The ES Log-normal Distribution Determined by the Einstein Median as the Scale Parameter and the Shannon Shape Parameter

The guiding principle of this contribution is the mutual interplay between the Solar gravitational field and the Maxwell-Boltzmann distribution of speeds of atoms and the observed Fraunhofer lines. We know from numerous experiments that the Newtonian gravitational constant does not depend on the atomic mass, temperature, pressure and many other particle parameters. Therefore, we should discover a universal distribution function that could be used for all atoms and their properties for a given gravitational field. We have introduced the ES log-normal distribution fully determined by the Einstein median as the scale parameter and the Shannon shape parameter σ = 1/√6. Shannon formulated this shape parameter for the log-normal distribution describing systems with the maximum entropy formation. This ES log-normal distribution function determines the most effective mutual interactions between the gravitational field and the Maxwell-Boltzmann particles. In order to make the Einstein median formula more general, we have introduced the model of the active solid angle of the source of gravity with values 1 ≤ Ω ≤ 4 steradians. We have tested this ES log-normal distribution with three datasets measured on the Solar disc and two datasets measured on the surface of the Earth using the Mössbauer effect. There were predicted some new properties of those datasets. This model might stimulate and promote new initiatives to collect new better datasets for the Solar disc and the Mössbauer effect.