Tidal frequency dependence of the Saturnian k<inf>2</inf> Love number

Abstract

Context. Love numbers describe the fluid and elastic response of a body to the tidal force of another massive object. By quantifying these numbers, we can more accurately model the interiors of the celestial objects concerned. Aims. We determine Saturn’s degree-2 Love number, k2, at four different tidal forcing frequencies. Methods. To do this, we used astrometric data from the Cassini spacecraft and a dynamical model of the orbits of Saturn’s moons. Results. The values obtained for k2 are 0.384 ± 0.015, 0.370 ± 0.023, 0.388 ± 0.006, and 0.376 ± 0.007 (1σ error bar) for the tidal frequencies of Janus–Epimetheus, Mimas, Tethys, and Dione. Conclusions. We show that these values are compatible with a constant Love number formulation. In addition, we compared the observed values with models of dynamical tides excited in Saturn’s interior, also finding a good agreement. Future increases in the measurement precision of Love numbers will provide new constraints on the internal structure of Saturn.