Hubble's law has been the subject of study in recent years, the problem of the Hubble Tension with respect to the existence of various values of the parameter and the results of dark energy with respect to a change in the trend of the parameter value about 6.5 billion years ago have brought it into play. Through the study of the Rh=ct universe model and by going deeper into it, we have addressed these problems. This model of the linear expansion universe, Rh=ct, studied in recent years by Professor Fulvio Melia, is one of the best to respond to the new challenges posed by experimental research in astrophysics. For this reason, we have opted for this model to apply our hypothesis regarding the use of relativistic Doppler equations in calculating the speed at which galaxies move away from the observation point, the Earth. This has allowed us to develop, within the framework of this model of the universe, a new equation that relates the Hubble parameter with the red shift. The result, in light of their predictions, appears to be consistent with some of the issues raised by the Hubble Tension and Dark Energy.