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{\bf Introduction to Astrophysics I, 29:119\\
     Fall, 2008\\
Fifth Homework Set...October 10, 2008.\\ Due October 16, 2008 (Radio Astronomy Day!)}\\
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Show calculations and give reasons for your answers. Don't go around 
confused and despondent; if you do not know how to get started, ask me for help.\\


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{\bf (1)} A spectroscopic binary shows the lines of a single star, which is a main sequence, spectral class K star. The spectral lines of the K star show a periodic Doppler shift, with a period of 2.5 days. The maximum observed Doppler shift is 198 km/sec. \\
(a) What can you say about the mass of the unseen companion?\\
(b) Based on the answer to (a), is it a star or a degenerate object? Explain your reason. {\bf Hint:} Think of the mass-luminosity relation.\\
(c) What can you say about the nature of the unseen companion, i.e. what type of star, degenerate object, etc, is it?\\     

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{\bf (2)} Consider main sequence stars, although the questions below would probably have the same answers for other luminosity classes. \\
(a) At what spectral class are the Balmer lines of hydrogen strongest?  Quote the spectral class including the number, i.e. M4, not just M.  \\
(b) At what spectral class is the 4226\AA  ~line of neutral calcium strongest?\\

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{\bf (3)} Describe what you would expect for the {\em continuum spectrum} of an O5 star.  Show your work, and give a numerical answer when possible.  \\ 

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{\bf (4)} Problem 8.2 from the book. \\

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{\bf (5)} Demonstrate that equation 8.1 in the book is properly normalized. Remember what I told you about intelligent changes of variables in problems like this (``Mama tried, Mama tried \ldots'').\\

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{\bf (6)} Derive equation 8.2 of the book. \\

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{\bf (7)} Derive equation 8.3 of the book. \\

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{\bf (8)} A gas is at a temperature of 8000K.  What fraction of the particles have thermal energies greater than 3.0 eV?  \\


 
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