[time-nuts] gravity controlled pendulumn clock?
Jim Lux
jimlux at earthlink.net
Mon Dec 12 18:26:25 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.
>
If the mass is spherically symmetrical (which I assumed), then Gauss's
law says that the gravitational force at a distance r from the center is
M* G/r^2 pointing directly inward where M is the total mass within
radius r. Mass beyond radius r has no net effect (like potential inside
a conductive sphere, it all exactly cancels)
wikipedia "Shell Theorem" has a nice exposition.
(which I will readily confess I did not remember)
As other posters have pointed out, if the mass distribution isn't
spherically symmetric, then g will change. Interestingly, until there
were artificial satellites, you couldn't tell that the earth is slightly
pear shaped.
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