[time-nuts] gravity controlled pendulumn clock?

[Jim Lux]

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.