29:50 Stars, Galaxies, and the Universe
First Homework Set...June 28, 2004

Note: Be sure to consult the Appendices in your book.
Problems toward the end of the list will require exposure to material presented in the week of June 28.
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. You observe a star that is known to be like the Sun (Question: How could you know that?). It has an apparent magnitude of 9.8. How far away is the star? You can figure this out either with tables presented in the lecture notes or in the book, or with formulas given in the book. What kind of instrument would you need to see it, i.e. naked eye, binoculars, small telescope, large telescope?

2. A star has a parallax of 0.01 arcseconds. How far away is it in parsecs? How many light years away is it?

3. Approximately how much more luminous than the Sun is Arcturus?

4. What would the apparent magnitude of Vega be if it were 100,000 parsecs away?

5. The Sun has surface temperature of 5800 K and is brightest at a wavelength of 500 nanometers ( $5.0 \times 10^{-7}$ meters). The star Spica (brightest star in Virgo, visible just west of the meridian when it gets dark) is brightest at a wavelength of 126 nanometers ( $1.26 \times 10^{-7}$ meters). What is the surface temperature of Spica?

6. Based on information presented in class, and contained in your textbook, approximately what is the surface temperature of Vega? How about Antares? Give reasons for your answer. This is science, feelings and unjustified opinions don't count!

7. The star Capella, currently visible in the northeast sky before dawn, is of spectral class G and has an absolute magnitude of -0.7. In terms of the terminology of the Hertzsprung-Russell diagram, what kind of star is it, i.e. main sequence, giant, supergiant, etc?

8. Explain in words why it is that nuclear fusion reactions occur only in the centers of stars.

9. Here is a question that is relevant to exobiology, or the inquiry as to whether life could exist elsewhere in the universe. As we have discussed in class, the Sun and planets formed 4.5 billion years (Gyr) ago. However, the first multicellular life, like you, your dog, and jellyfish, only arose 500 million years (0.5 Gyr) ago. Assuming that this timing in the evolution of life is typical throughout the universe, what does this say about the types of stars that could host life-bearing planets? Be quantitative in your answer.

10. The ``Trapezium'' is a star cluster in the middle of the Orion Nebula, the nearest major star formation region which is visible in the winter sky. The brightest star in the Trapezium is $\theta_1^C$ Orionis, which has been measured to have a mass of 45 solar masses. What does this tell you about the age of the Trapezium and the Orion Nebula?