Observed radial velocity of a Binary Star system

[hydrogène]

Homework Statement

Consider a double-star system with two stars, A and B, in circular orbits of the same period T about their center of mass. The Earth is in the plane defined by these orbits at a distance R of many light-years. Let the speed of A in its orbit be u; then at any instant it has a velocity v (=u cosθ) along the line from the double-star system to the earth. When light emitted from A reaches the earth, its observed Doppler shift (change of wavelength of characteristic spectral lines) reveals the value of v at the instant of emission.

If the speed of light from A to the Earth were modified by the motion of A, so as to be equal to c+v, show that the value of v, as inferred from the spectroscopic observations on earth, would appear to varying with time in accordance with the following equation if u<<c:
v = u sin[(2Pi/T)(t - R/c - Rv/c^2)]

Homework Equations

i have no idea wat equations i should have for this problem...

The Attempt at a Solution

i know it's sth related to the doppler effect, but all i hv learned abt the doppler effect is the very basic ideas like the apparent frequency of the siren from an approaching poilce car and such. But when it comes to the doppler effect for EM waves, i hv absolutely no idea how i should take c into account.

can anybody suggest also some references for me on the topic of (relativistic?) doppler effect?? it seems to me that the main idea of this problem has nothing related to the leature material of mine (which was doing something like an introduction to special relativity, but all we have done so far is to study the Michelson-Morley experiment, and from that i can see no relation to the doppler effect)

 

[Kurdt]

The binary star system is a bit like a Michelson-Morley experiment. What you have is a light source changing with respect to an ether frame. Rather than measuring interference you are measuring the Doppler shift. If u << c then you don't have to take into account relativistic effects.