Re: Riddle me this

From: Notch.Johnson (notch.johnson_at_bigstring.com)
Date: 12/23/04 

Date: 22 Dec 2004 17:58:36 -0800

hi robert

a pendulum clock in zero gravity will stop

do you think time stops too ?

robert j. kolker wrote:
> Assume a perfectly spherical earth and a spherical shell concentric
with
> earth with a 100,000 mile radius.
>
> Now take two identical pendulum clocks. One is located a 0 lat 0 long
on
> the earth, the othe other is located at at 0 lat 0 long on the shell.

> Now pull the pendulum out by a small angle for both clocks, and using
a
> light signal half way between signal to let the pendula go.
>
> The period of the lower pendulum is T_low = 2*pi*sqrt(L/g), where L
is
> the length of the pendula (the same in both cases) and g is the
> gravitational acceleration at the surface of the erth. The period of
the
> upper pendulum is T_high = 2*pi*sqrt(L/g') where g' is the
gravitational
> acceleration at the surface of the shell. g' < g, which mean T_low is

> less than T_high. This means the pendulum on the shell swings more
> slowly than the pendulum at the surface of the earth.
>
> If I am not mistaken this says the clock on the shell is running
slower
> than the clock on the surface. But the gravtitational field on the
shell
> is less than the gravitational field on the surface. I am confused. I

> thought clocks in the lesser grav field are supposed to run -faster-.
>
> Can some one help to clear this up. TIA.
>
> Bob Kolker

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