A Threshold Model for Micrometeoroid Atmospheric Entry: Filippov Dynamics, Survival Estimates, and Survivor-Only Inverse Limits

Micrometeoroids enter Earth’s atmosphere at hypervelocity speeds and experience rapid coupling between drag, heating, radiation, melting, ablation, and deceleration. This paper develops a reduced threshold model for the thermal survival boundary of spherical micrometeoroids. The model uses free molecular drag, an exponential atmosphere, projected-area heating, full-sphere radiative cooling, and a surplus-heat ablation rule at the melting temperature. The switching surface $T=T_m$ is treated as a Filippov/complementarity surface. Sustained melting occurs when the local heating-to-radiation ratio exceeds unity. Under the additional Allen–Eggers assumptions of constant radius, constant entry angle, negligible gravity during the main heating interval, and constant transport coefficients, this threshold yields the classical approximate survival scaling $r_0^{\mathrm{c}\mathrm{r}\mathrm{i}\mathrm{t}}\sim v_0^{-3}$. An exact radius-loss identity is obtained along the prescribed Allen–Eggers trajectory, and a perturbative stability estimate explains when this expression approximates the full reduced model. The inverse problem is formulated through a transfer matrix from pre-atmospheric entry bins to observed survivor bins. Entry bins with zero survival probability lie in the survivor-only null space and require external information for reconstruction. The framework gives a compact analytical description of threshold entry survival and identifies the information lost when only surviving particles are observed.