Catastrophically evaporating rocky planets provide a unique opportunity to study the composition of small planets. The surface
composition of these planets can be constrained via modelling their comet-like tails of dust. In this work, we present a new
self-consistent model of the dusty tails: we physically model the trajectory of the dust grains after they have left the gaseous
outflow, including an on-the-fly calculation of the dust cloud’s optical depth. We model two catastrophically evaporating planets:
KIC 1255 b and K2-22 b. For both planets, we find the dust islikely composed of magnesium–iron silicates(olivine and pyroxene),
consistent with an Earth-like composition. We constrain the initial dust grain sizes to be ∼ 1.25–1.75 μm and the average (dusty)
planetary mass-loss rate to be ∼ 3 M⊕Gyr−1. Our model shows that the origin of the leading tail of dust of K2-22 b is likely a
combination of the geometry of the outflow and a low radiation pressure force to stellar gravitational force ratio. We find the
optical depth of the dust cloud to be a factor of a few in the vicinity of the planet. Our composition constraint supports the
recently suggested idea that the dusty outflows of these planets go through a greenhouse effect–nuclear winter cycle, which gives
origin to the observed transit depth time variability. Magnesium–iron silicates have the necessary visible-to-infrared opacity
ratio to give origin to this cycle in the high mass-loss state.