Homework Assignment #5
Revision 2
This assignment is due at the beginning of class on Friday, October 17. Late homework will not be accepted, including homework turned in at the end of class. If you can't make it to the beginning of class, make sure to turn your homework in to me beforehand.
You must do the first three problems. Each of those problems will be worth 10 points. If you make a sincere, honest effort to answer each question, you will receive at least 5 points of credit. Do not abuse this, or I will stop doing it later in the term!
Staple your homework! If you require more than one page to complete the homework, fasten the multiple pages together with a staple; folding the corner won't cut it. If your homework has multiple pages but you fail to staple, you will be docked 3 points.
The last three problems are given to you as additional review problems. You do not need to turn them in, and they will not be graded when you do. However, solutions to them will be posted along with the solutions to the first three problems. You may want to do them if you think you need extra review in the class. I recommend you at least look at and think about problem 4. Even though there are no "dark matter" problems on this homework set, dark matter will be covered on future tests and the final.
Please write out the problem statement at the top of your solution. (This is for two reasons; it is so I can know which problem you answered, and that you answered the right problem from the book. It also will make your graded homework more useful as a study aid later.)
Chapter 19, Question 5 (page 508). The same argument you make could also be applied to our solar system, or to our Galaxy.
Chapter 19, Question 15 (page 508).
Chapter 19, Question 11 (page 508).
In class, we discussed the rotation curve of the Milky Way (and other spiral galaxies) as evidence for dark matter. Similarly, many (though perhaps not all!) elliptical galaxies show evidence for dark matter, and we can find evidence for dark matter in clusters of galaxies. Since these systems consist of objects (stars or galaxies) randomly moving about in all directions, and don't have an ordered rotation, the same "rotation curve" arguments we used for our Galaxy won't apply. Instead, we talk about velocity dispersion: the range of velocities (measured from the Doppler shift) that galaxies in a cluster show. Consider two hypothetical clusters of galaxies, each 10kpc in diameter, and each with an identical number of galaxies of identical brightnesses. One of these hypothetical clusters (from our Universe) has dark matter, but the other has absolutely none. Which cluster will show a greater range of velocities? (Hint: remember that these clusters are held together by gravity, and that their size is dominated by how far galaxies can get before they are pulled back to the cluster. Also think about what would happen if you dropped a ball on the Earth compared to dropping one on the Moon (where gravity is lower), or what would be different if you wanted to throw a ball to a height of 10m on Earth as compared to throwing a ball to a height of 10m on the Moon.)
Chapter 19, Question 14 (page 508).
When we look at very distant galaxies, we are looking at them as they were far in the past, because the light from them took time to reach us. Even though we're looking at distant galaxies, we talk about "looking at the earlier Universe", as if what we saw applied to the history of galaxies near us. Why do we think we can do this? What observational evidence supports these assumptions?
(The problems below will not be graded, and need not be turned in.)