Astro 250: Astronomy Bizarre
Spring 2008

Assignment #1
Due: Wednesday, January 30, 2008

Name: ______________________________________

1. Ancient astronomers and philosophers assumed that all of the stars were eternal and unchanging. Is there any simple observation they could have made, coupled with a cogent line of reasoning, that could have led them to conclude that stars don't live forever: that is, that they are born, that they change as they live, and/or that they 'die'? Remember that they didn't have telescopes, cameras, or any other advanced technology, so that the observations had to have been simple (or even metaphorical).

    

    

2. Briefly (in one page or less) describe what will happen to the Sun from the time it arrives on the Main Sequence until its final state. Please associate numbers with your discussion (in terms of time spent in each stage, and approximate size of the past and future Sun), but do be sure to construct a proper short essay (i.e. English, grammar, all those things).

    

    

3. In this exercise, we will explore the time scales for two phases in the life of a massive star of 20 solar masses: its main sequence phase, and its last stable nuclear burning phase. To do this, you will need to do some simple computations (ones that will provide answers that are quite interesting). Please show all of your work when you hand this in.
   1. How long will a 20 M_sun star live as a main sequence star that is converting hydrogen to helium?
      You can do this by scaling quantities to those of the Sun, or computing the lifetime explicitly. The information below will be helpful, I hope. Depending on how you approach the problem, some of these points may or may not be needed:
      • A good example of a main sequence star is our Sun, which will shine for nearly 10¹⁰ years by converting about 10% of its mass from hydrogen into helium.
      • A 20 M_sun star has 20 times the amount of fuel than our Sun, but has a luminosity of 160,000 L_sun. It too will convert 10% of its mass from hydrogen to helium while on the main sequence.
      • In the conversion of 1 gram of hydrogen into helium, 0.007 grams is converted into energy via E=mc², where E is the energy produced (in ergs) and m is the mass converted (in grams). Thus conversion of 1 gram of hydrogen produces 0.007 x c² ergs of energy. So, in converting 1 gram of hydrogen into helium, 6.3x10¹⁸ ergs of energy is produced.
      • The speed of light is 3x10¹⁰cm/s, the current luminosity [energy loss per second] of the Sun is nearly 4x10³³erg/s, and the Sun's mass is 2x10³³ grams.
      • Note that the luminosity is proportional to energy/time, the energy is proportional to mass, and we need to know the time.

      Express your answer in years (there are 3.16x10⁷ seconds in one year).

       

       

   2. How long with the same star spend burning neon?
      Such a star, after it is done burning hydrogen, will burn helium in the core, then heavier elements. At a late stage of evolution (nearly at the point of supernova collapse) it will burn neon (Ne) and produce silicon (Si) - in the end, again only 10% of the total mass will be converted. How long will it be able to do that? Here are key points you need to know:
      • The yield of energy from burning Ne is only 1/60 that of hydrogen burning.
      • The luminosity at this time is ten times higher than on the main sequence - but ...
      • the star is losing most of its energy in the form of neutrinos - in fact, the neutrinos carry away 30,000 times more energy than photons.

    

    

    

4. Final question - free response. Tell me something about you, and about what you might expect from Astro 250. Any problems that you forsee? Suggestions?