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

#### kevindin

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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#### Drakkith

Staff Emeritus
2018 Award
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.

What would the curve look like and what would the formula be?
That I can't answer. Perhaps someone here can provide the math.

#### snorkack

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.

#### DrStupid

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.

#### sgphysics

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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