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Thread: Grandfather clock on a collapsing planet

  1. #1
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    Grandfather clock on a collapsing planet

    Let's say we have a planet the same size as Earth and there is a grandfather clock standing on the surface.

    This planet starts to collapse slowly.

    What I want to know is how a distant observer will see the clock's pendulum.

    The strength of the time dilation at the surface will gradually increase, but then so will the strength of gravity.

    So will the pendulum appear to keep the same rate of swinging, will it increase its rate, or will it slow down?

    (this is just a thought experiment. obviously a planet size object shouldn't just collapse)
    Formerly Frog march.

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  2. #2
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    Speed up, then slow down.
    You could graph it for yourself. In this scenario, the period (in the proper time at the planet's surface) varies directly with r, where r is the radius of the planet. The time dilation for a distant observer varies with sqrt(1-rs/r), where rs is the Schwarzschild radius for the planet.

    Grant Hutchison
    Blog

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  3. #3
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    grandfather clock.jpg

    Does that look right?
    Formerly Frog march.

    Newscaster: ... But I've just had a report that a representative of Disaster Area met with the environmentalists this morning and had them all shot, so now nothing stands in the way of the concert going ahead this afternoon on this beautiful sunny day.

  4. #4
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    Does the turn around happen at four times the Schwarzschild radius?
    Formerly Frog march.

    Newscaster: ... But I've just had a report that a representative of Disaster Area met with the environmentalists this morning and had them all shot, so now nothing stands in the way of the concert going ahead this afternoon on this beautiful sunny day.

  5. #5
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    1.5 Schwarzschild radii. In Schwarzschild radii the apparent clock rate is a function of (r-1)/r3, which differentiates to (3-2r)/r4, which zeroes at r = 1.5, reflecting a maximum rate at that point.

    Grant Hutchison
    Blog

    Note:
    During life, we all develop attitudes and strategies to make our interactions with others more pleasant and useful. If I mention mine here, those comments can apply only to myself, my experiences and my situation. Such remarks cannot and should not be construed as dismissing, denigrating, devaluing or criticizing any different attitudes and strategies that other people have evolved as a result of their different situation and different experiences.

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