1) The graph below represents the current situation in a marathon. Each data point represents an individual runner, and the best-fit line showing the relationship between distance travelled and average speed is shown extending from the origin to point A with coordinates (X, Y).

a) (9 pts) In terms of X and Y, express mathematically how long this race has been going on. You do not need to explain your reasoning... just a simple equation will do as an answer.

b) (3 pts) What will be the units of your answer?

2) Suppose we plot a graph of distance vs velocity for galaxies in a different Universe with the same age as our own (about 13 billion years old), and it turns out looking like the one below.

a) (3 pts) How will you expect the metallicity of the objects on this graph to change as you look at objects with increasing distances (increase, decrease, stay the same, can't determine)?

b) (9 pts) Explain your answer to (a).

3) Our current estimate of the overall density of the Universe suggests that it is only about 20% of the critical density. Suppose a new discovery is made tomorrow in Astronomy. Scientists have discovered that the size scale of the Universe is 100 times larger than previous experiments have indicated, although the total amount of mass we measure (normal matter and dark matter) is still the same.

a) (4 pts) How would this affect our estimate of the overall density of the Universe? Very short answer will do.

b) (8 pts) How would this affect our view of the eventual fate of the Universe? Explain.

4) The diagram below shows two different observations of a lensed quasar. In each observation, the cluster in the middle is 10 million light years away from us and the quasar behind the cluster is 20 million light years away from us.

a) (4 pts) Which of the two clusters is more massive? (A, B, same, can't determine)

b) (8 pts) Explain your answer to (a).

5) The graph below represents the abundance of some unknown material plotted versus distance to the object in question.

a) (3 pts) Is this material something that (increases, decreases, stays the same, can't tell) as the Universe grows older?

b) (3 pts) What element might this material be (there is more than one possible answer)?

c) (6 pts) Explain your answer to (b).

6) The Microwave Background Radiation is not completely uniform. In one direction on the sky, the peak of the radiation curve (intensity versus wavelength) occurs at a shorter wavelength than any other part of the sky. What causes this?

7) Give two pieces of evidence that can be used to argue that the Universe has a finite age. Do not just name the observations, but also explain how they lead us to the finite age conclusion.

8) Einstein's theory of Relativity tells us that mass bends space. Empty space has a naturally negative curvature (like a saddle), and any mass we add to empty space adds a positive curvature (like a sphere). If the density is equal to the critical density, then the two kinds of curvature are equal, and we are left with a "flat" Universe. Use the theory of the inflation to explain why the observed density of the Universe is very close to the critical density.

9) Suppose we consider this same graph in another Universe in which the expansion was much slower so that the time during which nucleosynthesis lasted was much longer than 3 minutes.

a) (3 pts) Assuming this other Universe has the same age as our own Universe, would the abundance of Helium in the "slow" Universe after 13 billion years be (greater than, less than, same as, can't determine) the abundance of Helium in our Universe after 13 billion years?

b) (9 pts) Explain your answer to part (a).

10) Over the past year, there has been a lot of controversy over the analysis of a meteorite that fell on Earth after being blasted off the surface of Mars by an impact. Some scientists claim to find evidence of fossilized life in the meteorite while others are more skeptical. How does this controversy (and its eventual resolution) affect our opinion of whether or not there is other intelligent life in the galaxy?