Fragmentation and ablation during entry

This note discusses objects that both fragment and ablate during entry, using the results of previous reports to describe the velocity, pressure, and fragmentation of entering objects. It shows that the mechanisms used there to describe the breakup of non-ablating objects during deceleration remain valid for most ablating objects. It treats coupled fragmentation and ablation during entry, building on earlier models that separately discuss the entry of objects that are hard, whose high heat of ablation permits little erosion, and those who are strong whose strength prevents fragmentation, which are discussed in ``Radiation from Hard Objects,`` ``Deceleration and Radiation of Strong, Hard, Asteroids During Atmospheric Impact,`` and ``Meteor Signature Interpretation.`` This note provides a more detailed treatment of the further breakup and separation of fragments during descent. It replaces the constraint on mass per unit area used earlier to determine the altitude and magnitude of peak power radiation with a detailed analytic solution of deceleration. Model predictions are shown to be in agreement with the key features of numerical calculations of deceleration. The model equations are solved for the altitudes of maximum radiation, which agree with numerical integrations. The model is inverted analytically to infer object size and speed from measurements of peak power and altitude to provide a complete model for the approximate inversion of meteor data.