Within density functional theory, we have obtained the structure of (4)He droplets doped with neutral calcium atoms. These results have been used, in conjunction with newly determined ab initio (1)Sigma and (1)Pi Ca-He pair potentials, to address the 4s4p (1)P(1)<- 4s(2) (1)S(0) transition of the attached Ca atom, finding a fairly good agreement with absorption experimental data. We have studied the drop structure as a function of the position of the Ca atom with respect to the center of mass of the helium moiety. The interplay between the density oscillations arising from the helium intrinsic structure and the density oscillations produced by the impurity in its neighborhood plays a role in the determination of the equilibrium state, and hence in the solvation properties of alkaline earth atoms. In a case of study, the thermal motion of the impurity within the drop surface region has been analyzed in a semiquantitative way. We have found that, although the atomic shift shows a sizable dependence on the impurity location, the thermal effect is statistically small, contributing by about 10% to the line broadening. The structure of vortices attached to the calcium atom has been also addressed, and its effect on the calcium absorption spectrum discussed. At variance with previous theoretical predictions, we conclude that spectroscopic experiments on Ca atoms attached to (4)He drops will be likely unable to detect the presence of quantized vortices in helium nanodrops.