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FIZIKA B 4 (1995) 1, 11-28
 
STABILITY OF GRAVITATIONALLY-BOUND MANY-BODY SYSTEMS
ANTUN RUB�I� and JASNA RUB�I�
Department of Physics, Faculty of Science, University of Zagreb, Bijeni�ka cesta 32,
POB 162, 41 001 Zagreb, Croatia
Received 21 December 1994
Revised manuscript received 17 March 1995
The semimajor axes of planetary orbits and of major satellites of the planets in the
solar system are described by a simple parabolic law, rn = const�n2,
where n is an integer. The orbital periods Tn are proportional to n3
, thus obeying the third Kepler's law. The radical change, compared with the previous
approaches, is that n = 1 is assigned to all terrestrial planets, n = 2
to Jupiter, etc. This is strongly suggested by the analysis of astronomical data. Hence,
terrestrial planets are considered as a subgroup of Jovian planets, and have been formed
between the Sun and Jupiter in place of one giant planet of the Jovian group. The reason
seems to be the temperature limit of about 200 K, corresponding to a distance of about 5�1011
m (3.4 a.u.), that causes similar consequences as the well-known Roche limit for
satellites of a planet. Relationships for rn, Tn and
other relevant quantities, which also depend on the integer n, are related to the
discretization of angular momentum per unit mass of orbiting body. The mass of a central
body appears as a scaling factor giving a unique approach to all systems. The mean
deviation of observed orbital radii from the parabolic law for rn is from 3.5%
to 7.6% , depending on the system. On the basis of the analysis, we propose the hypotheses
on stability of gravitationally-bound many-body systems.
UDC 523.2, 531.35
PACS 95.10.Ce, 95.10.Fh, 96.30.-t
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