Solution (source code)

= Solution

\b[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.