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We extend to three dimensions the Concentric Maclaurin Spheroid method forobtaining the self-consistent shape and gravitational field of a rotatingliquid planet, to include a tidal potential from a satellite. We exhibit, forthe first time, the important effect of the planetary rotation rate on tidalresponse of gas giants. Simulations of planets with fast rotation rates likethose of Jupiter and Saturn, exhibit significant changes in calculated tidallove numbers $k_{nm}$ when compared with non-rotating bodies. A test model ofSaturn fitted to observed zonal gravitational multipole harmonics yields$k_2=0.413$, consistent with a recent observational determination from Cassiniastrometry data (Lainey et al., 2016). The calculated love number is robustunder reasonable assumptions of interior rotation rate, satellite parameters,and details of Saturn's interior structure. The method is benchmarked againstseveral published test cases.

The Concentric Maclaurin Spheroid method with tides and a rotational enhancement of Saturn's tidal response