Homework Assignment #4

This assignment is due at the beginning of class on Friday, October 3. Late homework will not be accepted, including homework turned in at the end of class.

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.

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.)

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1. How many radio photons (assume a wavelength of 1m) does it take to equal the energy of a single ultraviolet photon (assume a wavelength of 100nm, remembering that one nanometer (nm) is 10^-9m)?

2. You want to escape from the Solar System! Waaaah! You strap yourself into your rocket and blast off from the vicinity of the Earth. Assuming that you've already managed to escape from the Earth (but are still travelling along in the direction of Earth's orbit), and now only need to break free of the gravitational grip of the Sun, in which direction do you want to point your rocket so as to escape using the minimum possible amount of fuel? Do you want to point it towards the Sun, away from the Sun, in the same direction as Earth's motion about it's orbit, in the direction opposite Earth's motion, or in some direction between one of these four "cardinal" directions? Justify your answer in terms of energy; your goal is to get a very large distance away from the Sun.

   
   
   
   

3. Atomic emission "lines" as described in class always happen at exactly one wavelength: the wavelength where photons have the same energy as a specific atomic transition. In fact, atronomers usually observe "broadened" lines from astrophysical sources, where a line at a given wavelength is spread into nearby wavelengths. One very common mechanism for this broadening is called "Doppler broadening": if a gas cloud is turbulent, with atoms moving about randomly, some of the atoms in the cloud will be moving towards you, some away from you. There will be a blueshift or a redshift of the light emitted by atmos moving towards or away from you, and as the light from all of the atoms is added together you get a smeared out (or broadened) line. Consider the 6563Å line of Hydrogen. Suppose from a nebula it is observed to be spread from 6560-6566Å. What range of speeds towards/away from you would you conclude the atoms in this nebula are moving, if you interpret this broadening as a doppler broadening? (Give your answer in km/s.)

   
   
   
   

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   (The problems below will not be graded, and need not be turned in.)

4. Is it easier to find planets around stars whose orbits are "face-on" (i.e. you are looking "down" on the plane of the orbit) or "edge-on" (i.e. you are looking at "the side" of the plane of the orbit)? Why?

5. When an object is moving away from you, not only are the wavelengths of any emission or absorption lines shifted to the red, but the total energy flux you observe from the object is lower than what you would have observed it the object were not moving relative to you. (This effect is very small for objects moving with modest velocities.) Give at least one reason why this might be so, given what we've discussed in class to date.

6. The 6563Å line of Hydrogen from the Andromeda galaxy is observed at 6556Å.

   • (a) Is the Andromeda galaxy moving towards us or away from us?
   • (b) How fast (at what speed) is the Andromeda galaxy moving along the line of sight?
   • (c) If the Milky Way and Andromeda galaxies are 2.6 million light-years apart, and you assume that there is no tangential velocity (velocity perpendicular to the line of sight), how long will it be before the two galaxies either collide, or until the distance between them doubles? (Indicate which will happen.)