Firstly gravitational force and pressure are related but different concepts.

Looking at gravity inside a planet. If we just look at an object like Jupiter and ignore any interactions with other bodies (such as the Sun) the reason the gravitational force drops with depth can be conceptually seen quite simply. Any mass in the centre of Jupiter is attracted by the rest of the mass of the planet but because this mass is in an even shell all around it, all the various gravitational forces, thus also being even, cancel themselves out. The mass in the very centre is not attracted to any other part of the planet gravitationally! (It will be attracted to the Sun of course, the whole planet needs to orbit that

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For some reason this has really stuck in my head from first year Physics, Gauss's law (wonderful thing!) and all that.

Now pressure is defined as "force applied perpendicular to the surface of an object per unit area over which that force is distributed." Or you could say, a little bit simpler, it's the total weight of everything above an area. Now in the previous example gravity has not magically switched off, it's just on a point by point basis decreased due to the effects of large masses cancelling each other out. In the case of calculating pressures, if you were to pick an arbitrary square metre

*area* inside Jupiter, you will see the large force of all the weight above it that is pushing in that perpendicular direction.

I suppose the way to think about it is that a huge mass will form a sphere and instigate powerful attractive forces inward symmetrically, hence all the mass in the centre will want to be compressed together. However the deeper you go, the less the gravitational force becomes so matter close to the centre has less impact on pressure than mass on the surface! (And calculating pressure with depth can be quite involved.

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