Hal Murray wrote: > What is the Q of the Earth? It might be on one of your web pages, but I > don't remember seeing it. Google found a few mentions, but I didn't find a > number.
3.1415 * 86400 * 365 * 100 / 0.002 = 5e12, or 5 trillion. Here's why: (1) Among other things, the quality-factor, or Q is a measure of how slowly a free-running oscillator runs down. There are lots of examples of periodic or damped oscillatory motion that have Q -- RC or LC circuit, tuning fork, pendulum, vibrating quartz; yes, even a rotating planet in space. In the high vacuum of space you'd think the Earth would rotate forever, but the moon affects earth's rotation; it causes "tidal friction". Astronomers have measured the slowing as roughly "2 ms per day per century". For example, the average length of a day in 1900 was about 86400.000 seconds and the average length of a day in 2000 was about 86400.002 seconds. That's a deceleration, or slight loss in rate, or slight gain in period, of 2 ms/day per century. Since the spinning earth oscillator is slowing down, you can calculate its Q factor. (2) The common definition of Q is 2pi times the number of periods it takes for the energy to fall to 37% (1/e). Although correct and simple, it is sometimes awkward to use this definition. I mean, it can take forever to lose 63% of your energy if Q is really high or the period is really long. Another definition of Q is 2pi over dE/E, the latter term being called the "decrement", which is the relative energy loss per period. For example, if your wine glass oscillator loses 1% of its energy each period, then its Q = 2pi/1%, or 628. This formula for Q is more convenient because you can do it with data from a single period. For earth the period is 1 day. So what's the decrement, the relative energy loss for one day? (3) Rotational energy goes as w^2, where w (omega) is the rotation rate. This means energy drops twice as fast as rotation rate drops. And how fast does the earth rotation rate drop? That would be 2 ms per day per century, which is 2.3e-8 per century, or 2.3e-10 per year, or 6.3e-13 per day. So the relative loss of energy per period (day) is twice that: 1.3e-12. Plug that into the decrement definition of Q and your calculator gives 5e12. So the Q of the earth is 5 trillion. https://www.google.com/#q=3.1415+*+86400+*+365+*+100+/+0.002 /tvb p.s. This Q is really high, and you might expect a similarly superb Allan deviation. But no, not at all: http://leapsecond.com/museum/earth/ The reason the ADEV is so poor compared to the Q is that Earth, as a timekeeper, is an unstable mess inside and out. There are all sorts of massive perturbing factors from the liquid core to the swirling atmosphere to the annual redistribution of water and biomass; these all affect the short-term performance. ----- Original Message ----- From: "Hal Murray" <hmur...@megapathdsl.net> To: "Tom Van Baak" <t...@leapsecond.com>; "Discussion of precise time and frequency measurement" <time-nuts@febo.com> Cc: <hmur...@megapathdsl.net> Sent: Saturday, July 23, 2016 5:59 PM Subject: Q/noise of Earth as an oscillator > > t...@leapsecond.com said: >> Earth is a very noisy, wandering, drifting, incredibly-expensive-to-measure, >> low-precision (though high-Q) clock. > > What is the Q of the Earth? It might be on one of your web pages, but I > don't remember seeing it. Google found a few mentions, but I didn't find a > number. > > I did find an interesting list of damping mechanisms in a geology book. > Geology-nuts are as nutty as time-nuts. Many were discussing damping of > seismic waves rather than rotation. > > I've seen mention that the rotation rate of the Earth changed by a few > microseconds per day as a result of the 2011 earthquake in Japan. Does that > show up in any data? Your recent graph doesn't go back that far and it's got > a full scale of 2000 microseconds so a few is going to be hard to see. > _______________________________________________ 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.
