On 12/2/2018 7:04 PM, John Clark wrote:
On Sun, Dec 2, 2018 at 4:29 PM Brent Meeker <[email protected]
<mailto:[email protected]>> wrote:
/> The Earth is 3.9e22 times heavier than Cavendishes cannon ball. /
The mass of the earth is irrelevant because we're talking about
measuring the difference in the strength of gravity as distance
increases not its absolute value.
>> In 1798 technology was good enough for Cavendish to measure
the gravitational attraction between 2 cannonballs a few
inches apart (andby doing so determine the value of the
Gravitational Constant) but until a few months ago no
technology was good enough to measure the difference in
strength of a gravitational field that was 637,000,000
centimeters from the center of the Earth and one that was
637,000,001 centimeters from the center of the Earth. But the
technology is good enough now thanks to this new clock.
> /N//o. The potential difference measured by the cesium clock when
raised 1cm relative to the Earth was 2.03e9 times bigger than the
smallest difference measured by Cavendish (assuming he could
measure 0.00025m deflection). The Earth is 3.9e22 times heavier
than Cavendishes cannon ball. So 300yrs ago Cavendishes
technology was good enough;/
If you are on the Earth's surface and you raise a clock by one
centimeter you've increased its distance from the earth's center by
one part in 637,000,000, it is now 1.0000000016 times further away.
The intensity of the gravitational field is proportional to the square
of the distance so gravity was 1.0000000031 times stronger before you
raised raised the clock. Cavendish did not have a scale good enough to
measure that, even today the very best (and very expensive) lab weight
scale might be able to measure a change of 1.0000001 but the clock can
do several hundred times better.
He was measuring the change in a much smaller gravitational field.
> (assuming he could measure 0.00025m deflection).
When Cavendish measured a deflection he was measuring the strength of
the attraction between 2 canon balls, he was not measuring the
difference in the gravitational field at 2 points. Cavendish used a
torsion balanceand its very good at measuring weak forces but it can't
measure the super small difference between 2 strong forces, to do that
he'd need a weight scale, or a super accurate clock.
He was measuring the difference between the force on the torsion balance
with the cannon balls present vs absent.
Brent
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