Exponential Distance Relations in Planetary-like Systems Generated At Random

TLDR: In this article, it was shown that pure chance or random processes only cannot explain the planetary and satellite distance distributions, in particular the exponential spacings, by comparing the distance relations of real systems to these of planetary-like systems generated at random.

Abstract: It is often thought that the exponential distance relations that can be found amongst the distances of the planets and of the satellites of Jupiter, Saturn, and Uranus, of the form an = αβn, with an being the semi-major axis of the nth body, can be similarly represented by sequences of sorted random numbers generated with some constraints corresponding to certain physical processes. We give in this paper some indications showing that pure chance or random processes only cannot explain the planetary and satellite distance distributions, in particular the exponential spacings, by comparing the distance relations of the real systems to these of planetary-like systems generated at random.