A binary star system consists of two stars, P P\,P and QQQ, orbiting their common centre of mass. An observer in the plane of the orbit views the system. At a particular instant, star P P\,P is moving directly towards the observer with speed vvv, and star Q Q\,Q is moving directly away from the observer with speed vvv (where v≪cv \ll cv≪c).
A spectral line has an emission wavelength λ0 \lambda_0\,λ0 and frequency f0 f_0\,f0 in the rest frame of the stars.
Which row correctly describes the observed wavelength λP \lambda_P\,λP from star P P\,P and the observed frequency fQ f_Q\,fQ from star QQQ?
λP=λ0(1+vc)\lambda_P = \lambda_0\left(1 + \frac{v}{c}\right)λP=λ0(1+cv) and fQ=f0(1−vc)f_Q = f_0\left(1 - \frac{v}{c}\right)fQ=f0(1−cv)
λP=λ0(1−vc)\lambda_P = \lambda_0\left(1 - \frac{v}{c}\right)λP=λ0(1−cv) and fQ=f0(1−vc)f_Q = f_0\left(1 - \frac{v}{c}\right)fQ=f0(1−cv)
λP=λ0(1−vc)\lambda_P = \lambda_0\left(1 - \frac{v}{c}\right)λP=λ0(1−cv) and fQ=f0(1+vc)f_Q = f_0\left(1 + \frac{v}{c}\right)fQ=f0(1+cv)
λP=λ0(1+vc)\lambda_P = \lambda_0\left(1 + \frac{v}{c}\right)λP=λ0(1+cv) and fQ=f0(1+vc)f_Q = f_0\left(1 + \frac{v}{c}\right)fQ=f0(1+cv)