Oscillating Formation of Spherical Mass in elastic universe

[FallenApple]

Situation, a empty universe where there are only concentric spherical shells of mass dm spaced apart by distance dx and contracts under gravity to form a sphere. Assume that there is a point mass in the middle of all the shells. I don't think it would work without it. case1 is an inelastic universe.
case 2 is an elastic universe.

case1: There is potential energy in a separation of masses because they have a natural tendency to accelerate towards each other. As infinitely far away concentric shells contract, they contract faster and faster. As the shells of masses fall on top of each other, they hit the uncompleted sphere at slower and slower final velocities. Because the uncompleted sphere is not moving, it has internal energy. So the internal energy of the inner parts will be more than the internal energy of the outer parts. Until it all evens out. So what we should have in the end is a vibrating sphere of mass M( sum of all the dm).
Case2: the first concentric sphere will rebound off of the center point mass and have an radially outward momentum because this collision is completely elastic. The second shell seems like it will have less momentum, but it was further away by an amount, say dx, resulting in the equal but opposite momentum with the second shell. This causes an inelastic rebound of the second of the second shell and so on. Finally, the last shell will just rebound, then the second to last, and so on. So the sphere will just disassemble itself in an elastic universe. And this process will just keep oscillating in an elastic universe.

So in an elastic universe with only these concentric shells, it will just be a continuous formaton and deformation of a sphere of mass with time. Is this logic correct?

 

[eljose79]

I would like to provide some insights and clarifications on the scenarios described above.

Firstly, in a universe with only concentric shells of mass, there would still be potential energy present even without a point mass in the center. This is because the shells themselves have mass and therefore, they would still have a natural tendency to accelerate towards each other due to gravity. However, the presence of a point mass in the center would certainly affect the dynamics of the system.

In case 1, where the universe is considered to be inelastic, the scenario described is plausible. As the shells contract towards the center, they would gain kinetic energy and eventually collide with the uncompleted sphere. The resulting collisions would lead to the redistribution of energy, resulting in a vibrating sphere with a total mass equal to the sum of all the shells.

However, in case 2, where the universe is considered to be elastic, the described scenario may not be entirely accurate. In an elastic collision, the total kinetic energy before and after the collision remains constant. Therefore, the shells would not lose any energy as they rebound off the center point mass. The momentum transfer between the shells would also result in a continuous oscillation of the sphere, but it would not disassemble itself as described.

Additionally, it is important to consider the effects of angular momentum in this scenario. The shells would not only have radial momentum but also angular momentum as they contract towards the center. This could affect the dynamics of the system and lead to a different outcome than described.

Overall, the logic presented in both cases is plausible, but it may not accurately describe the dynamics of such a universe. More research and calculations would be needed to fully understand the behavior of this system and to determine the accuracy of the described scenarios.