Answer any 9 of the following 10 questions. Each is worth 11 points.
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!
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.
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).
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.
7) One of the first observations in cosmology was the dark night sky. Although everyone knew this, few people thought of the implications.
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.
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.