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. Also the ratio h H0 / me c^2 = (G me mp) / e^2. Starting with Mach’s principle, that ‘mass’ of an object is because of its ‘cosmic gravitational potential energy’, we arrive at a possibility that every chunk of matter and energy should experience a fixed value of acceleration H0 c. For the purpose of comparison we express the ‘cosmological red shift’ as deceleration of the photon, and find that the deceleration experienced by the photon matches perfectly with the expected value H0 c. 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 explanation proposed here.