On Thu, Dec 20, 2018 at 11:57 PM Brent Meeker <[email protected]> wrote:
>> The mass of the Earth played no part in Cavendish's determination of G >> because he was measuring gravitational attraction in a direction that >> was parallel to the Earth's surface. > > > * > But in comparing it to the clock precision you have to consider that > the clock is measuring the change over a cm of a very much greater > potential, * > Yes, that makes it even more valuable. > > > *while Cavendish is measuring a much smaller change in a much smaller > potential.* > No, the change Cavendish measured was much larger not smaller. >> the new clock can detect the difference in time dilation between 1g and >> 1.000000003g, so I'm sure it could detect the time dilation caused by a 348 >> pound mass a foot or so away. > > * > Could it? * > Yes indeed. > > *The gravitational time dilation factor is tau = sqrt[1 - 2GM/rc^2]. So > a clock that can detect a one cm change in height at the Earth's surface is > in fact not accurate enough to to detect the difference between being > adjacent to a 348lbm 18" ball and being arbitrarily far away from it.* > Cavendish could not detect the gravitational field arbitrarily far away from an object nor can anybody else because that would take infinite precision, but lets calculate what he did do. The gravitational time dilation factor is sqrt[1 - 2GM/rc^2] so if G is 6.67 × 10^-11 m3 kg^-1 s^-2 and c is 1*10^8 meters/sec then the gravitational time dilation factor caused by being 9 inches (.0002 kilometers) away from the center of a 248 pound (112 kilogram) lead ball is, if I did my arithmetic correctly, 1-square root of [1- 112 *(13.3 *10^-11) / .0002 *(3*10^8)^2)] = 1-(2.6*10^-6) = .999997. So Cavendish was able to detect a gravitational field that would make a time dilation of about 3 parts in a million, but this new clock could detect the change in a gravitational field that would make a time dilation of about 3 parts in a billion, a thousand fold improvement. John K Clark -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
