Spherically averaged center-of-mass-motion (extracule) densities $d(R)$ in position space and $\overline{d}(P)$ in momentum space represent probability densities of finding center-of-mass radii $|{\mathbf{r}}_{j}+{\mathbf{r}}_{k}|/2$ and $|{\mathbf{p}}_{j}+{\mathbf{p}}_{k}|/2$ of any pair of electrons $j$ and $k$ to be $R$ and $P,$ respectively. Theoretical analysis shows that in the Hartree-Fock approximation, the individual spin-orbital-pair component of the extracule density has a definite relation with the corresponding one of the relative-motion (intracule) density, but the total extracule and intracule densities are not related in a simple manner. Using the numerical Hartree-Fock method, the extracule densities $d(R)$ and $\overline{d}(P)$ are constructed and examined systematically for the atoms from He to Xe in their ground state. In position space, the extracule density $d(R)$ is a monotonically decreasing function for all the atoms. In momentum space, however, the extracule densities $\overline{d}(P)$ are found to be classified into two types according to the location of a maximum. These different behaviors of the densities $d(R)$ and $\overline{d}(P)$ are studied in detail based on the contributions of electrons in a pair of atomic subshells and spin orbitals.