[time-nuts] gravity controlled pendulumn clock?
jimlux at earthlink.net
Mon Dec 12 18:17:03 EST 2011
On 12/12/11 2:19 PM, Magnus Danielson 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.
Oh.. I see.. you're thinking that approximating the field as that of a
point mass when you're close to the surface of a sphere isn't valid.
Hmm. this sounds like one of those integration over a volume problems I
was doing 35 years ago in school.
integrate (1/r^2)dm for dm over a sphere..
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