# Stellar object ejects a jet Special Relativity

1. Dec 5, 2011

### crimsonidol

1. The problem statement, all variables and given/known data
A stellar object at some known large distance ejects a ‘jet’ at speed v towards
an observer obliquely, making an angle θ with the line of sight. To the observer the
jet appears to be ejected sideways at speed V . Prove V = c sin θ (c/v − cos θ )−1 , and
show that this can exceed c, for example, when θ = 45◦ . [Indeed, such apparently
superluminal jets once had observers worried—briefly.]
Question from Rindler 2.21

2. Relevant equations
Nothing more is supplied in the question.

3. The attempt at a solution
I have tried to use the velocity transformation in the frame of stellar object?(Say frame S). Since I know the speed of the object in observers frame(say S') which is V in the y direction and velocity u'(0,V,0) say in standart configuration.and I know the vcosθ is the speed in x direction vsinθ is the speed in y direction and velocity u(vcosθ,vsinθ,0) in the frame S. However I do not know the observer's relative speed in stellar object's frame.
I tried to find by applying velocity transformation in x direction first to find relative speed of observer and then applied in y direction but no use. I have found out to satisfy the given equation speed of the observer should be c relative to the stellar object. What do I miss? I think I'm missing something silly but I cannot find out. I have been thinking for days. Please give me clue.

2. Dec 6, 2011

### crimsonidol

I need a spark :S
If anything is unclear I may rewrite it.

3. Dec 8, 2011

### crimsonidol

it is not a homework but i need to solve this. it is killing me slowly and i'm in a closed loop coming to the same point everytime. please help me about it.

4. Dec 8, 2011

### crimsonidol

Sorry I'm not comfortable with the codes so I wrote a paper and uploaded it. Hope some1 can tell me where I have gone wrong.
http://imgur.com/ZN50J

5. Dec 8, 2011

### e.bar.goum

You could read a paper about the quasar 3C 273 for hints.

6. Dec 9, 2011

### crimsonidol

ok i thing I figured it out.
Thanks e.bar.goum I look for quasar and found this https://docs.google.com/viewer?url=...05218/49609/excerpt/9780521849609_excerpt.pdf

too many assumptions in it by the way. you should take the speed of the stellar object's velocity too small relative to jet. Lorent'z transformation again does not much help here. You need to send two photons in consecutive times Δt seperated. And then calculate the time observer will measure and divide that time by vsinθ/Δt.Then you will get it.