1) Given below is the Period-Luminosity relation for Cepheid variables as well as the light curves of two particular Cepheids. You may assume for this problem that the two Cepheids have the same average apparent luminosity as seen from Earth and that there are no interstellar medium corrections (X = 0) to be concerned with.

a) (2 pts) Which of these Cepheids is probably closer to the Earth? (A, B, same)

b) (12 pts) Justify your answer to part (a) fully.

2) Read very carefully, please! Suppose *all* of the visible matter and dark matter in our galaxy were concentrated at a single point in the center of the galaxy except for a few stars with very small masses sprinkled throughout the disk (assume the masses of these stars are zero compared to the mass of the galaxy).

a) (8 pts) If you were to plot a rotation curve, showing the relationship of the orbital velocity of these stars vs distance from the center of the galaxy, would it more closely resemble (a) a Keplerian curve, (b) a curve with velocities slightly higher than Keplerian, (c) a flat rotation curve or (d) a solid body rotation curve? Justify your answer (you do not need to explain the shape of the curve, just why you picked the one you did).

b) (6 pts) In a solid-body rotation curve, the orbital (or rotational) velocity is directly proportional to the distance from the center of motion (or axis of rotation). Briefly explain why this relationship exists for a solid body (a simple diagram may help but is not required). In other words, explain the shape of the solid body rotation curve.

3) One the most exciting developments in recent Astronomical research has been the advent of new space-based telescopes such as the Hubble Space Telescope and the proposed Next Generation Space Telescope (NGST).

a) (8 pts) Name and very briefly explain two reasons why it is useful to observe stars, galaxies and other objects above the Earth's atmosphere instead of from the ground.

b) (6 pts) What wavelengths will the NGST primarily observe in, and what observations of significance can we make at these wavelengths that cannot be made at other wavelengths? In other words, why is observing at these wavelengths important?

4) A stunning discovery made by radio astronomers in the past few decades has been that an extremely massive black hole lurks at the very center of our galaxy.

a) (5 pts) Explain briefly how we know there is a black hole there.

b) (4 pts) Why can the region around this black hole only be observed via radio wavelengths rather than other wavelengths, such as visible light?

c) (5 pts) One way to resolve small details at great distances like at the center of the galaxy is to use interferometry, a technique that improves resolution by correlating the signals from several linked radio telescopes. Briefly explain why this is not yet feasible to do for optical telescopes.

5) Among the major differences between spirals and ellipticals are the facts that their overall shape and composition is very different (spirals are disk-shaped and gas-rich) and that they are generally found in different parts of galaxy clusters.

a) (8 pts) Use the formation scenario for spiral galaxies to explain why the initial shape of spiral galaxies is disk-like, then explain why any gas remaining in the halo would quickly become part of the disk (while stars would not).

b) (6 pts) Use the principles behind the merger hypothesis to explain why elliptical galaxies are more often found near the centers of galaxy clusters while spirals tend to be found isolated or near the less densely populated edges of clusters.

6) One popular method of distance determination is the Standard Candle method, which requires accurate knowledge of the absolute luminosity of a "standard" object as well as confidence that some distant object that looks similar to the standard object has the same absolute luminosity as the standard object.

a) (7 pts) Explain why the brightest galaxy in a given cluster is likely to have a similar absolute luminosity compared to the brightest galaxy in some other cluster.

b) (7 pts) Supernovae from white dwarf explosions are thought to be excellent standard candles. Why are these sorts of supernovae thought to have very predictable absolute luminosities while supernovae from other types of stars do not?

7) Hubble's relation today is assumed to be a perfectly straight line if you assume that the motions of galaxies in the Universe have been constant since the beginning, as shown below. Assume for this problem that the Hubble constant implies that the age of the Universe is 10 billion years.

a) (6 pts) On the graph below, sketch how you think the Hubble relation looked about 5 billion years ago. Assume no acceleration or deceleration, just constant galaxy velocities over time. Explain your drawing.

b) (8 pts) On the graph below, sketch how you think the Hubble relation would look (at the current time) under the assumption that gravitational forces have been gradually slowing the expansion since the beginning. Explain your drawing.

8) The discovery of the Microwave Background Radiation (MBR) in the 1960's was seen as an important confirmation of the Big Bang theory.

a) (6 pts) Explain briefly what the MBR is and how we think it originated.

b) (8 pts) Why is the existence of the MBR seen as an important piece of observational evidence in favor of the Big Bang while Hubble's Law is not as critical (since the Big Bang wasn't widely accepted by many scientists before the discovery of the MBR).