Distance law and formation of satellite systems

Abstract

In the solar system satellite systems of Jupiter, Saturn and Uranus are typical ones. The distribution of the semi-major axis of satellite orbits in each system may be expressed by an empirical formula corresponding to the Titius-Bode law. We found that it can be written as a, = B' . B", where B' and B are constants. Values of B' and B depend on formation conditions of each system.Satellites should be formed in the gas-satellitesimal disk around a planet and by aggregation of satellitesimals. The Ras is the major component in the disk and its damping effect must play an important role in the process ofaggregation ofsatellitesimals. It may be proved that radial small perturbation in the disk can cause the gravitational instability and the formation of gaseous rings with increased density, where satellitesimals can easy aggregat into satellites. Distance law of satellite systemsThere are three typical satellite systems in the solar system, those of Jupiter, Saturn, and Uranus. In each system there are more than 15 satellites. The distribution of their orbital semi-major axis may be expressed by an empirical formula like the Titius-Bode law or that or Blag-Richardson or other (NIETO 1972, PRENTICE et al. 1979, NOWOTNY 1979, DOBO 1981. However, it is difficult to understand the evolutionary implications of n = -co, 0 and negative values. We found a more rational experimental formula of the distance law, in which n is a positive integer; it can be written as (Hu et al. 1984) (1)Some satellites have been discovered in recent years and their orbital semi-major axes do not accord with the same formula. If satellites in each system are divided into groups then similar laws are valid in each group (Fig. 1). Values of B' and B, observed a",,* and calculated aca, for each group and the relative derivation, d = (a,,, -aca,)/aohs, are listed in Tables I , 2

Exoplanet predictions based on the generalized Titius–Bode relation

“…Other analyzes of the Solar System tend to use the generalized 2 parameter TB relation as we have done in this paper (Prentice 1978;Basano & Hughes 1979;Neuhäuser & Feitzinger 1986;Zhong-Wei & Zhi-Xiong 1987;Graner & Dubrulle 1994).…”

Frequency Analysis of Distributions of Near Earth Asteroids Semi-Major Axes

“…Hypotheses that the space of possible orbits in the gravitational systems is discrete long have been the subject of study (Chechelnitsky, 1983;Gulak, 1986aGulak, , 1986bQuiroga, 1984aQuiroga, , 1984bZhong-wey, 1987;Voloshchuk, 1989). According to these theories in the relaxation process of the planetary system during orbiting the central massive body, objects begin to gravitate to certain areas of the space of possible orbits.…”