Quantitative analysis of the Dermott-Gold theory for Uranus's rings

A summary is presented of an investigation which supplements the largely qualitative analysis conducted by Dermott and Gold (1977). Dermott and Gold have attempted to explain the locations of Uranus's rings in terms of resonances between ring particles and pairs of satellites. An equation of motion, analogous to that of a pendulum, is derived, taking into account a study by Wilkens (1933) of possible three-body resonances involving one minor and two major planets. Dermott and Gold had concluded that the observed pattern is probably due primarily to the effect of Ariel-Titania and Ariel-Oberon pairs. However, on the basis of the values derived in the reported investigation it is seen that Miranda plays the key role rather than Ariel, in spite of the small mass of the former. It is concluded that a decisive test of the Dermott-Gold theory has to await further observational details concerning the Uranus's rings.