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{\bf Introduction to Astrophysics II, 29:120\\
     Spring, 2007\\
Seventh Homework Set...March 30, 2007. Due April 5, 2007}\\
{\em Nunc et in umbrosis, Fauno decet immolare lucis \ldots Horace}
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{\bf (1)} Using an equation or graph of the {\em initial mass function}, 
calculate the fraction of stars with $M > 15 M_{\odot}$.\\

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{\bf (2)} Calculate the Kelvin-Helmholtz timescale for the Sun, using its present luminosity.  \\

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{\bf (3)} Adopt the number in the book for the surface temperature of Sirius B, $T=27,000$ K. Using only this number, and the relative brightness of Sirius A and B, compute the radius of Sirius B.    \\ 


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{\bf (4)} Generalize the derivation of the Fermi Energy presented in class to the case of a 2 dimensional star, i.e. particles are confined to a box of size $L$ in both the $x$ and $y$ directions.  Compare your result to the equation derived in class for 1D, and the correct value for the Fermi Energy given in eq. 15.2 of the book.  
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{\bf (5)} Problem 15.2 from the textbook. 
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{\bf (6)} Problem 15.3
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{\bf (7)} Problem 15.5 \\

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{\bf (8)} Problem 15.6 \\


 
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