g Astronomy and the Relativistic Doppler Shift Correct Suppose that you\'d like

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g Astronomy and the Relativistic Doppler Shift Correct 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 - Part D at such low fractions of the speed of light these stars are moving quite quickly (thousands of kilometers a second) compared to the standard velocity dispersion in the Milky Way galaxy (which is around 300 km/s). Suppose the star was actually moving toward the earth at a more reasonable 300 km/s What wavelength would the 656 46-nm line move to? Use 299, 792 km/s for the speed of light the one dy Mo with a wavelength of 656.46 nm Express your answer in nanometers to five significant figures nti Part E at high of the Tne

Explanation / Answer

We know from the Doppler Effect, formula for change in wavelength;

= SvS/c

Where, S = wavelength of the source, 656.46 nm

vS = velocity of the source toward a stationary observer, 300 km/s

c = wave velocity, in this case, the speed of light, 299792 km/s

Therefore, = SvS/c = 656.46 * 300 / 299792 = 0.657

Since the star is moving towards the earth, the wavelength decreases. Therefore, the 656.46 nm line would move to = 656.46 - 0.657 = 655.80 nm

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