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If we take an imaginary planet which consists entirely of water (i.e. a big ball of water in space), what would be the pressure at the center of it?

My friend argued that it would be zero, since the forces coming from every direction would cancel out, furthermore, at the center gravity is zero. I find this very hard to believe, but couldn't point out the fallacy in his argument (I'm a biologist).

What is the true answer?

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$P = \frac{GM^2}{8\pi R^4}$ in the approximation of constant density.

Where $P$ is the pressure at the center, $G$ is the gravitational constant, $M$ is the mass of the planet and $R$ is the radius of the planet.

see Hydrostatic Equilibrium and Planetary Differentiation

Pressure is maximal at the center of a planet.

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