Thanks Tom, I would agree LIGOs efforts are beyond heroic, I will try to find some of their phase noise plots.
Regarding Q of the earth, I would agree one could compute an UNloaded Q for the earth as if it were a mass element in some form of a mechanical oscillator. The first sticky point is which Q, a loaded Q (QL) would assume it's oscillating (which as many have outlined) it's not, an unloaded Q (1/DF, or X/R) would be a reasonable value to commute for some specific frequency. It is interesting (although expected) I have arrived to similar Q as you, though through different reasoning, but similar assumptions. Taking inspiration from the many brilliant controls and analog Engineers from the analog computing days, we can create a circuit equivalent model for the rotational dynamics of the earth. Some physical parameters: omega_e = 7.3E-5 rad/s (angular rate of the earth) alpha_e = -6.3E-22 rad/s^2 (angular deceleration of the earth) J_e = 8E37 kg m^2 (Inertia of the earth) Mapping the torque-(angular displacement) space to the volt-coulomb space Capacitor - Torsional Spring Q = C V, tau = k theta Resistor - Damper / Friction Qdot = V/R, tau = B thetadot Inductor - Mass Qdotdot = V/L, tau = J thetadotdot In this circuit equivalent model the inertia of the earth would be represented by an inductor of inductance L = 8E37 kg m^2 An approximate rotational friction coefficient (tidal friction, doubt it's a first order relation, but for the sake of Q, assume it is, and other losses) can be found from the net angular deceleration. B = J * |alpha_e|/omega_e = 6.9E20 Nm s Solving as an equivalent resistance yields, Rs = 6.9E20 Nm s Finally the unloaded Q at 11 and change uHz, Q = XL/Rs = (7.3E-5)(8E37)/(6.9E20) = 8.5E12 8.5 Trillion, not bad for an inductor at 11 uHz... Now if you really wanted an 11 uHz oscillator you could ram a torsional spring up the earth's south pole. >From a circuit perspective, the earth's rotation looks like a monster near superconducting inductor that at some point and somehow was precharged to a current Io, and then had its terminals crowbarred. Our solar time is like watching a reference electron run round and round a coil. Björn and Dave, thanks for the gyro reference I will take a look. On Fri, Jul 29, 2016 at 1:19 PM, Tom Van Baak <[email protected]> wrote: > Scott Stobbe wrote: > > I believe a phase noise plot deep into the uHz or lower would apply to > the > > rotation rate of the earth. > > Yup. You'll see lots of uHz to Hz noise plots by people working with > seismic noise, for example. My introduction to the subject were the many > plots and papers that describe the heroic effort LIGO goes through to > measure tidal and seismic noise in order to keep their gravity wave servos > locked. Short-term, the surface of the earth is a very noisy place. But if > you can model or measure it before it hits the mirrors, you can mostly back > it out. > > One can use PN and ADEV statistics on earth rotation, just like any other > clock or oscillator. And it seems we can also compute Q for the earth, as > if it were a mechanical oscillator. > > The remaining question in this thread is if earth Q measurement has actual > meaning, that is, if the concept of Q is valid for a slowly decaying > rotating object, as it is for a slowly decaying simple harmonic oscillator. > And that's were get into the history and definition(s) and applicability of > Q to non harmonic oscillators, such as coils, capacitors, atomic clocks, > planets, pulsars, etc. > > /tvb > > _______________________________________________ > time-nuts mailing list -- [email protected] > To unsubscribe, go to > https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts > and follow the instructions there. > _______________________________________________ time-nuts mailing list -- [email protected] To unsubscribe, go to https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts and follow the instructions there.
