Kepler's constant in celestial mechanics, in electromagnetism and in cosmology

- Mykola Kosinov

## Abstract

It is well known that the Kepler constant R^3/T^2 is a constant of celestial mechanics. It is shown here that the ratio of the cube of the distance to the square of time is a constant for many physical objects and is of a universal nature. The cosmological equation GMUTU 2 =RU 3 is obtained, which includes the constant RU^3/TU^2 as a ratio of the parameters of the Universe. The cosmological equation combines 4 parameters of the Universe: mass MU, radius RU, time TU and the Newtonian constant of gravitation G. In the cosmological equation, the constant RU^3/TU^2 is a constant of the Universe. The electrodynamic equation e 2 t0 2 =mere 3 4πε0 is obtained, which includes the constant re^3/t0^2 as a ratio of the parameters of the electron. The equation combines 4 parameters of the electron: mass me, classical radius of the electron re, characteristic time t0, electric charge e. In the equation containing the electron parameters, the constant re^3/t0^2 is a constant of electromagnetism. These equations show that the limits of applicability of Kepler's ratio R^3/T^2 go far beyond planetary mechanics. Ratio R^3/T^2 is a constant not only of celestial mechanics, but also a constant of the Universe and even a constant of the electron.17 Oct 2024Submitted to *ESS Open Archive * 22 Oct 2024Published in *ESS Open Archive *