- #1
Silviu
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Homework Statement
A body emits photons of frequency ##\omega_*## at equal rates in all direction in its rest frame. An observer is moving with speed V relative to the body in the x direction. Find the rate at which the photons are received per unit solid angle ##dN/dt'd\Omega'## a large distance away in the observer's frame as a function of angle ##\alpha'## from the x'-axis. Find the luminosity per unit solid angle ##dL'd\Omega## a large distance away as a function of ##\alpha'##
Homework Equations
##cos\alpha'=\frac{cos\alpha + V}{1+Vcos \alpha}##
The Attempt at a Solution
If in the stationary S frame we have N photons per ##dt## per ##d\Omega## this means in the S' the same number of photons per ##dt'=dt/\gamma## per ##d\Omega'##. ##d\Omega = sin(\theta)d\theta d\phi## so in S' ##d\Omega' = sin(\theta') d\theta' d\phi'##. As they say long distance, I assume we can work in small angle approximation. Also as they want as a function of ##\alpha'## I can take both ##\omega## and ##\phi## to be ##\alpha##? But I am not sure how to go from the original formula to something useful to plug in here.
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