Forbidden Mass Ranges for Shower Meteoroids

Burns et al. (1979) use the parameter beta to describe the ratio of radiation pressure to gravity for a particle in the Solar System. The central potential that these particles experience is effectively reduced by a factor of (1- beta ), which in turn lowers the escape velocity. Burns et al. (1979) derived a simple expression for the value of beta at which particles ejected from a comet follow parabolic orbits and thus leave the Solar System; we expand on this to derive an expression for critical beta values that takes ejection velocity into account, assuming geometric optics. We use our expression to compute the critical value and corresponding mass for cometary ejecta leading, trailing, and following the parent comet's nucleus for 10 major meteor showers. Finally, we numerically solve for critical beta values in the case of non-geometric optics. These values determine the mass regimes within which meteoroids are ejected from the Solar System and therefore cannot contribute to meteor showers.