ObservationalCosmology

Self-test problems

Use these questions as you proceed through the unit, to judge whether your coverage of the material and level of understanding are adequate. Answers are just a click away, via the      button, but you will greatly reduce the diagnostic value of the questions if you look at the solutions before making a serious attempt to answer the question yourself.

1. Calculate the Doppler shifts which would arise from (i) the rotation of the Earth, (ii) the Earth's orbital motion, (iii) the solar motion around the Galaxy 
2. If a spectrograph operates in the band 5000-9000 Angstrom, over what redshift range will the H_alpha(6563 A) and H_beta(4861 A) Balmer lines from galaxies both fall within the bandpass? (It is hard to determine a redshift with a single line!) 
3. If typical peculiar velocities for galaxies are 500 km/s, how far away must a galaxy be for its velocity and distance to constrain H₀ to 10%, assuming (unrealistically) perfect measurements of v and d? 
4. What is a good way  to determine whether one is in a comoving frame? (Hint:  think about  background  radiation) 
5. What are the main observations which support the Cosmological Principle (ie isotropy & homogeity)? 
6. The accompanying figure shows a sketch of the Hertzsprung-Russell diagrams for two star clusters. The Main Sequence and MS turnoff can be seen. 

(i)Which cluster is more distant?,
(ii) Approximately how much more distant is it?,
(iii) What can you say about the ages of the two clusters? 
7. If the period:luminosity relation of Cepheids is given by M _V=-2.76(logP-1.0)-4.16, where P is the period in days, calculate the distances to two galaxies which contain Cepheids with identical mean apparent magnitudes, m_V=24.5, but with periods of 37 and 81 days, respectively. 
8. How large a spatial scale must one consider before typical fluctuations in the mean density of the Universe drop to ~10%?  (Hint: look in Ned Wright's cosmology tutorial.)     
9. What is the resolution of Olber's paradox? Is there more than one effect at work?     
10. What is the energy density of the CMB radiation? Compare this with the energy density of sunlight at the Earth. 
11. Why are the predictions of nucleosynthesis important in the Big Bang model? 
12. Why do the nucleosynthesis results rule out there being sufficient baryons to close the Universe?