The smooth Newtonian model of gravity is quantized using the results obtained from the combined theory of Special Relativity (SR) and Quantum Mechanics (QM). The resulting quantum model of gravity, unlike the classical Newtonian model, predicts that there exists an upper limit to the distance between a given pair of masses, called the action distance, beyond which they become gravitationally unbound. Equivalently, at any given radial distance from a large gravitating body of mass, there exists a minimum mass below which the particle would not gravitationally bind to the gravitating body. The attractable mass limit of a gravitating body is determined by equating action distance with the surface radius of the body. Moreover, the quantum model of gravity indicates that the escape velocity from a large gravitating body is a function of the mass of the escaping particle as well. This quantum effect of gravity become significant if the mass of the escaping particles, such as the gas molecules from the exosphere of a planet, are comparable to the attractable mass limit of the planet. The significant discrepancy observed in the escape rates of CH_4 and N_2 species from Pluto's exosphere is used to constrain the reference mass of the combined SR-QM theory to m= 3.2E-45 (kg). The latter is thought to be the physical cut-off limit for massless particles. An Earth-bound experiment is also proposed to test the predictions of the combined SR-QM theory and determine the reference mass with a higher accuracy.