In the previous work, we established a connection between the age of the universe, or the resulting Hubble radius, and the proton radius. Thereby we already noticed that the dimensionless fine structure constant α (1/137.036) is a link of several numerical correlations of the atomic world and the universe. And we also noticed that the delta value 1.00602 (we will call it δ_H hereafter) not only arises, if one considers the ratio from the mass square of the hydrogen atom by the product of electron mass and proton mass ( m_H²/(m_p*m_e) and divides this value by 10/3 * 4/α, but also arises in other contexts, if one assumes that the ratio between electromagnetic force and gravitational force between proton and electron exactly corresponds to the value 20/3 * 2^128 and makes for this a minimal adjustment of the currently accepted value of the gravitational constant. Based on the consideration that 3/10 of the classical electron radius r_e would be the physically more sensible electron radius and that this radius is only a touch away from the proton radius r_p - and that this small difference between 3/10*r_e and r_p can be described by δ_H, we will derive two very similar equations for determining m_p/m_e, both only dependent on alpha and of the form: m_p/m_e = 10/3 * 4/α + 9 + x(α) - where x(α) in both cases is a value of the order of δ_H-1 = 0.00602 With 1836.15267446 and 1836.15267148 they deliver values that correspond to 9 digits with the current CODATA value for the ratio m_p/m_e and, with this accuracy, are even within the range of the current precision measurements for the fine structure constant α.