The wavelength of one particular emission of a certain galaxy has been shifted f

Question

The wavelength of one particular emission of a certain galaxy has been shifted from 572 to 483 nm due to the Doppler effect. What is the radial speed of the galaxy relative to Earth?

I got the answer but they were wrong, only last chance...

Explanation / Answer

Let Radial speed of the galaxy be Vs. Then call r = Vs/C where C = 3*10^8 m/sec Then lamda1 = lamda * (1+r)/sqrt(1-r^2) =>(1+r)/sqrt(1-r^2) = 572/483 = 1.184265 =>(1+r)/1.184265 = sqrt(1-r^2) =>1+r^2+2r = 1.402483615-1.402483615r^2 =>2.402483615r^2+2r-0.402483615 = 0 =>r = 0.1675281415,-1 But r cannot be negative. So r = 0.1675281415 =>Vs = r*C = 0.1675281415c = 5.025844245 * 10^7 m/sec

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