Imagine the whole ball being separated into a handful of concentric shells, with the outermost shell being the crust with the surface, and the lower shells ever deeper, hotter, and ghastly regions of the internals of our planet. Mercury is smaller and less massive than Earth, so it cannot generate as much compression from its gravity. In fact this compression causes Earth to become denser than Mercury, even though the latter is overwhelmingly iron. This means the pressure required to balance gravity deep inside Earth is sufficient to compress the material and make it more dense than it normally would be. This is comparable to and maybe larger than the bulk modulus of the materials that make up the Earth for instance Encyclopedia Britannica gives a bulk modulus of only 160 GPa for steel (an iron-based alloy) under ambient conditions. Second, the maximum pressure noted above is 360 GPa. Thus is seen in the plot where the mantle meets the denser material in the core (rock -> iron). So if there is an increase in density (more mass packed into the same volume), the gradient jumps. Actually it is proportional to force per unit volume, whereas gravity at any point is a certain amount of force per unit mass. First, it was mentioned above that the pressure gradient is proportional to the local gravitational force. Lajos Volgyesi, M Moser "The Inner Structure of the Earth", Periodica Polytechnica Chemical Engineering (1982) 26(3).Ī couple additional features should be noted in the above plot. Note carefully that, as expected where the gravity is locally zero, the total pressure levels off until its gradient is zero at the center but the total pressure itself is maximized there instead of dropping to zero. The pressure at the center of Earth is about 360 GPa. Instead of zero, the pressure at the center will be a maximum. True, gravity at that point is zero, but it and therefore the pressure gradient have already been integrated over the whole radius (and mass) of the Earth. The maximum occurs at the point towards which gravity is directed in a spherical mass, which is the center.
When that force is integrated over a distance, the pressure gradient is integrated to accumulate a total pressure. It is the pressure gradient that is proportional to the local gravitational force.
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