We first find here that the ratio of: (loss in energy of cosmologically red-shifting photon) and (loss in electrostatic potential-energy of an electron at the same distance D) remains equal to the famous ratio (G me mp) / e2 leading us towards a possibility that ‘cosmological red-shift’ may be due to gravitational effect. So we consider three different possibilities how the reduction in energy of the photon can be understood in terms of gravitational effects; namely: (i) absorption and re-emission of intergalactic photons by the ‘virtual particles’ in space, (ii) photons have to climb the gravitational potential well produced by their own energy, and (iii) the quantum jumps of the photons causing repeated productions and collapses of gravitational fields giving rise to gravitational waves or ripples. Then it is argued that if such a deceleration is true for a chunk of energy called photon, then it must be true for every particle of matter too. Strikingly, the decelerations experienced by the space-probes Pioneer-10, Pioneer-11, Galileo and Ulysses, as carefully measured by Anderson J.D. et. al. match perfectly with the deceleration of the ‘cosmologically red-shifting photons’; thus providing supportive evidence for the simple explanation proposed here.