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Derivation of the Doppler formula and the apparent speed of a relativistic source on the sky:...

Derivation of the Doppler formula and the apparent speed of a relativistic source on the sky: The Death star is moving towards Earth with velocity v and at an angle q with respect to Earth’s direction. The apparent speed of the Death star on the Sky is Vapp=5 c. The Death star shoots with its Laser of known frequency w’ (measured in its own rest frame). The observed frequency of the Laser at Earth is wobs=5 w’. Calculate the Lorentz factor and the angle that the velocity of the Death star makes with respect to our line of sight.

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vapp 5

ren 3. Jt 24.7C avp

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