# Maths Chapter 12

Topics: Doppler effect, Redshift, Relativistic Doppler effect Pages: 3 (610 words) Published: February 1, 2013
6. Find the wavelength shift 'O that an astronomer (on Earth) would observe in a spectral line of wavelength 589.0 nm from star B in the position shown in the diagram. Is this a red shift or a blue shift?

7. Find the wavelength shift 'O that an astronomer (on Earth) would observe in a spectral line of wavelength 589.0 nm from either star when it is in the position C on the diagram. Is this a red shift or a blue shift?

8. In many binary stars, the two stars are not perfectly lined up when seen from Earth. This means that there will not be any dimming or brightening of the light, because the dimmer star will not block out the light from the brighter one. How might an astronomer tell, from the spectrum, that there are in fact two stars moving about their common centre of mass as described in this question?

Practice with the relativistic Doppler shift equation
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These questions give you practice with the relativistic Doppler shift equation, which says that the ratio of wavelength observed from a moving source to the wavelength emitted by the source is k O observed O emitted 1 v / c 1 v / c

v / c = 0.5 Imagine that a source of light waves is moving away from you at half the speed of light. 1. For v / c = 0.5: x write down the value of the term 1 + v / c

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x x x x

write down the value of the term 1 – v / c write down their ratio calculate the value of the Doppler shift factor k compare the value of k with the value of the non-relativistic shift 1 + v / c. Which is the larger?

v / c = 3 / 5 = 0.6 2. Repeat the calculations in question 1 for a larger relative velocity, v = 3 / 5 c.

v / c = 0.9 3. Repeat the calculations in question 1 for the very large relative velocity, v = 0.9 c.

v / c = 0.1 4. Repeat the calculations in question 1 for the smaller relative velocity, v = 0.1 c.

Now that you have seen some examples of how the...