Like jets emitted from some galaxies (see Figure 1-41), some distant astronomical objects can appear to travel at speeds greater than c across our line of sight. Suppose distant galaxy AB15 moving with velocity v at an angle θ with respect to the direction toward Earth emits two bright flashes of light separated by time Δt on the galaxy AB15 local clock. Show that 

(a) The time interval Δt_Earth = Δt(1-β cos θ) and 

(b) The apparent speed of AB15 measured by observers on Earth is

(c) For β = 0.75, compute the value of u for which v_app = c.

Figure 1-41

Transcribed Image Text:

Vapp AXEarth AtEarth ß sin 0 1 ß cos 0