Imagine that you have found an object out in space. When you use the inverse square law to compute its luminosity, you get a ridiculously large value. You therefore suspect that relativistic beaming is at work - the radiation is coming from a jet traveling at speed v directly towards the Earth, which enhances the observed flux by a factor a (i.e. the measured flux is times greater than it would have been if v=0).

Question

Derive an equation for the velocity v needed to produce an amplification factor a, and write your answer as an equation in the box below. If necessary, use the symbol c in your answer to denote the speed of light, and the symbol G to denote the Gravitational constant.

Answer 1

Just trying to see the answer

Answer 2

v=v^a-v/1-v^a/c^2

Answer 3

v = c*sqrt(1-4/a)

a = 4/θ^2
θ = sqrt(4/a)

inverse formula sqrt(1-v/c^2), so in this case.
v = c*sqrt(1-4/a)