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# Velocity transformation/relativistic doppler effect

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?

#### Solution Preview

(a)
You are right to use the Lorentz transformation.

As to the axes note the text "... Klingon fighter ship approaches from the opposite direction ...".
This means the two ships move along the same straight line towards each other.
Therefore you can just choose this line ...

#### Solution Summary

Velocity transformation and relativistic doppler effect is investigated. The speed each measure of the signal as traveling and frequencies are determined.

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