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B Oscillating Formation of Spherical Mass in elastic universe

  1. Nov 30, 2016 #1
    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 continous formaton and deformation of a sphere of mass with time. Is this logic correct?
    Last edited: Nov 30, 2016
  2. jcsd
  3. Dec 5, 2016 #2
    Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.
  4. Dec 5, 2016 #3
    I guess I just wrote too much. I was curious what would happen from a qualitative perspective what happens when there are concentric spherical shells of mass(ones that are allowed to stretch and shrink radially).

    I guess to make it simpler: say there are two shells of mass.

    I found it curious that from gausses law, we see that the inner shell doesn't move( do to it being uninfluenced by the gravitational force of the outer shell since the field inside a shell is 0 inside of it and the inner shell is inside). But that the outer shell contracts to the inner shell.

    So basically, it appears very strange that the inner shell causes the outer shell to accelerate but the outer shell does not do the same to the inner shell. What explains this? I mean, if a ball falls on the earth, we know that the earth will be pulled up by a negligible amount. Or that when object at rest fragments, it was due to the some sort of inner potential energy( springs, chemical etc).

    I wonder it could be explained in the following manner: So in the space in between the two shells, only the gravitational field of the inner shell exists. So It's the field due to the inner shell that is doing work on the outer shell. As the outer shell contracts, it does work on the field between them. So the inner shell doesn't need to move because the field and the outer shell are doing work on eachother?

    I think this is the situation I want to explore. Once I know more, I'll think about momentum/oscillation. Though, I cannot edit the title and OP.
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