HOMEWORK SET #4
DUE: 14 NOVEMBER

• show all steps in the simple required calculations. That way, if you make an arithmetic error on a question, it still may be possible for us to assign partial credit.

• write complete sentences. Be legible! We can't give a grade to something we can't read.

• cleanly labeled diagrams are almost always helpful and sometimes are required for a complete explanation.

• come to the help sessions if you are not absolutely clear on how to do any of the questions.

1. A certain main-sequence star has a mass equal to 0.4 times the mass of our Sun. Determine the following quantities for this star: a) its absolute luminosity; b) its absolute magnitude (the Sun's absolute magnitude is about +4.7); c) its surface temperature; d) its radius; e) its average density; and f) its main sequence lifetime.

2. For the star discussed in Question 1, describe its evolution in terms of: a) its path through the HR diagram; b) cut-away views of its interior at various significant stages of its evolution; and c) a small paragraph of descriptive comments.

3. We know that planetary nebulae are the outer shells of stars that are expanding away and fading out, leaving white dwarf remnants. The typical velocities are about 25 km/sec, and the largest ones we can see before fade-out of the expanded shells are about 2 parsecs in diameter. From these two facts, compute the time length from shell "lift-off" from the central star to fade-away. This is the "lifetime" of the planetary nebula phase. Let's put this another way. If the star's total lifetime is like that of the Sun, what fraction of its lifetime is spent ejecting its outer shell as a planetary nebula?

4. For how long could a 60-watt light bulb burn, using the energy produced by the TOTAL annihilation of 1 gram of matter?

5. Suppose that the Sun is hot and dense enough in its interior to eventually convert 10% of its mass from H--->He in the proton-proton cycle. How much total energy will have been released when all these reactions are complete? (Assume that the mass of a proton is essentially the mass of a whole hydrogen atom). Then under steady fusion conditions, how long will the Sun live, assuming that its absolute luminosity is constant?

6. If a neutron star has a radius of 10 km and rotates with a period of about 0.05 seconds, what is its (equatorial) rotation speed? What fraction of the speed of light is this?

7. If the Earth's moon were magically replaced by this star, what would be its angular diameter as seen from the Earth?

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