# Pressure (gravitational) applied by a hollow, uniform, spherical shell on an object inside it

1) It's a well-known result that the net force inside a hollow, uniform spherical shell is zero at all points.

However, for a spherical shell with finite mass inside of it, we say that the mass inside pulls the shell inwards on all sides equally, thereby creating mechanical pressure that the shell must bear. By Newton's third law, this should imply that there is an outward force (albeit one that sums up to zero at every point) being applied on the object that is inside as well.

But how will a spherical non-rigid body at the center change its shape with time due to an equal amount of force being applied from all sides? Say, if I kept a semi-solid object at the center, would it stretch all the way till the walls and stick to it? What if it was off-center?

2) Will a rigid body at the center not feel pressure from being pulled from all sides? In stars and planetary bodies approximated as uniform spheres (for example, Irodov 1.216 pg45: https://imgur.com/pMCiWqW), while calculating the pressure at an arbitrary radius inside the sphere, we consider elemental shells and integrate the pressure experienced by all of them by the spheres inside. However, we neglect the forces of the outer shell(s). If the inner body pulls the outer shell, why neglect the other way around?

• I don't follow your argument that there is a force on the central body. The inwards gravitational force on the shell is resisted by equal and opposite compressive forces in the material of the shell. There is no force on any body inside the shell. – John Rennie Dec 4 '19 at 11:20
• @JohnRennie The resistive forces are not relevant here. I'm talking about the reaction force. Gravitation is mutual, so if the inner body is responsible for pressure on an outer shell, that should mean that there is a reaction force on the inner object, albeit the object can't accelerate because it is being pulled equally in all directions (thereby making the NET force zero). Are you telling me that the inner body creates no pressure on the outer shell? – Arnav Das Dec 4 '19 at 11:34
• This is your second time asking the same question based on the same misconception. So far, five separate people have tried to get you to reconsider that misconception. Perhaps you should ask a question directly targeted on how forces combine to get good (and hopefully persuasive) answers on that? – Bob Jacobsen Dec 4 '19 at 14:08
• Related post by OP: physics.stackexchange.com/q/517590/2451 – Qmechanic Dec 4 '19 at 15:09