1) Below is the graph showing the situation in a car race after a certain amount of time has passed. Each large dot represents one of the cars on the track. You may assume that all cars in the race are moving at a constant velocity.

a) (7 pts) How long has this race been going on? Show your work.

b) (7 pts) On the graph above, draw a line representing the situation in the race as of one hour ago. It doesn't have to be precisely correct. No explanation is required for this part.

2) In order to calibrate the Tully-Fisher relation, astronomers must know how the spectral line widths of galaxies are related to their rotation velocities (or, if you prefer, the orbital velocities of the objects within the galaxies).

a) (7 pts) Do galaxies with narrow spectral line widths necessarily have small rotation velocities? Explain.

b) (7 pts) Why is it only possible to use the Tully-Fisher relation with galaxies that are relatively close to our own?

3) Although the Hubble relation is typically presented as a linear relationship between radial velocity and distance as shown below, recent observations have shown that the Universe may be accelerating, implying the existence of a cosmological constant.

a) (8 pts) On the graph below, sketch how observations deviate from the Hubble relation and to the right, explain why you alter the graph in the way you did.

b) (6 pts) Explain why Einstein first proposed the cosmological constant in his model of the Universe.

4) In 2-3 sentences each, summarize two different versions of the Anthropic Principle.

5) Astronomers tell us that some of the star-like objects in the sky seen through a telescope are not nearby stars but rather quasi-stellar objects, or quasars, that are among the most distant and luminous objects in the Universe.

a) (7 pts) Explain how we know that quasars have very high absolute luminosities.

b) (7 pts) Explain how we know that quasars are very small relative to a galaxy.

6) The quasar spectrum below contains Hydrogen absorption lines from the Milky Way galaxy as well as three other intervening systems. There are other absorption lines (from hydrogen and metals) at a variety of redshifts that are too insignificant to show.

a) (2 pts) Which system probably has the lowest observed metallicity? (A, B, C)

b) (12 pts) Explain your answer to part (a).

7) The Microwave Background Radiation (MBR) is not completely uniform. In actually shows differences in different directions.

a) (7 pts) Explain why in one direction on the sky, the MBR peak wavelength is shorter than in any other direction on the sky while the opposite part of the sky has an MBR spectrum that peaks at a longer wavelength than any other place.

b) (7 pts) If we correct for the effect in (a), Astronomers still predicted there would be lumpiness and structure in the MBR (which was subsequently found by the COBE satellite). Explain why this prediction was made.

8) The era of nucleosynthesis in the early Universe is definted by the time during which the composition of the Universe changed from 100% Hydrogen to a mix of 90% Hydrogen and about 10% Helium.

a) (7 pts) Explain why this era where new atoms were being created did not begin until after the age of the Universe was about one second.

b) (7 pts) Explain why the era of nucleosynthesis ended after about three minutes.