The pressure gradient towards the center of a large planet, such as Earth, reaches its maximum due to the weight of the overlying material, despite the gravitational field falling to zero at the center. The pressure can be mathematically represented by the equation P=∫ρgdr, where g is defined as g=Gm/r² and m=∫4πr²ρdr. The radial distribution of density (ρ) is crucial in determining the pressure curve, which eases off as one approaches the center. High temperatures do not significantly affect this distribution in this context.
PREREQUISITESStudents and professionals in planetary science, astrophysics, and physics, particularly those interested in the dynamics of pressure and gravitational effects within large celestial bodies.
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?
kevindin said:What would the curve look like and what would the formula be?
snorkack said:There would be no effects due to high temperature. What matters is the radial distribution of ρ.
Drakkith said:It reaches its maximum, as the pressure is the result of the weight of the overlying material.