The frequency-dependent dipole polarizabilities are calculated for the five lowest states 4(1)S, 5(1)S, 4(1)P, 4(3)P and 5(3)S of Ca by using a time-dependent gauge invariant method. The difference of the polarizability (alpha(P-3) - alpha(S-1)) of 112.9 a.u., between the excited P-3 state and the 4(1)S ground state calculated from the TDGI method is in good agreement with the two experimental measurements of 96.5 +/- 16.4 and 90.4 +/- 13.8 a.u. obtained from the Stark frequency and phase shifts, respectively, by Morinaga et al. [Phys. Rev. A 54 (1996) 21]. As a consequence of our previous work referring to the Mg atom, the length formulation of the oscillator strengths has been used. Estimations of the long-range dispersion coefficients for the first molecular state dissociations of Ca-2 and CaMg are proposed. Most of the results are new, and predict a repulsive behaviour for the (1)Pi (g,u) and (3)Sigma (+)(g,u) states of the 4(1)S-4(1)P and 5(1)S-4(1)P interactions, respectively.