AP French Relativity chapter 3 problem

[ka_reem13]

Homework Statement

the question is contained in my attempt at a solution as I can't add images anywhere else

Relevant Equations

I assume we will have to use the relativistic doppler shift in order to find our answer, but that's all I can really gather from how to attempt this

 

[PeroK]

Relevant Equations:: I assume we will have to use the relativistic doppler shift in order to find our answer, but that's all I can really gather from how to attempt this

I think French wants you to assume that the speed of light depends on the motion of the source. In which case, you cannot use the relativistic Doppler shift, but have to calculate the shift for yourself.

 

[TSny]

Relevant Equations:: I assume we will have to use the relativistic doppler shift in order to find our answer, but that's all I can really gather from how to attempt this

This problem does not require any results from relativity. The star's speed is much less than the speed of light. Consider the following:

(1) What is the function $v_r(t)$ that expresses $v_r$ as a function of time $t$ and the orbital period $T$? For convenience, choose $t = 0$ when the star is farthest from the earth.

(2) Suppose someone on earth at an arbitrary time $t$ observes light from the star. At what earlier time $t_0$ was this light emitted from the star under the assumption that the light travels from the star to earth at speed $c+v_r(t_0)$? Express $t_0$ in terms of $t$, $R$, $c$, and $v_r(t_0)$.