Non-Newtonian gravity, fluctuative hypothesis and the sizes of astrophysical structures

We show that the characteristic sizes of astrophysical and cosmological str uctures, where gravity is the only overall relevant interaction assembling the system, have a phenomenological relation to the microscopic scales whos e order of magnitude is essentially ruled by the Compton wavelength of the proton. This result agrees with the absence of screening mechanisms for the gravitational interaction and could be connected to the presence of Yukawa correcting terms in the Newtonian potential which introduces typical inter action lengths. Furthermore, we are able to justify, in a straightforward w ay, the Sanders-postulated mass of a vector boson considered in order to ob tain the characteristic sizes of galaxies.