Astronomy 102, Fall 2004

Homework Assignment #3

This homework set is due at the beginning of class on Friday, September 25. It must be turned in by 9:10AM that day. Late homework will not be accepted. This is includes your being late to class!

Staple. If you have more than one page, staple them together; do not just fold the corner. If you have multiple pages and do not staple, I will deduct one point from your score..

The first three problems are required. The remaining problems are optional, and will not be graded; they are here as additional review problems for you. After the homework has been graded, solutions will be posted to all problems.

Please write out the problem statement at the top of your solution. (This is for two reasons; it is so I can know which problems you answered, and that you answered the right problem from the bit. It also will make your graded homework more useful as a study aid later.)

You may consult with other students (as well as with the TAs and professor) on this homework set. However, your final answer should be your own. Do not write down an answer you don't understand, and do not "dictate" an answer to somebody else.

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.)
Chapter 2, Question 9 in Pasachoff & Filippenko (p. 32).
The luminosity of the Sun (i.e. the amount of energy it puts out each second) is 3.9×10²⁶ W. It radiates this energy approximately as a blackbody.
- (a) If the radius of the Sun were to double while keeping its surface temperature the same, what would be its luminosity? How would the color of the Sun change?
- (b) If the temperature of the Sun were to double while keeping its size the same, what would be its luminosity? How would the color of the Sun change?
The problems below are optional; they need not be turned in, and they will not be graded.
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.
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.)