1) Two major differences between elliptical galaxies and spiral galaxies are: (1) Elliptical galaxies are more likely to be found at the centers of galaxy clusters, and (2) Elliptical galaxies tend to have less gas and dust relative to spirals. Explain both of these observations.

2) When we collect galaxy data for a Hubble diagram, we find that there is a general correlation between radial velocity and distance. This correlation is not perfect, however, because some galaxies have other elements contributing to their velocities besides the Hubble expansion. In addition, the slope of the Hubble diagram is not really the Hubble "constant" at all...it changes over time!

a) (6 pts) As the Universe gets older, will the value of the Hubble constant increase or decrease? Explain your answer (a simple graph may help, but 1-2 sentences of explanation is also required for credit).

b) (5 pts) Explain why galaxies close to the Milky Way arenžt as likely to obey the general trend seen in the Hubble diagram compared to galaxies far away.

3) Astronomers attempt to understand the amount of dark matter in galaxy clusters by measuring the Doppler shift of a galaxy in a cluster of galaxies. For this problem, assume all velocities are measured with respect to the center of a galaxy cluster. Donžt worry about Hubble expansion or other issues external to the cluster.

a) (5 pts) The radial velocity measured using the Doppler shift will probably be (greater than, less than, the same as) the true velocity of the galaxy. Explain your answer.

b) (6 pts) The true velocity of the galaxy will probably be (greater than, less than, the same as) the escape velocity of the galaxy from the cluster. Explain your answer.

4) Hubbležs observations of galaxy radial velocities seem to imply that virtually all galaxies in the sky are moving away from our location. However, the Copernican Principle states that there is no „special placeū in the Universe. Is there a contradiction then? In other words, is there something about Earth that is special, something that repels galaxies away from our particular location? Explain how to resolve the conflict between Hubbležs Law and the Copernican Principle.

5) The light curve of a star being lensed by an intervening planet-sized object (called a MACHO) is different in two ways from the light curve of a Cepheid variable (which repeats itself after some time and also has a shape that changes depending on which color you observe).

a) (6 pts) Explain why the light curve of a MACHO-lensed star does not repeat like the light curve of a Cepheid variable.

b) (5 pts) Explain why the light curve of a MACHO-lensed star does not depend on the color you observe with, unlike a Cepheid light curve.

6) The Microwave Background Radiation is a uniform „wall of lightū seen in all directions with a spectrum exactly like the one you would expect from a blackbody radiator (like a star) with a temperature of 3 degrees above absolute zero.

a) (5 pts) Explain how the observation of this radiation lends support to the Big Bang theory.

b) (6 pts) We actually donžt see the uniform nature of the radiation in our observations without first correcting for an effect that causes the radiation to look bluer in one direction and redder in the opposite direction. Explain what causes this.

7) One of the first observations in cosmology was the dark night sky. Although everyone knew this, few people thought of the implications.

a) (6 pts) How does the observation of the dark night sky lead us to believe that the Universe is finite in some way (either space or time)? Explain.

b) (5 pts) Even given a finite Universe of the size observed today, the sky would still be fairly bright from the light of distant sources if it werenžt for the expansion of the Universe. Explain how the Hubble expansion contributes to the dark night sky.

8) The equation of orbital velocity is given below:

Explain how we use this equation, along with observations of the motion and distance to the Large Magellanic Cloud (the LMC is a galaxy that orbits our Milky Way) to prove the existence of dark matter in our galaxy.

9) According to the Tully-Fisher (TF) relation, the faster a galaxy rotates, the higher that galaxy's absolute luminosity will be. This information can be used along with the inverse square law (given below) to find the distance to that galaxy.

a) (5 pts) The TF relation, when used as a distance indicator, gets less and less reliable when used for galaxies at higher and higher redshift. Explain why.

b) (6 pts) Galaxy A and galaxy B have the same apparent luminosity, but galaxy A has a smaller rotation velocity. Which galaxy is more distant and why?

10) Suppose there were a stick, exactly 1 meter long, located at some unknown distance from you across a large parking lot. In your hand, you have a device to measure the angular size of the meter stick. Explain how you could find the distance to that meter stick.