Astro 250: Astronomy Bizarre
Spring 2008

Assignment #3
Due: Monday, March 31, 2008

Name: ________________________________

 

  1. List two distinct properties of the Cosmic Microwave Background radiation that have been measured, and describe what we believe those measurements tell us about the origin and early evolution of our Universe.

     

     

     

     

  2. We will discuss the concept of dark matter in cosmology:
    1. Describe, briefly, two unrelated pieces of evidence that there is far more matter in the Universe than can be seen in the form of stars, gas, and other luminous matter.  

       

       

       

       

    2. How do we know that much of this dark matter, while gravitating, cannot be made of ordinary "baryonic" matter?  

       

       

       

  3. Using Kepler's third law, adapted by Newton, we can use a measured orbital velocity (v) at a distance (r) from the center of a galaxy to compute the mass of the galaxy (M) contained within that radius r. The formula is:
    v = 0.119 km/s √(M/r)
    where v is the orbital velocity in km/s, r is the radius of the orbit in light years, and M is the mass of the galaxy (in solar masses) contained within the orbit.

    In the galaxy M87, astronomers have measured the rotation velocity near its center with the Hubble Space Telescope.  They find a rotation velocity of 550 km/s (see the HST press release on M87 for details) at a distance of 60 light years from the center.  Compute the mass of the galaxy that lies within 60 light years of the center. How does your answer compare to that found by the Hubble astronomers?

  4. Observations show that objects in the Milky Way galaxy, and in many other spiral galaxies, revolve about the galactic center at the same velocities, regardless of distance from the center, beyond about 20,000 light years from the center. However, the light from these galaxies is concentrated in the inner 20,000 light years. The Sun lies 30,000 light years from the center of the Milky Way, and moves at 220 km/s in its orbit.
    1. Compute the mass of the Galaxy contained within the Sun's orbit using Kepler's third law in the above form, and the numbers given for the velocity and radius of the Sun's orbit.  

       

    2. Several different objects in our galaxy have orbits far beyond the Sun's orbit. For example, a molecular cloud lies 6 times farther away than the Sun from the center of the Milky Way but has the same orbital velocity as the Sun. Use Kepler's law to compute M, the mass of the Galaxy (in solar masses) that lies within the orbit of the globular cluster. How many times larger is this mass than that found within the Sun's orbit?