29:50 Stars, Galaxies, and the Universe
Second Homework Set...July 20, 2004

Note: Having problems? Don't go around confused and despondent! Ask for help! The purpose of these problem sets is to help you learn something.

1. Planetary nebulae have the same sort of red glow as the Orion Nebula or the Rosette Nebula, even though they are vastly different types of objects. Why is the glow the same? The answer can be in words, but should use physical principles you have learned.
2. Organic molecules are found in molecular clouds. This makes sense in terms of other facts about the universe we have discussed. Why does it make sense? Hint: Think about the definition of an organic molecule.
3. If the star $\eta$ Carinae really does have a mass of 100 $M_{\odot}$, what is its lifetime before it produces a stellar end product? Any well-thought-out number is OK. Answer at a level of mathematics that is comfortable for you.
4. Some neutron stars are visible as continuous sources of light in addition to (or instead of) being pulsars. Describe in words and with diagrams where you would expect to find them on the Hertzsprung-Russell diagram. Hint: Think of where white dwarfs are, then think about the difference between white dwarfs and neutron stars.
5. The star Arcturus is 10 billion years old, as opposed to 4.55 billion years for the Sun. What would you expect the relative abundance of elements such as carbon, oxygen, and nitrogen to be in Arcturus relative to the Sun? Hint: Remember that stars form out of the interstellar medium.
6. As your lab project, you make observations of a weird binary star. One of the components is a spectral class G main sequence star and is clearly moving in an orbit. You cannot detect the light from the other component of the binary, but from your measurements you deduce that it has a mass of 5 $M_{\odot}$. What kind of star or other object is it?
7. How can we be sure (i.e. what types of physical arguments do we use) that white dwarf stars are of the order of the size of the planet Earth rather than the size of the Sun?
8. For most visual binary stars, we have not seen them change their positions relative to each other since observations began about 150 years ago. What does this tell you about these star systems? Why couldn't you determine the masses of such stars?
9. How many times further away is the (relatively) nearby galaxy M81 (visible with binoculars in Ursa Major) than the galactic center of the Milky Way?
10. Look at the picture of the Andromeda Galaxy, M31, in your textbook on p535 or in the class notes on the Web. If M31 really is like the Milky Way, what differences can you measure in the spectra of stars in the upper right part of the galactic disk with respect to the stars in the lower left portion?
11. Imagine that you get in a spaceship and travel to a planet which is 8.5 kiloparsecs from the center of a giant elliptical galaxy like M87 in Virgo (a picture of M87 is given on p602 of the textbook). Night falls, and the stars come out. Describe how the night sky you see differs from the one we see on Earth.
12. Don't try this one until you have learned about Hubble's Law. A galaxy is observed to be receding from us at a speed of 75,000 km/sec. How far away is it?