Light is gathered from a distant star and one of teh spectral lines is observed at 520nm when it should be 400nm. The velocity of this star is ______km/s

Answer 1

For this large shift in wavelength, the usual approximation v/c = (delta lambda)/lambda is not good enough. The valid equation is in terms of frequency f: f/f_o = 1 - v/c = lambda_o/lambda, where the subscript "o" refers to rest or normal frequency or wavelength. In this case, with slight rearranging, v/c = 1 - 400/520 = 0.2308. With c = 299,800 km/s, the velocity of the star is about 69,200 km/s away from the observer.