Exponential distance relations in planetary-like systems generated at random |
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| Authors: | Vladimir Pletser |
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| Institution: | (1) Institut d'Astronomie et de Géophysique G. Lemaître, University of Louvain-la-Neuve, Belgium |
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| 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 a
n
=  
n
, with a
n
being the semi-major axis of the n
th 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.Exponential distance relations for the present planetary and satellites systems of Jupiter, Saturn and Uranus are described, considering the two cases without and with introduction of  holes for the large spacings observed in the sequences of bodies.Random systems are created by generating distances at random following uniform, normal and exponential distributions, with no consideration for other orbital elements or masses as we are only interested in distance relations. Random systems without constraints are first compared to the real systems. In a following step, random systems with a corresponding number of bodies to that of the real systems and with the constraint of having a number of large spacings equivalent to that of the real systems are investigated. In a later step, we impose on the generation process the additional constraint of the closeness not too close condition, i.e. for the random systems to have distances between adjacent bodies greater than critical attraction distances calculated by considering the present masses of the real main planets and satellites.Comparisons of the regression coefficients means of the exponential distance relations of random systems to the characteristics of the real systems show that there are significant differences, in particular the coefficients of the random systems are on average smaller than for the corresponding real systems, except for some particular cases which are shown not to be significant.It is concluded that distance relations observed in the present real systems can not be compared to sequences of sorted random numbers. Furthermore, additional physical processes other than the closeness not too close, have to be considered to explain the observed distance relations and in particular the exponential spacings. |
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