Based on a postulate that photons of low frequencies (undetectable by current technology) are the gravity force carrier, the paper derives quantitative results that are the same as or very similar to those derived in the special and general relativity theories and explains experiments and observations better. These quantitative results are the mass-energy formula, the energy momentum equation, and those for relative mass, the transverse Doppler effect, gravitational red shift, planetary precession, the deflection angle of light in gravitational lensing, the orbits around a black hole, and the strength and direction of gravitational waves (orbit decay of pulsars). At the detailed level, the results and explanations are different from some of those achieved using Einstein’s relativity theory, such as the explanation of the null experimental result for the Doppler effect of electromagnetic waves reflected from a transversely moving surface, the reason for gravitational red shift, and the size of the light sphere around a black hole. The paper claims that both the high-order Doppler effect and the gravitational red shift occur only at the point of photon emission. The paper also explains why the predicted deflection angle of gravitational lensing is slightly greater than the measured deflection angle and why the predicted pulsar orbit decay is close but differs from calculations based on observations.