This letter presents some new expressions for gravity without the big G and proposes their possible wave-theoretical-explanation. This attempt leads to some insight that: (i) We need the proportionality-constant G because we measure masses and distances in our arbitrarily-chosen units of kg. and meters; but if we measure ‘mass’ as a fraction of ‘total-mass of the universe’ M0 and measure distances as a fraction of ‘radius-of-the-universe’R0 then there is no need for the proportionality-constant G. However, large uncertainties in the M0 and R0 limit the general application of this relation presently. (ii) The strength of gravity would be different if the total-mass of the universe were different. Then this possibility is supported with the help of wave-theory. (iii) This understanding of G leads to an insight that Planck’s-length, Planck-mass and Planck’s unit of time are geometric-mean-values of astrophysical quantities like: total-mass of the universe and the smallest-possible-mass h H0 / c^2. (iv) There appears a law followed by various systems-of-matter, like: the electron, the proton, the nucleus-of-atom, the globular-clusters, the spiral-galaxies, the galactic-clusters and the whole universe; that their ratio Mass / Radius^2 remains constant. This law seems to be more fundamental than the fundamental-forces because it is obeyed irrespective of the case, whether the system is bound by strong-force, electric-force, or gravitational-force.