A new approach to the Finson-Probstein method of interpreting cometary dust tails

The inversion of the Finson-Probstein equation is considered along with the time-dependence of the particle size distribution. By means of the new approach, it is possible to obtain two of the three unknown functions as solutions of a linear algebraic system and define a criterion of convergence toward the third unknown function. The method must be classified as an ill-posed problem because it does not provide a unique solution that depends continuously on the data. Thus, the solution is defined as the least-square fit of the oversampled linear system regularized by new smoothing equations. This approach is applied to the dust tails of two comets: Comet Arend-Roland (1957III) and Comet Bennett (1970II). The results obtained confirm the occurrence of outbursts in the dust production rate.