# Relativistic Doppler Effect

Light from an astronomical source is found to be shifted to a one percent lower frequency than had the source been at rest. What radial velocity could cause such a shift?

A. $3.0*10^7$ m/s moving away from the observer
B. $3.0*10^6$m/s moving away from the observer
C. $3.0*10^6$ m/s moving toward the observer
D. $1.5 *10^6$ m/s moving toward the observer
E. $1.5Ã*10^6$ m/s moving away from the observer
the relativistic Doppler factor is

$F s/F0 = \sqrt{(1-\beta)/(1+\beta)}$

where $\beta = v/c$

$F s= 99%*F0 =0.99*F0$

$(1-\beta)/(1+\beta) =0.9801$

$1- \beta = 0.9801 +0.9801*\beta$

$0.0199 =1.9801*beta$

$\beta =0.010049997$

$V = c*\beta$

$V = 3.015*10^6$ m/s

The shift is toward lower frequencies (red shift), it means the source is moving away from the observer.