Discuss the below:
Velocity transformation/relativistic doppler effect
Q: The Starship Enterprise approaches a planet at a speed of 0.8 c. The planet is considered at rest. A Klingon fighter ship approaches from the opposite direction at 0.6 c.
(a) What speeds do people at each location see the other traveling?
(b) A light signal of 100 MHz is issued by Enterprise. What speed does each measure the signal as traveling and at what frequency?
In part a, I am assuming I should be using the Lorentz velocity transformation, but am unsure of how to do this since I don't know what direction (x, y) the rockets are traveling.
In part b, if I use the relativistic Doppler Effect, I have two unknowns:
f_O = (?1- v/c / ?1 + v/c) f_S
I need to find both the velocity (v) and the observed frequency (f_O). How do I do this?