3.5: Problems
- Page ID
- 141608
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- What polytrope(s) would you use to describe the structure of the sun? How well do they match the standard solar model?
-
Consider a gas sphere that undergoes a pressure-free collapse. Let the free-fall time for material at the surface R be \(\mathrm{t}_f\). Find the mass distribution for an isothermal sphere and polytropes with indices \(n\) of 3, and 1.5 at: \[\begin{array}{ll}
\mathrm{a} & \mathrm{t}=0.1 \mathrm{t}_f, \\
\mathrm{b} & \mathrm{t}=0.5 \mathrm{t}_f, \text { and } \\
\mathrm{c} & \mathrm{t}=0.8 \mathrm{t}_f .
\end{array}\nonumber\] - Use the Virial theorem to find the fundamental radial pulsation period for a star where the equation of state is \(\mathrm{P}=\mathrm{Kp}^\gamma\). Find the behavior of this period as \(\gamma \rightarrow \infty\).
- Find the mass of a main sequence star for which the energy production by the p-p cycle equals that of the CNO cycle.