Abstract <p>In the framework of nonextensive statistical mechanics of Kaniadakis, the integral stability theorem of Chandrasekhar has been generalized for a spherically symmetric distribution of matter and blackbody radiation in a protoplanetary cloud being in a state of gravitational equilibrium. For this purpose, we use the elements of deformed thermodynamics for an ideal gas, the deformed canonical Gibbs distribution, as well as the effective gravitational constant evaluated within the Verlinde formalisms. In the κ-statistics context, the modified thermodynamic properties of blackbody radiation, specifically, the analog of Stefan’s law for the radiation energy and the generalized expressions for the entropy, heat capacity, and radiation pressure, have been obtained. The proposed method of combining the mentioned anomalous physical processes provides an alternative to the classical procedure of Chandrasekhar’s derivation of the well-known integral theorems for gaseous configurations being in gravitational equilibrium. These results are to be used in modeling the processes of joint formation and evolution of protostars and an exoplanetary cloud from a single nebula.</p>