A new analytical model that is calibrated against numerical simulations performed with the CTH shock physics code provides a useful description of the entry of Periodic Comet Shoemaker-Levy 9 into the Jovian atmosphere. Mass loss due to radiative heating of fragments larger than 100 m in diameter is insignificant because of energy conservation during the ablative process. Nevertheless, radiative ablation is a major contributor to atmospheric energy deposition at high altitude and plays an important role in early-time fireball evolution. The analytical model provides the initial conditions from which fireball and plume evolution can be calculated using CTH. The results from these simulations suggest that if the tops of the plumes originated from a specific level of the Jovian atmosphere then maximum plume heights are independent of fragment size provided the fragments penetrated at least 30 km below this level. If the tops of the plumes originated from the visible cloud tops, then fragment masses greater than 4 × 1012 g, corresponding to 200 m diameter fully dense water ice, are required to explain the observations. If the plumes originated from the NH4SH layer then masses greater than 3 × 1013 g (400 m water ice) are required. The lateral extent and mass of the observable plume are functions of fragment size and contribute to the lateral extent and albedo of the debris patterns after re-impact with the atmosphere.