The Doppler Effect

1. The problem statement, all variables and given/known data
There is a classic story (likely apocryphal) about an astronomer who was caught by a policeman for running a red light. The astronomer went to court and pleaded innocent, saying that the motion of his car made the red light (with a wavelength around 700 nm) shift to a green color (with a wavelength around 500 nm) due to the Doppler shift. The judge said something like “OK, you’re innocent of running a red light, but by your own testimony I am convicting you of speeding!” How fast would the astronomer have to have been speeding for his story to have been true? That is, calculate the velocity needed for the claimed color shift to be true. [express this velocity as a fraction of the speed of light.]

2. Relevant equations
Given: (V_rad/c)=Δλ/λ_o

3. The attempt at a solution

V_rad = -85714.29km/s

*********Am I doing my math correctly here? What is the significance of a negative value for V_rad? Do I just need to specify what direction I call positive and negative to eliminate the negative sign?

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