# Period of pulsation of a star and its relation to free fall and acoustic waves

In this paper, 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.

• Please define all the symbols. – Rob Jeffries Sep 1 '19 at 12:50
• Done. I would appreciate a comprehensive answer to the two questions posed above – wrb98 Sep 1 '19 at 13:15
• Check the paper I have provided at the beginning of the question for explicit definitions of q and s. – wrb98 Sep 1 '19 at 13:30
• Write down a) and b) and divide them by $\Pi$? Or what else do you mean with 'relate'? – AtmosphericPrisonEscape Sep 1 '19 at 21:31