Love number k₂ in dependence on the ratio of core mass to total mass for theoretical two-layer models consisting of a constant density core and an n = 1 polytropic envelope, see Eqs. (7) and (8). The lines show solutions for core radii of x_c = 0.05 (solid), 0.10 (dashed), 0.15 (dotted) and 0.20 (dash-dotted). The black diamond shows the solution for the core-less polytropic planet. To obtain different values for M_core/M_total the parameter q has been varied. q = π gives the minimum value of M_core/M_total. Thick lines show the region where 0.9π < q < π which corresponds to realistic ρ₁(x_c)/A ratios.