An unaccounted component on the Prometheus and Pandora offset angular positions

Abstract

Near the turning of this millennium (1996–2004) it was detected that Prometheus and Pandora were not in their angular positions as predicted from their discoveries by the Voyager spacecrafts (1980). This is known as the problem of the lags of Prometheus and Pandora. The explanation for the origin of these lags is the chaotic motion associated with 121:118 mean motion resonance between the satellites. In the present work we revisit this problem and adopting the most extensive set of lags data, given by [R.G. French et al., Icarus 162, 143 (2003)], to show the need of unaccounted effects to produce the measured lags. By the analysis of conservation of angular momentum it can be verified that the mutual interaction between Prometheus and Pandora should be inversely proportional to the ratio of their masses. In this way, only the gravitational interaction between the two satellites does not explain such values. Consequently, the ratio between the lags of Prometheus and Pandora, Q, should be constant, and approximately the value of the inverse ratio between their masses (0.56, from [R.G. French et al., Icarus 162, 143 (2003)]). However, the values of Q from the measured lags are much higher, ranging from 48% up to 68% larger. Beyond that, the values increase over time in a rate given by the equation Q(t = 0.067 + 0.013t). Therefore, this analysis clearly shows the need of other mechanisms beyond the mutual interaction between Prometheus and Pandora in order to produce such values of lags. We estimate that at least one effect that produces an additional variation of mean motion of about 0.45°/year in one of the satellites for about 20 years would be necessary.