On Sat, Dec 22, 2018 at 2:36 AM Brent Meeker <[email protected]> wrote:
* > I'm not sure why you converted 9" to kilometers instead meters,* > Oh that's very easily explained. I was stupid. > *> but: 2(6.67e-11)112/0.2(9e16) = 8.3e-25* > Yes, I get 8.3*10^-25 too. And the square root of (1 - 8.3^10^-25) is 0.9999999999999999999999995850. In my previous post I claimed it was .999997 which was dead wrong, and as you correctly say that is "*Waaay closer to 1.0 than the time dilation due to raising a clock 0.01m above the Earth's surface*". So I was entirely wrong and you are entirely correct, thank you for correcting my careless error. > *He *[Cavendish] *claims to have measured the deflection of the smaller > masses within 0.25mm.* But in Cavendish's day nobody had a scale sensitive enough to measure or even detect the difference in gravity caused by the elevation of a meter or even a kilometer, much less a millimeter as this new clock can. The torsion balance Cavendish used could only detect forces parallel to the Earth's surface. > *Which is not only wrong arithmetically, it is comparing the time > dilation factor which depends on the potential (goes as 1/r) to the > acceleration (which goes as 1/r^2).* > Yes but that means the difference in gravitational potential and the resulting time dilation of a clock 6.37* 10^9 mm from the Earth's center and a clock (6.37* 10^9) +1mm from the center must be really really small if it changes only linearly with distance and doesn't change according to the distance squared; and yet this clock could still detect that tiny change. But you're right, acceleration is not the key factor to gravitational time dilation, it's escape velocity. If you were on the surface of a planet that was larger and more massive than the Earth the surface acceleration could still be at just one g like on the surface of the Earth if the planet were less dense than the Earth because then the mass is greater but you're further from the center and they could cancel out. So although you're still at one g the escape velocity needed to get free of the planet would be greater and General Relativity says the gravitational time dilation would be the same as Special Relativity says it would be if you were moving at the escape velocity in empty space far from any strong gravitational field. 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.
