Ratio of Gravitational Force to Electric Force from Empirical Equations in Terms of the Cosmic Microwave Background Temperature

Abstract

Previously, we presented several empirical equations using the cosmic microwave background (CMB) temperature. Next, we propose an empirical equation for the fine-structure constant. Considering the compatibility among these empirical equations, the CMB temperature (<i>T</i><i>_c</i>) and gravitational constant (<i>G</i>) were calculated to be 2.726312 K and 6.673778 &#215; 10^&#8722;11 m³&#8729;kg^&#8722;1&#8729;s^&#8722;2, respectively. Every equation could be explained in terms of the Compton length of an electron ( &lambda; <i>_e</i>), the Compton length of a proton ( &lambda; <i>_p</i>) and a . Furthermore, every equation could also be explained in terms of Avogadro&#8217;s number and the number of electrons in 1 C. However, the ratio of the gravitational force to the electric force cannot be uniquely determined when the unit of the Planck constant (Js) is changed. In this study, we showed that every equation can be described in terms of Planck constant. From the assumption of minimum mass, the ratio of gravitational force to electric force could be elucidated.