Astronomy 100 - Problem Set 6

Due: Tuesday 8 April 2008
Name:

Fill in the box with the correct answer (answers should be just a few words or a number).

  1. What is the most common element in stars?

  2. What is the name of the nuclear burning cycle that fuels the most massive main sequence stars?

  3. The triple-alpha nuclear cycle takes three helium nuclei and produces what element that is fundamental to the existence of life?

  4. What type of object is found at the center of a "planetary nebula"?

  5. When the Sun has exhausted all of its nuclear fuel, what type of object will it become?

  6. Take a look at Figure 8-8 in your book. The figure shows the amount of "binding energy" which holds together atomic nuclei across the periodic table. When a fission or fusion reaction occurs the amount of binding energy released depends on the difference in energy between the "fuel" and the resulting end product. As long as the end product is more tightly bound than the fuel, energy is released.

    Based on the plot, which is the most tightly bound element of all, and thus one that cannot be "burned" in order to liberate energy?

  7. When a star collapses to become a neutron star, it ``spins up'' due to conservation of angular momentum. The angular momentum of a star is given by:

    L = (2 M R2)/(5 T)

    where M is the mass of the star, R is its radius, and T is its period of rotation (that is, how long it takes the object to turn around once completely). Currently, the sun rotates on its axis once every 30 days. If the sun collapsed into a neutron star, its radius (R) would shrink by a factor of 30,000, and its angular momentum would remain the same. What would its new period of rotation be?

  8. Consider figure 13-13 in your book. Approximately how long does it take a Type II supernova to fade to 1/100 of its peak brightness?

  9. The Crab Nebula is the remnant of a supernova explosion. It is 1.4 parsecs in radius and is expanding at a velocity of 1300 kilometers per second. Calculate when the Crab Nebula supernova should have occurred. To do this, remember that a supernova is the explosion of a star. All the material in the Crab Nebula started out in the center (where the star used to be) and ended up as a shell. How many years did it take the material to get from the center to the edge of the shell, 1.4 parsecs away, if it was traveling at a speed of 1400 km/sec (note that 1 parsec = 3.086 x 1013 km)? Subtract that number from 2006 (this year) to find out the year the supernova occurred. The "Crab Nebula Supernova" is believed to be one that was observed by Chinese astronomers in 1054 A.D. If you work things out correctly you should get a year not too far from 1054.

  10. What is the size of the Schwarzschild radius of a black hole with 50 times the mass of the Sun? (you don't need to work through the equations in detail, just note that if the Sun were crushed the resulting black hole would be 3 kilometers in size and scale the result).