Cosmology is primarily based on the measured value of Hubble’s constant. Though its value is still being refined, the currently available value shows interesting relations with the other physical constants, as derived here. These relations can be helpful for: (i) arriving at theoretical value of Hubble’s constant, and (ii) for understanding correct mechanism behind the cosmological red-shift. The relationship of Hubble’s constant H0 with the other constants derived here are: (h H0 / me c^2) = [ ( G me mp ) / h c ] = [ λC / R0 ] = [ (G mp / c^2) / λC ] = [ mp / M0 ]^1/2 ; here: h is Planck’s constant, c the speed of light, and λC is Compton-wavelength of the electron, and me and mp are masses of the electron and proton respectively. These relations suggest that either the cosmological red-shift is based on gravity, or gravity is due to the cosmological red-shift-effect on the photons exchanged between the particles.