It is actually possible to interpret gravitation as a property of space in a purely classical way. We note that an extended self-gravitating system equilibrium depends directly on the number of dimensions of the space in which it evolves. Given these precisions, we review the principal thermodynamical knowledge in the context of classical gravity with arbitrary dimension of space. Stability analyses for bounded 3D systems, namely the Antonov instability paradigm, are then associated to some amazing properties of globular clusters and galaxies.