- #1
AStaunton
- 105
- 1
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:
[tex]\frac{d^{2}r}{dt^{2}}=-\frac{Gm}{r^{2}}-4\pi r^{2}\frac{\partial P}{\partial m}[/tex]
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:
[tex]\tau_{dyn}=\frac{R}{v_{esc}}=\sqrt{\frac{R^{3}}{2GM}}[/tex]
But again, I am really stuck as to how to use these equations to solve this problem, any advice is greatly appreciated.
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:
[tex]\frac{d^{2}r}{dt^{2}}=-\frac{Gm}{r^{2}}-4\pi r^{2}\frac{\partial P}{\partial m}[/tex]
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:
[tex]\tau_{dyn}=\frac{R}{v_{esc}}=\sqrt{\frac{R^{3}}{2GM}}[/tex]
But again, I am really stuck as to how to use these equations to solve this problem, any advice is greatly appreciated.