We present simulated observations of the Doppler shifts of the solar Mg I Fraunhofer line scattered by asteroidal, cometary, and trans-Neptunian dust particles. The studies are based on the results of integrations of orbital evolution of particles under the gravitational influence of planets, the Poynting-Robertson drag, radiation pressure, and solar wind drag. The derived shifts in the centroid and profile of the line with solar elongation are different for different sources of dust. A comparison of the velocities of zodiacal dust particles based on these numerical integrations with the velocities obtained from WHAM observations shows that the fraction of cometary dust particles among zodiacal dust particles is significant and can be dominant. A considerable fraction of trans-Neptunian dust particles among zodiacal dust particles also fits different observations. The mean eccentricity of zodiacal dust particles is estimated to be about 0.5.