[time-nuts] Q/noise of Earth as an oscillator

Azelio Boriani azelio.boriani at gmail.com
Wed Jul 27 09:58:52 EDT 2016


Exciting the Earth with a new frequency (and an adeguate amount of
energy) sets a new rotational speed: you cannot retune a (for example)
quartz crystal in the same way...

On Wed, Jul 27, 2016 at 3:42 PM, Tom Van Baak <tvb at leapsecond.com> wrote:
> Hi Michael,
>
> I sympathize with both your and Attila's comments and would like to dig deeper for the truth on this.
>
> Clearly both the earth and a pendulum (and many other periodic systems) exhibit a decay of energy, when you remove the periodic restoring force. And if you take the classic definition Q = 2 pi * total energy / energy lost per cycle then it would seem earth has a Q factor.
>
> In fact, if you use real energy numbers you get:
>
> - total rotational energy of earth is 2.14e29 J
> - energy lost per cycle (day) is 2.7e17 J
> - so Q = 2pi * 2.14e29 / 2.7e17 = 5e12, the same 5 trillion as my earlier calculation.
>
> But your point about resonance is a good one and it has always intrigued me. Is this one difference between a pendulum and the earth as timekeepers?
>
> On the other hand, if you swept the earth with an external powerful frequency in the range well below to well above 1.16e-5 Hz (1/86164 s) would you not see a resonance peak right at the center? Given the mass of the planet and its pre-existing rotational energy, it seems like there is a "resonance", a preference to remain at its current frequency. Plus it has a slow decay due to internal friction. This sounds like any other timing system with Q to me.
>
> Or imagine a planet the same size as earth made from a Mylar balloon. Much less mass. Give it the same rotational speed. Much easier to increase or decrease its energy by applying external force. Far lower Q than earth, yes?
>
> It might also be useful at this point, to:
>
> read the history Q and its definition:
> http://www.collinsaudio.com/Prosound_Workshop/The_story_of_Q.pdf
>
> and read the patent in which Q first appeared:
> http://leapsecond.com/pages/Q/1927-US1628983.pdf
>
> or view the first paragraph in which Q appeared:
> http://leapsecond.com/pages/Q/1927-Q-patent-600x300.gif
>
> /tvb
>
> ----- Original Message -----
> From: "Michael Wouters" <michaeljwouters at gmail.com>
> To: "Discussion of precise time and frequency measurement" <time-nuts at febo.com>; <attila at kinali.ch>
> Sent: Wednesday, July 27, 2016 5:43 AM
> Subject: Re: [time-nuts] Q/noise of Earth as an oscillator
>
>
>> On Wed, Jul 27, 2016 at 8:08 AM, Attila Kinali <attila at kinali.ch> wrote:
>>
>> "I am not sure you can apply this definition of Q onto earth."
>>
>> It  doesn't make sense to me either.
>>
>> If you mark a point on the surface of a sphere then you can observe
>> that point as the sphere
>> rotates and count rotations to make a clock. If you think of just a
>> circle, then a point on it viewed in a rectilinear coordinate system
>> executes simple harmonic motion so the motion of that point looks like
>> an oscillator, so that much is OK.
>>
>> But unlike the LCR circuit, the pendulum and quartz crystal, the
>> sphere's rotational motion does not have a
>> resonant frequency. Another way of characterizing the Q of an
>> oscillator, the relative width of the resonance, makes
>> no sense in this context.
>>
>> It seems to me that the model of the earth as an oscillator is
>> misapplied and that the 'Q' is not a meaningful number.
>> I think the confusion arises here because of a conflation of a
>> rotation of the sphere (which marks out a time interval) with an
>> oscillation. Both can be used to define an energy lost per unit time
>> but the former doesn't have anything to do with the properties of an
>> oscillator.
>>
>> Something else that indicates that the model is suspect is that the
>> apparently high 'Q' implies a stability which the earth does not have,
>> as Tom observes. Viewed another way, this suggests that the model is
>> inappropriate because it leads to an incorrect conclusion.
>>
>> Time for bed. I'll probably lie awake thinking about this now :-)
>>
>> Cheers
>> Michael
>>
>> On Wed, Jul 27, 2016 at 8:08 AM, Attila Kinali <attila at kinali.ch> wrote:
>>> Hoi Tom,
>>>
>>> On Tue, 26 Jul 2016 12:36:37 -0700
>>> "Tom Van Baak" <tvb at LeapSecond.com> wrote:
>>>
>>>> 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.
>>>
>>> I am not sure you can apply this definition of Q onto earth. Q is defined
>>> for harmonic oscillators (or oscillators that can be approximated by an
>>> harmonic oscillator) but the earth isn't oscillating, it's rotating.
>>> While, for time keeping purposes, similar in nature, the physical
>>> description of both are different.
>>>
>>>                         Attila Kinali
>>>
>>> --
>>> Malek's Law:
>>>         Any simple idea will be worded in the most complicated way.
>>> _______________________________________________
>>> time-nuts mailing list -- time-nuts at febo.com
>>> To unsubscribe, go to https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts
>>> and follow the instructions there.
>> _______________________________________________
>> time-nuts mailing list -- time-nuts at febo.com
>> To unsubscribe, go to https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts
>> and follow the instructions there.
> _______________________________________________
> time-nuts mailing list -- time-nuts at febo.com
> To unsubscribe, go to https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts
> and follow the instructions there.


More information about the time-nuts mailing list