Find out if a distant star is moving relative to the earth

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Suppose that you'd like to find out if a distant star is moving relative to the earth. The star is much too far away to detect any change in its brightness as it moves toward or away from the earth. Instead we can use the Doppler effect to determine its relative speed. For this problem we are going to look at the spectral lines from hydrogen, specifically the one with a wavelength of 656.46 nm. Part B What is , the speed at which the star is moving relative to the earth? Express your answer as a fraction of the speed of light to two significant figures. Part C Suppose that you measured a peak at 680 nm instead. What is the relative speed of the star to the earth in this case? Express your answer as a fraction of the speed of light to two significant figures. Part E The hydrogen atoms in a star are also moving at high velocity because of the random motions caused by their high temperature. As a result, each atom is Doppler shifted a little bit differently, leading to a finite width of each spectral line, such as the 656.46-nm line we were just discussing. For a star like our sun, this leads to a finite width of the spectral lines of roughly . If our instruments can only resolve to this accuracy, what is the lowest speed , greater than 0, that we can measure a star to be moving? Express your answer in kilometers per second to two significant figures.

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