Astronomy 102, Fall 2004

Homework Assignment #7

This homework set is due at the beginning of class on Friday, November 12. 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.

How many kg of mass is the Sun losing each second by converting mass into energy?
- (a) Hydrogen fusion has an efficiency of about 0.7% for converting mass into energy. Assume that the Sun will use 10% of its Hydrogen for fusion (and that it is mostly Hydrogen). Given the Sun's luminosity, how long will it shine?
- (b) We know that the Sun is not "on fire" because chemical reactions are not nearly efficient enough to keep the Sun shining at its current luminosity for anything like the amount of time we know it's been around. The efficiency of chemical burning of Hydrogen in the reaction:
  
  2H₂ + O₂ --> 2H₂O
  
  is about 2x10^-10: that is the fraction of its mass that gets converted into energy.
  Assuming that the Sun were made up of Oxygen and Hydrogen in just the right proportions, and that it was able to burn all of its mass, how long (for how many years) would it be able to shine at its current luminosity using chemical reactions?
- (c) Another possible energy source is the energy released from gravitational contraction. When you drop something from a height, energy is released; you may use that energy to make a sound, break something, etc. Suppose that you consider all the mass of the Sun to have been "dropped" from a great distance on to the Sun. The total energy released is approximately G M^2/R, where M is the mass of the Sun and R is the radius of the Sun. If this were where the Sun got its energy, for how long would it be able to shine at its current luminosity?
Right now the Sun is a main-sequence star. Later in its life, it will become a red giant: it's luminosity will go up hundreds or thousands of times, it will be many (between ten and a hundred) times larger, and it will be a bit cooler.
- (a) Will the rate at which the Sun converts some of its mass to energy be higher or lower when it is a red giant as compared to now? Why?
- (b) Do you expect that the pressure near the surface, but inside the Sun, will be higher when the Sun is a red giant than it is now? Why?
- (c) The "solar wind" is a stream of particles coming off of the surface of the Sun. Do you expect the solar wind to be more intense (i.e. more particles coming off of the Sun per second) when it is a red giant or now? Why?
The problems below are optional; they need not be turned in, and they will not be graded.
Consider a two large clouds of gas with solar abundances (i.e. mostly Hydrogen and Helium, with just a little bit of other things mixed in). Take one cloud of this gas, and make sun-like stars out of it. Let the sun-like stars live their main sequence lifetimes, and then (somehow, magically) disperse those sun like stars back into a cloud of gas. Qualitatively, how will the relative elemental abundances in the cloud which was processed through sun-like stars compare to the cloud which just remained a large, quiet cloud of gas?