What is the Derivation for Pressure at the Centre of a Star?

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SUMMARY

The pressure at the center of a star can be derived using the formula P = (Gm^2)/(8πR^4). The discussion highlights the relationship between gravitational force and surface area, where the gravitational force is given by f = G*m^2/R^2 and the surface area is 4πR^2. The confusion arises from the incorrect application of these formulas, specifically the factor of 4 instead of 8 in the denominator. Proper understanding of the derivation process is essential for accurate calculations.

PREREQUISITES
  • Understanding of gravitational force (Newton's law of gravitation)
  • Familiarity with basic calculus (for derivation processes)
  • Knowledge of stellar structure and physics
  • Concept of pressure in a physical context
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Brewer
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I've been asked to derive the pressure at the centre of a star (well show that it is (Gm^2)/(8*pi*R^4).)

I've worked it through as follows:

Pressure = force/area

f=G*m^2/R^2

surface area = 4*pi*R^2

and then I put the two formulas together but as you can see I only have a 4 on the bottom instead of 8. Have I missed something clearly obvious here?

Any help would be appreciated.
Thanks
 
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If you're looking for the pressure at the center of the star why are you using the force and area at the surface of the star?
 
Because I couldn't think of another way to do it - it seemed logical to me when the equation I had to get has both the radius and mass of the star. Am I totally lost?
 

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