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Thread: Centrifuges

  1. #1
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    Centrifuges

    Many phenomenon in space look like perfect centrifuges running for millions of years.
    Am I correct in thinking this is somewhat ignored in accepted models of star formation and alike?
    So stars are assumed to have similar makeup from the material the were formed from and not largely depleted in heavier elements by centrifugal action.

    I am thinking about any object rotating fast enough to flatten-out away from being a sphere & where there is internal pressure.
    So this would include accretion disks, protostars, protoplanetary disks & quasars etc.

    Looking at the modelling of angular momentum being transferred outwards in these object they all have forces generated by material rotating faster than orbital velocity balancing weight pressing in.
    But the mixture of material involved could vary in density by factors of 10,000
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    Quote Originally Posted by PetTastic View Post
    Many phenomenon in space look like perfect centrifuges running for millions of years.
    Am I correct in thinking this is somewhat ignored in accepted models of star formation and alike?...
    No, you are not correct about this. None of the things you mention spin fast enough for centrifugal forces to outweigh gravity. For example, accretion disks are no different in this regard than Saturn's rings. No separation of lighter and heavier isotopes will occur from such a process.
    Forming opinions as we speak

  3. #3
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    Well, Jupiter and Saturn are flattened spheres because of their fast rotation, but their heavier materials are at their cores due to their enormous gravity. It is not really like a centrifuge.
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    Quote Originally Posted by antoniseb View Post
    No, you are not correct about this. None of the things you mention spin fast enough for centrifugal forces to outweigh gravity. For example, accretion disks are no different in this regard than Saturn's rings. No separation of lighter and heavier isotopes will occur from such a process.
    In normal orbits or Saturn's rings rotational forces balance gravity and there is zero or very little physical or magnetic pressure in the system.
    For a steady state you have: rotational forces == gravity

    In system where angular moment is being transferred outwards pressure is required to create the physical or magnetic 'friction'.

    The outside the pressure is created by the weight of material pressing in.
    On the inside to stop material falling in faster and faster or the disk getting thicker and thicker rotational forces need to balanced against the weight.

    As rotating material is pushed inwards by the weight of material behind it conservation of angular momentum makes it spin faster & faster until forces are balanced.
    For steady state : rotational forces == gravity + weight of material pressing in
    So rotational forces are larger than gravity.
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    Any reasonably sized body of normal matter that spun fast enough to separate elements, would probably tear itself apart.
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    Quote Originally Posted by Noclevername View Post
    Any reasonably sized body of normal matter that spun fast enough to separate elements, would probably tear itself apart.
    Rather by definition. For centrifugal force to cause separation by density instead of gravity, it would have to exceed gravity, which would leave surface tension the only thing binding the object together.

    Rotation also brings Coriolis effects into play, which would tend to stir things up.

  7. #7
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    Yes to these last two comments.

    A centrifuge, to do anything at all, must be strong enough to hold together on its own internal structure. The entire point of a centrifuge is that denser or more massive material will try to escape (by inertia) but can't (because they'e constrained).

    Gravitationally-bound bodies, like the Sun and Earth are not held together by an internal structure (on large scales), but by gravity. The moment you negate gravity (by spinning it), those parts of the Sun - or the Earth - will simply ... leave.

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    Spent a bit of time checking I am not talking rubbish.
    (very long reply edited down & down…)
    So, looking through stuff to see how finite elements are setup for rotating objects in space.
    Radial forces on finite element in general case: s(r) + w(r) + d(r)a(r) + d(r)g(r) = f(r)
    r: radial distance
    s: supporting pressure
    w: weight pressing down
    a: radial acceleration
    g: radial gravity
    d: relative density (I am adding this as most papers are only interested in hydrogen)
    f: resulting net force (zero at steady state)
    So, in steady state we have (dropping all the (r)): s + w + da + dg = f = 0

    At large r on the outer edges of object w & s drop to near zero, giving: da + dg = 0 or a + g = 0 (orbit, Saturn’s rings etc)

    In the Jupiter case suggested above, flattening is 0.06487 so rotational forces are relatively small.
    g(r) is zero at centre of planet, reaches max below cloud tops & then falls off with inv square.
    Inside planet supporting pressure balances weight pressing down: s + w = 0
    This leaves dominant force as dg, density acting under gravity. (dense material sinks, light stuff rises)

    When rotation forces are high with a high degree of flattening and there is pressure/friction to transfer momentum outwards.
    Accretion disk hanging over black hole is only held up by rotational forces. The weight w comes from new material joining disk. The disk is thin because supporting pressure is low compared to rotational forces. s(r) is zero in very inner edge of disk hanging over black hole and reaches a max at point where new matter joins disk.
    For ‘most’ of the disk s + w < 0 so da + dg >0 at steady state. (dense material rises, light stuff sinks)

    Protostars & their disk’s is like above but gravity g(r) is zero at the centre of the disk and only slowly increases depending on mass distribution (can even go negative if centre of disk is thin enough in binary star producing models). s(r) varies widely in models (super sonic collapses don’t increase pressure ahead of shock front)
    Long-period steady state modelling is not applicable as everything in moving inwards but over short time-frames for ‘most’ of the disk/protostar s(r) and g(r) are small compared w(r) and d(r)a(r). (dense material moves inward slower than low density (hydrogen))
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    Too late to edit
    The 'most' & 'mostly' mean large part of volume where there is meaningful density.
    As in the Earth's atmosphere is 'mostly' nitrogen & oxygen.
    However, if draw the Earth's atmosphere to linier scale, by volume it is 86% hydrogen helium.
    Last edited by PetTastic; 2020-Feb-19 at 02:31 AM.
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  10. #10
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    Quote Originally Posted by PetTastic View Post
    Too late to edit
    The 'most' & 'mostly' mean large part of volume where there is meaningful density.
    As in the Earth's atmosphere is 'mostly' nitrogen & oxygen.
    However, if draw the Earth's atmosphere to linier scale, by volume it is 86% hydrogen helium.
    Can you explain that last statement? Do you mean this?
    https://en.wikipedia.org/wiki/Atmosp..._by_height.svg
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  11. #11
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    Quote Originally Posted by Jim View Post
    Can you explain that last statement? Do you mean this?
    https://en.wikipedia.org/wiki/Atmosp..._by_height.svg
    If you draw the diagram to scale the oxygen drops to negligible levels at about 700km up but the Exosphere extends to 10,000km up.
    So, oxygen only extends 14.3% of the full height of the atmosphere.
    Normally the tiny amount of gas/plasma in the Exosphere can be ignored, but in these situations ignoring it make the layers below expand upwards in calcs.

    The other thing that was pointed out to me was this should say 'go positive' as norm neg by convention.
    (can even go negative if centre of disk is thin enough
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  12. #12
    That has more to do with escape velocity than anything else oxygen usually exist as O2 which in molecular weight terms is 32, 8 protons, 8 neutrons times 2 each, Helium on the other hand is only 4, so helium has 1/8 the mass and escapes easier than oxygen.
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