In this article we have solved a hypothetical problem related to the stability and gross properties
of two-dimensional self-gravitating stellar objects using the Thomas?Fermi model. The formalism
presented here is an extension of the standard three-dimensional problem discussed in the book on
statistical physics, Part I by Landau and Lifshitz. Further, the formalism presented in this article
may be considered a class problem for post-graduate-level students of physics or may be assigned as
a part of their dissertation project.