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.
_______________________________________________
time-nuts mailing list -- time-nuts@febo.com
To unsubscribe, go to https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts
and follow the instructions there.
