[time-nuts] gravity controlled pendulumn clock?

[Bill Beam]

On 12/12/2011 1:19:31 PM, Magnus Danielson (magnus at rubidium.dyndns.org) wrote:
> On 12/12/2011 01:37 AM, Jim Lux wrote:
> > On 12/11/11 4:04 PM, Tom Van Baak wrote:
> >
> >> GCPC -- gravity controlled pendulum clock (elevation)
> >>
> >
> >
> > intriguing. From your parenthetical remark,
> I'm assuming you move the
> > whole assembly up and down to adjust the speed?
> >
> > I was thinking about a huge mass that moves around?
> >
> > let's
> see.. period is proportional to sqrt(1/g)
> >
> > g is proportional to 1/r^2, so period is proportional to r.
> >
> > Earth is roughly 7000 km radius, so moving it 1 meter higher or lower
> > changes the period by 1part in 7million... interesting.
> 
> Hmm... how does the near-field gravitational pull behave?
> 
> The far-field is surely r^-2, but wonder about the near-field effect.
> 
> Need to grab some paper and pen and convince myself.

For a spherical homogenious mass of radius R; g goes as r^+1 for r<R
and as r^-2 for r>R.  (This is a freshman undergraduate Physics problem.)

Bill

> 
> Cheers,
> Magnus
> 
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Bill Beam
NL7F