The paper demonstrates a new method of obtaining values of the Universe parameters. The method is based on the revealed relationship between the parameters of the Universe and fundamental physical constants. New ratios of the dimensional parameters of the observable Universe are derived, which give the fine structure constant alpha. This is an unexpected result, since the fine structure constant refers to the microcosm, but not to the Universe. There are many of these equations. They have no explanation. There is no answer as to why, on such enormous scales, the ratios of the dimensional parameters of the universe give the alpha constant. Despite the lack of explanation, the new equations open up new possibilities in cosmology. The constant "alpha" and the parameters of the Universe are present together in one equation. This makes it possible to use the high precision of the alpha constant to calculate the values of the parameters of the observable Universe. This provides a high accuracy of the parameters of the observable Universe close to the accuracy of the Newtonian constant of gravitation G. New cosmological equations are derived, from which the value of the cosmological acceleration is obtained. This result allows us to solve the long-standing Pioneer-anomaly problem.