The energy equations resulting from the dual particle-wave nature of protons, neutrons and/or electrons are used, in conjunction with the necessary relativistic corrections, to obtain an analytical expression for the gravitational constant, G, in terms of h, e, c, and the proton mass m(p), The analytically computed value of G = 6.676 x 10(-11) m(3)/(kg s(2)) is in excellent (within 0.04%) agreement with experiment. The stability of nuclei, also of chemical molecules, is analyzed by the same approach and the energies of formation of the He nucleus (-27.1 MeV), and the H-2 molecule (-4.52 eV) are computed analytically with high accuracy, without any typical quantum mechanical treatment. The unification of strong interactions, gravitational and electrostatic forces is also demonstrated and discussed. (c) 2005 Elsevier B.V. All fights reserved.