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760. An interstellar gas circles the core of earth's galaxy. If the wavelength of the light reflecting off the gas coming toward the earth is 499 nm, and the wavelength of light reflecting off the gas moving away from earth is 501 nm, what is the speed of the gas?

A. 4.2xl0^4 m/s

B. 1.2xl0^5 m/s

C. 6.0xl0^5 m/s

D. 1.5xl0^11 m/s

EK Physics says the answer is C, and that you have to divide the velocity by 2 because of the reflection. However, they don't divide by 2 when arriving at their answer.

Furthermore, I don't think the correct answer is even listed as an answer choice. Please correct me if I'm wrong.

We know the source wavelength is 500nm emitted from the earth because of information given in the problem. The wavelength shift APPEARS to be 1nm, but since really it is a double shift (a shift to 500.5nm or 499.5nm from the gas cloud acting as a moving observer, and then a shift to 501nm or 499nm from the gas cloud acting as a moving source when it reflects the light), the wavelength change we should use is .5nm.

Using EK's approximation formula (v/c=delta lambda / source lambda) solve for v, getting 3.0x10^5 m/s. This is analogous to using the double shift of 1nm, and dividing the calculated velocity by 2.

This is correct, right? and the EK answer choices are all wrong? If not, can somebody tell me the difference between this problem and other "double doppler shift" problems such as a stationary police radar gun targeting a moving car (http://hyperphysics.phy-astr.gsu.edu/hbase/sound/radar.html#c4) ?