Perturbed spherically symmetric dust solution of the field equations in observational coordinates with cosmological data functions

Using the framework for solving the spherically symmetric field equations i n observational coordinates given by Araujo & Stoeger, we present their for mulation and solution in the perturbed Friedmann-Lemaitre-Robertson-Walker spherically symmetric case wit observational data representing galaxy red-s hifts, number counts, and observer area distances as functions of redshift on our past light cone. The importance of the central conditions, those whi ch must hold on our world line C, is emphasized. In detailing the solution for these perturbations, we discuss the gauge problem and its resolution in this context as well as how errors and gaps in the data are propagated tog ether wit the genuine perturbations. Tis will provide guidance for solving and interpreting the solutions of the more complicated general perturbation problem with observational data on our past light cone.