|
| Properties of Stars |
 |
1. | We have noted in our study of astronomy several instances where temperature controls the color of an object. For example, we think that the color of stars and the color of the atmospheres of Saturn and Jupiter are strongly influenced by temperature. Is the reason that temperature controls the color the same in these two examples? Explain. |
 |
2. | Many examples of stars of a given spectral type can be found just by looking at the sky with the naked eye. However, it is much easier to find K and M stars than O stars with the naked eye. Why do you think this is so? |
|
3. | The bolometric absolute magnitude is defined to be the absolute magnitude that we would observe if we could observe all the light (not just the visible) from a star. The absolute magnitude is converted to a bolometric magnitude by multiplying by a factor. This factor (1) depends only on temperature and (2) is almost 1 for stars like the Sun, but is much larger for very hot or very cool stars. Explain these two facts. |
 |
4. |
Use the definitions of absolute magnitude M and and apparent
magnitude m to show that
where d(pc) is the distance in parsecs and log denotes the base-10 logarithm. |
|
5. |
Show that the equation m - M = 5 log
[d(pc) / 10] derived in Exercise 4 can be rewritten in the form
|
|
6. | If the distance modulus m-M of a star is ten magnitudes, how far away is it? |
|
7. | Suppose you are going to look for signs of intelligent life around some distant stars. Using the timescales for the evolution of life on Earth as a guide (since that is the only information that we have about life) and your knowledge of main sequence lifetimes, which spectral classes of stars would you guess to be the most profitable places to look? |
|
8. | A type Ia supernova is about 14 magnitudes brighter at peak than the average brightness of a Cepheid variable. Estimate how much further away a type Ia can be seen than a typical Cepheid variable. Why might this be important in astronomy? |
|
9. | Barnard's Star is the star with the largest observed proper motion (10.3 seconds of arc per year). How long will it take Barnard's Star to change its position on the celestial sphere by the equivalent of the diameter of the Moon? |
|
10. |
The distance to Barnard's Star is 1.83 parsecs. Combine this with the
information
in the preceding exercise to determine the component of velocity perpendicular
to
our line of sight in km/second. The following diagram may be helpful.
You may find it useful to use this star velocity calculator. |
|
11. | Go to the Dome of the Sky. Select "Enter the Dome" and then select sky charts for a northern latitude (say New Orleans, at 30 degrees N). Select the sky chart for December 20 and locate the characteristic shape of the constellation Orion on the celestial equator to the left of center. Click on the brighter stars in Orion to display information about them (use the status bar at the bottom of the browser to help ensure that you are over the star when you click; for example, it should display "Betelgeuse" when the cursor is over that star). Use the HTML Tablemaker to make a table of the following information (if given) for the brightest stars in Orion: Name, Spectral Class, Color Index, Distance, Visual Magnitude. Put this table into your astronomy homepage if you are constructing one (see the instructions on the Tablemaker interface). |
|
12. | How many kilometers are in a light second (the distance light travels in a second)? How many astronomical units is this? |
|
13. | The star Gliese 710 is presently 63 light years from Earth, but Hipparcos data suggest that in about a million years it will pass within one light year of Earth. Its apparent visual magnitude is +9. What is its absolute magnitude? What will its apparent visual magnitude be in a million years as viewed from Earth (assume that the intrinsic brightness remains the same as today)? What must the present radial velocity of Gliese 710 be if it will pass close to Earth in a million years? |
|
14. | In searching for stars that may come close to Earth in the future, or that may have passed close to Earth in the past, one criterion that is often used is to look first for stars that have very small proper motion and then do Doppler shift measurements on the spectra of those stars. Why is this a useful approach to the problem? In such searches using the Hipparcos precision astrometry data base, at least eight stars have been found having have space velocities that will bring them within five light years of Earth in the next million years. However, one caveat associated with this conclusion is that if any of those stars are (unknown to us) binaries, the predicted future motion could be in error. Why do you think this caveat is necessary? |