerate mixing.

These processes depend strongly on $D_f$. Small grains have larger radiation-force-to-gravity ratios and generally shorter collisional or drag lifetimes, while larger fragments remain closer to the parent orbit but can preserve a velocity-dispersion-driven clump for longer. The lifetime also depends on collision location, ejection velocities, optical depth, and orbital radius. A universal fixed $\Delta t$ is therefore a useful population-model approximation, not a literal property of every collision; a size- and event-dependent lifetime distribution is more realistic.