What is the pressure gradient towards the centre of a large planet?

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Discussion Overview

The discussion revolves around the pressure gradient towards the center of a large planet, specifically considering the implications of gravitational forces and the distribution of mass. Participants explore theoretical aspects of pressure curves, mathematical formulations, and the influence of temperature on pressure distribution.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants propose that as the gravitational field falls to zero at the center of a large body, the pressure curve may also ease off, but the exact behavior is uncertain.
  • Others argue that pressure reaches its maximum at the center due to the weight of the overlying material, suggesting that the pressure gradient decreases as one approaches the center.
  • A mathematical expression for pressure is presented as P=∫ρgdr, with g defined as g=Gm/r², and m as m=∫4πr²ρdr, though some participants express difficulty in determining the bounds for the integral.
  • One participant notes that while high temperatures are assumed not to affect the pressure gradient, another counters that high temperatures do influence the radial distribution of density (ρ).

Areas of Agreement / Disagreement

Participants express differing views on how pressure behaves towards the center of a planet, with no consensus reached on the exact nature of the pressure curve or the impact of temperature on density distribution.

Contextual Notes

There are unresolved mathematical steps regarding the integration bounds for pressure calculations, and the discussion hinges on assumptions about temperature effects on density distribution.

kevindin
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Given that the gravitational field falls to zero at the centre of a large body (e.g. the earth), what happens to the pressure curve? (Assuming no effects due to high temperature.) Does it ease off too? What would the curve look like and what would the formula be?
 
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kevindin said:
Given that the gravitational field falls to zero at the centre of a large body (e.g. the earth), what happens to the pressure curve?

It reaches its maximum, as the pressure is the result of the weight of the overlying material.

kevindin said:
What would the curve look like and what would the formula be?

That I can't answer. Perhaps someone here can provide the math.
 
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Simple rules
Pressure is
P=∫ρgdr
Where g is
g=Gm/r2
and
m=∫4πr2ρdr
Hm, cannot figure out an easy way to place the bounds on your ∫.
There would be no effects due to high temperature. What matters is the radial distribution of ρ.
 
snorkack said:
There would be no effects due to high temperature. What matters is the radial distribution of ρ.

High temperatures have an effect on the radial distribution of ρ.
 
Drakkith said:
It reaches its maximum, as the pressure is the result of the weight of the overlying material.

As you approach the center, less and less mass is added to the already overlying material. Hence the pressure gradient will be at its minimum.
 

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