I recently begun approaching special and general relativity. I found this problem in my book and I'm trying to solve it but I'm finding some difficulties:
An observer on Earth sees two twins A and B, in two different spacecrafts, leaving in opposite directions, both with
velocities $\beta=0.5$. After a time $\Delta t$, the observer on Earth sends a message to the twin A using an energy photon $E_0=hV_0$. When A receives it, it decides to send it also to the B so that it knows the information, and it does so by sending another photon with the same energy with which it has detected it. I have to find:
The frequency with which A receives the photon and also the frequency with which B receives the photon from A.
If, instead of photons,I send a mass particle $m$ with which energy the first twin A receives the particle? And with which energy the second twin B receives the particle from A?
I know that this involve the well known relativistic Doppler effect and I'm trying to use the relation: $\nu=\nu'\sqrt{\frac{1-\alpha}{1+\alpha}}$ however I can't understand how I can use it to find the frequency with which B receives photon from A. Moreover in the second part when I have no idea of which relationship I have to use