  We show that the characteristic sizes of astrophysical and cosmological
structures, where gravity is the only overall relevant interaction assembling
the system, have a phenomenological relation to the microscopic scales whose
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 introduce typical interaction
lengths. Furthermore, we are able to justify, in a straightforward way, the
Sanders--postulated mass of a vector boson considered in order to obtain the
characteristic sizes of galaxies.
