Let's say we have 2 planets, one being 'a' (the bigger one) and one being 'b'. Planet a is completely hollow inside with planet b is inside of it. My question is how much gravitational force would planet a have to exert on b to turn b into a molten core.(if it is possible) planet b is about 2.12x10^23kgs. I don't care how much planet a weighs, that's up to you.
TLDR : Not going to happen.
Despite the shell theorem there is a net force between the two.
Object (a) on the outside ("the shell") does not exert any net force on any part of object (b) ("the core") regardless of the relative positions as long as (b) is entirely enclosed in (a) and (a) is spherically symmetrical. That's an absolute result from the Shell Theorem.
But the core (b) does exert a net attraction on every part of the shell (a). The shell theorem does not apply outside an object.
So the core will attract the shell and, as there must be an equal and opposite reaction, the core will also feel a force balancing that.
But this is a very, very unstable configuration.
The instant the core's center shifts even a fraction off the exact center of the shell it will inexorably move off the center, most likely accelerating into a collision with the shell.
Likewise if either the core or the shell are not perfectly spherically symmetrical they will drift off and eventually most likely collide.
My question is how much gravitational force would planet a have to exert on b to turn b into a molten core.(if it is possible) planet b is about 2.12x10^23kgs.
Never going to happen.
The net force on every part of the core is not compressive (inward) but outward (an opposite reaction to the attractive force it exerts on the shell). So while there could be extreme sheering forces if they cease to be in a stable configuration (and they would eventually) there would no be compressive forces globally on the core, only perhaps (a maybe) on local parts of the core undergoing deformation as part of sheering. But that's unlikely to melt the core, so much as break it up.
Likewise the forces on the shell are all pulling it inward, but this would also require the shell to support itself. This would almost certainly be impossible - you're describing a Dyson Sphere, in fact.
If you want at least part of the core to be molten it would have to do it under it's own efforts. This either requires that :
- The core was formed in such a way that it has not yet dissipated it's heat of formation - actually Earth's condition, hence our own molten core.
- or the core had a very radioactive interior (unlikely to be significant, IMO)
The Earth would have been a molten ball early in it's formation. It has cooled gradually down. That's how it works.
I don't think your system is at all possible without artificial support, which would be a feat of staggering difficulty, beyond out current science and probably going to stay that way for many, many tens of thousands of years if at all.
The way your question is set up, it does not sound like planet B would become a molten core at all. If planet A surrounds B in the manner described, B will be gravitationally pulled outward by A, the gravity will reduce B's pressure inward, not raise it.
If you are thinking that A's gravity is so strong that B is fully pulled apart and is itself hollow, a hollow molten core pushing outward along the inner wall of the hollow planet A because the hollow cavity is large enough and A's crust thick enough for that much gravity, I don't think that would happen either, and even if it did then B would not be a separate planet anymore but rather would be part of planet A.
The pressures within our planet which contribute to our molten core would not be possible if it were not for the fact that all the rest of the world is sitting on top of it. In the case of your hollow world, nothing will be weighing upon planet B. Planet B can be considered a normal planet just like any other, and therefore treated as any other with its own normal geology, with the exception that it has the inner wall of another planet overhead.
The following assumes A is roughly spherical with a roughly spherical cavity which itself is centrally located within planet A. Now remember, even though the center of mass of A is at the center of its hollow cavity, B is being attracted to the matter of planet A, so it is actually being attracted outward. For a sufficiently large planet A, this could even result in a planet B rolling around the inner cavity wall of A.
For a planet B stabilized at the center of mass of A such that it is suspended in the center of the cavity, increasing the gravity will not pull B apart. If you increase A's gravity sufficiently, it would merely pull B out of its stabilized position with the entirety of B "falling" out toward some random direction and leave you with something more like the previous paragraph before this one.
That said, there is a catch to what I said, something that might still be close to what you are after, in a way. If B settles down (down is subjective here; I am meaning toward the surface of a sphere halfway between A's outer surface and inner cavity surface), and if A's crust is sufficiently thick that B can undergo similar geological activity within A just as our core does in Earth, then it could still become molten given the right conditions. However, there are now a few issues:
At this point, again, B is no longer a separate planet but is part of A
Once B becomes molten, if the material in A is the same all the way around, then B will likely become a molten sphere going around the entirety of A, a molten sphere sandwiched between solid material on the inside and out.
This all assumes that A can hold its hollow shape through the process. I am not sure if there is a natural planetary make-up that could, so I would hand-waive that problem away and suggest that A is an artificial planet. Or you could come up with some outlandish quasi-scientific rationale for the hollow planet that aided in the suspension of disbelief. "The planet is electrically charged, and the build-up of a static charge is causing the particles to repel from each other just like your hair does when charged, so it has developed a hollow cavity." That would not really work, and your science purists will role their eyes, but that should be sufficient to appease the laymen.