Astronomy and Astrophysics – Astronomy
Scientific paper
May 2008
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008dda....39.1806s&link_type=abstract
American Astronomical Society, DDA meeting #39, #18.06
Astronomy and Astrophysics
Astronomy
Scientific paper
The standard theory of density waves in planetary rings assumes that the orbit of the perturbing satellite is on a fixed orbit. However, resonant interactions between the moons of Saturn produce significant time-dependent variations in the orbital elements of the smaller satellites. Pandora, for example, is resonantly perturbed by Mimas and therefore exhibits a 1.4 km amplitude variation in its semimajor axis with an average period of 612 days (French et al. 2003, Icarus 162: 143). We will present a variational principle for slow, time-dependent modulations of linear density waves. The resulting wave equation describes how slow oscillations in the semimajor axis of the perturbing satellite produce temporal modulations that propagate with the local group velocity of the density wave. The amplitude of the modulations depends on the ratio of the fractional variation of the satellite's semimajor axis to the frequency of the variations. For the case of the Pandora 6:5 inner Lindblad resonance, the modulation is predicted to have an amplitude of about 5%, which agrees with observations reported by Miodrag Sremcevic at this meeting. These temporal modulations provide an important alternative method for measuring the group velocity, and hence the surface mass density, in density waves observed in Saturn's rings.
Miodrag Sremčević
Stewart Glen Robert
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