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% (C) 2010 by Eugeniy Mikhailov, <evgmik@gmail.com>
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\hw{11}

\problem{Problem 1 (5 points)}
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We derive free fall time (eq. 12.26), find how long does it take to
contract a cloud to half of it initial size. Assume no rotation, express
your answer as fraction of total free fall time. Hint: you will need to
solve a numerical equation.

\problem{Problem 2 (5 points)}
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Solve problem 12.18 from the textbook.
Hints: In (a) collapse stops when velocity is zero, not when the centripetal
acceleration equals to gravity pull.
Assume that moment of inertia does
not change in a,b, and c subproblems, also treat inner mass as spherical
object from the gravitational pull point of view.


\problem{Problem 3 (5 points)}
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Assuming (incorrectly) that solar radiation is all in ultraviolet, how
large would be the radius of the H II emission bubble if the Sun is placed
in the middle of hydrogen cloud with density of hydrogen is $10^8$ m$^{-3}$
and the recombination coefficient $\alpha=3\times10^{-19}$ m$^3$ s$^{-1}$.
Express your answer ion parsecs.




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