Hydrostatic equilibrium violated in the sun

[AStaunton]

Hi there

Problem is:

if hydrostatic equilibrium were violated by .01% so that 0.01% of the gravitational force were imbalanced by the pressure gradient, estimate how long it would take the sun to change its radius by 10%.

My attempts at solving problem:

My feeling is that the following relation must be relevant:

$$\frac{d^{2}r}{dt^{2}}=-\frac{Gm}{r^{2}}-4\pi r^{2}\frac{\partial P}{\partial m}$$

and going by the problem posed, the pressure quantity should be .01 greater than the gravity quantity...

Also, I feel that the dynamical timescale is relevant here, the equation I have is:

$$\tau_{dyn}=\frac{R}{v_{esc}}=\sqrt{\frac{R^{3}}{2GM}}$$

But again, I am really stuck as to how to use these equations to solve this problem, any advice is greatly appreciated.

 

[Geoff-Bigdad]

Suppose the equilibrium between pressure and gravitational forces were violated by 0.01%, so that 0.01% of the gravitational force is not balanced by the pressure force. This means it would actually be
dP/dr = -ρg +10^-4ρg
0.01% of the gravitational force could then pull the material inwards. For a gravitational acceleration of go = 2.7 x 104 cm s~2 the net acceleration would then be g(net) = 2.7 x 103 cms"2.

 

[Nugatory]

This thread is more than four years old - no point in reawakening it now.