Hydrostatic equilibrium violated in the sun

However, the question posed is, if this violation were to occur, how long would it take for the sun to change its radius by 10%? To answer this question, the equations of hydrostatic equilibrium and the dynamical timescale are relevant. The equation for hydrostatic equilibrium is d^2r/dt^2 = -Gm/r^2 - 4πr^2(dP/dm), where P is pressure, m is mass, and r is radius. The dynamical timescale equation is τdyn = R/vesc = √(R^3/2GM), where R is the radius of the sun, vesc is the escape velocity, and G is the gravitational constant. However, it is
  • #1
AStaunton
105
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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.
 
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  • #2
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.
 
  • #3
This thread is more than four years old - no point in reawakening it now.
 

FAQ: Hydrostatic equilibrium violated in the sun

What is hydrostatic equilibrium and why is it important in the sun?

Hydrostatic equilibrium is the balance between the inward force of gravity and the outward force of pressure in a star. In the sun, this balance is crucial for maintaining a stable and long-lasting source of energy through nuclear fusion.

How is hydrostatic equilibrium violated in the sun?

Hydrostatic equilibrium can be violated in the sun when there are changes in the balance of forces due to changes in temperature, density, or composition. This can lead to localized instabilities and disruptions in the fusion process.

What are some consequences of hydrostatic equilibrium being violated in the sun?

If hydrostatic equilibrium is disrupted in the sun, it can lead to changes in the rate of nuclear fusion, fluctuations in energy output, and even the formation of sunspots or solar flares. These disruptions can have impacts on Earth's climate and communication systems.

How do scientists study and measure hydrostatic equilibrium in the sun?

Scientists study hydrostatic equilibrium in the sun through techniques such as helioseismology, which uses sound waves to probe the interior of the sun, and spectroscopy, which measures the properties of light emitted from the sun's surface. These methods allow scientists to understand the dynamics and stability of the sun's internal structure.

Can hydrostatic equilibrium ever be completely violated in the sun?

No, it is highly unlikely that hydrostatic equilibrium could ever be completely violated in the sun. The sun's immense size and mass, along with the strong forces at work, make it a highly stable and self-regulating system. However, localized disruptions can still occur and have an impact on the overall balance of forces in the sun.

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