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Place the carbon and sulfur nuclei on a line separated by $r$, with masses $m_{\mathrm{C}}$ and $m_{\mathrm{S}}$. The center of mass lies between them and closer to the heavier sulfur nucleus. In the linear rigid rotor approximation, $r$ remains fixed while the molecule rotates.

The rotational state populations start at $N_0/N_0=1$. Their $2J+1$ statistical weight factor initially favors higher $J$, while the Boltzmann factor eventually suppresses them, producing one maximum followed by a tail tending to zero. The physically allowed values occur at integer $J$; a continuous curve only guides the eye.

Low rotational energy spacings can be excited in cold interstellar gas when electronic and most vibrational excitations are frozen out. A polar molecule such as carbon monosulfide has allowed electric dipole transition lines whose frequencies depend on its moment of inertia, providing a distinctive pattern for rotational spectral line assignment. Several matching spectral lines and their isotope shifts give a much stronger identification than one coincidence. The method is especially effective for polar species; a molecule without a permanent electric dipole moment lacks an ordinary pure electric-dipole rotational spectrum.