# Thread: Grandfather clock on a collapsing planet

1. Order of Kilopi
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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)

2. 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

3. Order of Kilopi
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grandfather clock.jpg

Does that look right?

4. Order of Kilopi
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Does the turn around happen at four times the Schwarzschild radius?

5. 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

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