The size distribution and orbital architecture of dust , grains , boulders , asteroids , and major planets during the giant branch phases of evolution dictate the preponderance and observability of the eventual debris , which have been found to surround white dwarfs and pollute their atmospheres with metals . Here , we utilize the photogravitational planar restricted three-body problem in one-planet giant branch systems in order to characterize the orbits of grains as the parent star luminosity and mass undergo drastic changes . We perform a detailed dynamical analysis of the character of grain orbits ( collisional , escape , or bounded ) as a function of location and energy throughout giant branch evolution . We find that for stars with main-sequence masses of 2.0 M _ { \odot } , giant branch evolution , combined with the presence of a planet , ubiquitously triggers escape in grains smaller than about 1 mm , while leaving grains larger than about 5 cm bound to the star . This result is applicable for systems with either a terrestrial or giant planet , is largely independent of the location of the planet , and helps establish a radiative size threshold for escape of small particles in giant branch planetary systems .