  We present analytical expressions for the tidal Love numbers of a giant
planet with a solid core and a fluid envelope. We model the core as a uniform,
incompressible, elastic solid, and the envelope as a non-viscous fluid
satisfying the $n=1$ polytropic equation of state. We discuss how the Love
numbers depend on the size, density, and shear modulus of the core. We then
model the core as a viscoelastic Maxwell solid and compute the tidal
dissipation rate in the planet as characterized by the imaginary part of the
Love number $k_2$. Our results improve upon existing calculations based on
planetary models with a solid core and a uniform ($n=0$) envelope. Our
analytical expressions for the Love numbers can be applied to study tidal
distortion and viscoelastic dissipation of giant planets with solid cores of
various rheological properties, and our general method can be extended to study
tidal distortion/dissipation of super-earths.
