At an Astronomical Conference, an Astronomer Gives a Report on a Star

At an astronomical conference, an astronomer gives a report on a star that interests astronomers because of hints that it may have a planet around it. In his report the astronomer gives the average speed with which this star is moving away from the Sun. How did the astronomer measure this speed?

A) by seeing how the luminosity of the star has been decreasing as it moves farther and farther away
B) by seeing the whole star become much redder than it used to be
C) by measuring the diameter of the star (which is easy to do) and noticing that it is getting smaller and smaller
D) by looking at the Doppler shift in the lines of the star's spectrum
E) the astronomer must be making up stories to impress his colleagues; there is no way to measure the speed with which stars move away or toward us.