Every 2 years, more or less, The New York Times publishes an article in which some astronomer

Question:

Every 2 years, more or less, The New York Times publishes an article in which some astronomer claims to have found an object traveling faster than the speed of light. Many of these reports result from a failure to distinguish what is seen from what is observed??that is, from a failure to account for light travel time. Here's an example: A star is traveling with speed v at an angle 0 to the line of sight (Fig. 12.6). What is its apparent speed across the sky'? (Suppose the light signal from b reaches the earth at a time at after the signal from a, and the star has meanwhile advanced a distance as across the celestial sphere; by "apparent speed" I mean As/At.) What angle 0 gives the maximum apparent speed? Show that the apparent speed can be much greater than c, even if v itself is less than c.