Prometheus and Pandora: masses and orbital positions during the Cassini tour

Hubble Space Telescope ( HST) images of Prometheus and Pandora show longitude discrepancies of about 20° with respect to the Voyager ephemerides, with an abrupt change in mean motion at the end of 2000 (French et al., 2003, Icarus 162, 143–170; French and McGhee, 2003, Bull. Am. Astron. Soc. 34, 06.07). These discrepancies are anti-correlated and arise from chaotic interactions between the two moons, occurring at interval of 6.2 yr, when their apses are anti-aligned (Goldreich and Rappaport, 2003a, Icarus 162, 391–399). This behavior is attributed to the overlap of four 121:118 apse-type mean motion resonances (Goldreich and Rappaport, 2003b, Icarus 166, 320–327). We study the Prometheus–Pandora system using a Radau-type integrator taking into account Saturn's oblateness up to and including terms in J 6 , plus the effects of the major satellites. We first confirm the chaotic behavior of Prometheus and Pandora. By fitting the numerical integrations to the HST data (French et al., 2003, Icarus 162, 143–170; French and McGhee, 2003, Bull. Am. Astron. Soc. 34, 06.07), we derive the satellite masses. The resulting GM values (with their standard 3- σ errors) for Prometheus and Pandora are respectively GM PR = ( 1.41 −0.25 +0.10 ) × 10 −2 and GM PA = ( 1.03 −0.19 +0.10 ) × 10 −2 km 3 s −2 . Using the nominal shape of the two moons (Thomas, 1989, Icarus 77, 248–274), we derive Prometheus and Pandora's densities, 0.40 +0.03 −0.07 and 0.49 +0.05 −0.09 g cm −3, respectively. Our numerical fits also enable us to constrain the time of the latest apse anti-alignment in 2000. Finally, using our fit, we predict the orbital positions of the two satellites during the Cassini tour, and provide a lower limit of the uncertainties due to chaos. These uncertainties amount to about 0.2° in mean longitude at the arrival of the Cassini spacecraft in July 2004, and to about 3° in 2008, at the end of the nominal tour.