[Exponential distance laws for satellite systems]

A revised Titius-Bode law for the solar system was proposed by Basano and Hugues (1979), by introducing three missing planets. This law can be written /b a//sub n/= alpha beta /sup n/ (with alpha =0.2853 AU and beta =1.5226), which gives the distances /b a/ /sub n/ of the /b n/th planet for successive integers /b n/. An new method is proposed to find this Basano-Hugues law for the solar system. Based upon the comparison of the ratios of successive distances, this method can be applied to the satellite systems of the three giant planets, Jupiter, Saturn and Uranus by introducing `missing satellites' to fill the gaps in satellites sequences. Three exponential distance relations are found similar to that of Basano-Hugues. All the empty places in the inner parts of satellite systems are occupied by rings and small satellites. In the Uranian system, there are two empty places which could be filled by new undiscovered small satellites.