Ancient Raindrops and the Paradox of a Faint Young Sun*

Recently, scientists found and studied traces of raindrops on stones from South Africa of a rain that occurred 2.7 billion years ago in the Archean Eon. Based on the experimental work, it was concluded that neither strong pressure-broadening infrared absorption of greenhouse gases nor the extreme pressure of carbon dioxide gas in the atmosphere are satisfactory explanations for warming the early Earth. In our theoretical work we used thermodynamics and hydrodynamics to establish that the size of drops in a steady rainfall is described by a lognormal distribution law, and the mass median diameter of raindrops depends on the gravitational acceleration. However, according to the large numbers hypothesis first proposed by Paul Dirac, for the scale of billions of years comparable to the age of the Universe, the gravitational acceleration on Earth may be not a constant. By applying the Dirac large numbers hypothesis, we find that the ratio of air dynamic viscosities between the current time and Archean Eon depends on the ratio of respective values of gravitational accelerations. Analyzing the dependence of air viscosity on temperature and composition, we conclude that stronger gravitational field on prehistoric Earth can be possible explanation of the "faint young Sun paradox".