<p>In <a href="https://www.mps.mpg.de/phd/solar-physics-lecture-2007-helioseismology" rel="nofollow noreferrer">this paper</a>, the period <span class="math-container">$\Pi$</span> of pulsation for a star can be obtained by means of the virial theorem:</p>

<p><span class="math-container">$$\Pi = 2\pi\sqrt{\frac{sR^3}{(3\gamma - 4)qGM}}$$</span></p>

<p>where <span class="math-container">$s$</span> and <span class="math-container">$q$</span> are constants relating to the star and <span class="math-container">$\gamma = c_P/c_V$</span> is the ratio of specific heat capacities at constant pressure and volume. I would like to know how one can relate <span class="math-container">$\Pi$</span> to: </p>

<p>(a) the time of free fall </p>

<p>and </p>

<p>(b) the acoustic travel time </p>

<p>from the surface of the star to its center.</p>

CC BY-SA 4.0
2019-09-01T12:50:22.097Z
Please define all the symbols.
ProfRob
CC BY-SA 4.0
2019-09-01T13:15:27.740Z
Done. I would appreciate a comprehensive answer to the two questions posed above
wrb98
CC BY-SA 4.0
2019-09-01T13:30:23.217Z
Check the paper I have provided at the beginning of the question for explicit definitions of q and s.
wrb98
CC BY-SA 4.0
2019-09-01T21:31:44.713Z
Write down a) and b) and divide them by $\Pi$? Or what else do you mean with 'relate'?
AtmosphericPrisonEscape
<star><stellar-astrophysics>
Period of pulsation of a star and its relation to free fall and acoustic waves
wrb98
# Period of pulsation of a star and its relation to free fall and acoustic waves

(Asked by: username_0 on 2019-09-01)

In [this paper](https://www.mps.mpg.de/phd/solar-physics-lecture-2007-helioseismology), the period $\Pi$ of pulsation for a star can be obtained by means of the virial theorem:

$$\Pi = 2\pi\sqrt{\frac{sR^3}{(3\gamma - 4)qGM}}$$

where $s$ and $q$ are constants relating to the star and $\gamma = c\_P/c\_V$ is the ratio of specific heat capacities at constant pressure and volume. I would like to know how one can relate $\Pi$ to:

(a) the time of free fall

and

(b) the acoustic travel time

from the surface of the star to its center.

**Tags:** star, stellar-astrophysics
> **Comments:**
> **username_1**: Please define all the symbols.  
> **username_0**: Done. I would appreciate a comprehensive answer to the two questions posed above  
> **username_0**: Check the paper I have provided at the beginning of the question for explicit definitions of q and s.  
> **username_2**: Write down a) and b) and divide them by $\Pi$? Or what else do you mean with 'relate'?  

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## 0 answers

