Waaay OT- Lunar physics question

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JMartin957 wrote:

John, I was agreeing with you up top that it would be less accurate, then at the bottom you said, in effect, that it would be just as accurate.
Did your fingers stumble or am I not understanding you? How could it be just as accurate if the pendulum has a slower cycle rate on the Moon? I am not trying to pick a fuss, but I fail to understand your point. And I do want to understand.
Hoyt W.
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It's both. :-)
Accurate in the sense that it will be self-consistent; that is, an hour measured this week will be the same length of time as an hour measured last week, next week, or next year (assuming that you keep the clock wound).
Inaccurate, in the sense that each hour measured by the clock on the moon will actually be about 144 minutes long, and thus the deviation from "correct" time will grow continuously.
So a pendulum clock designed for use on Earth, moved to the moon, will keep time consistently, and could be considered accurate for lunar timekeeping, as long as those who use it are willing to agree on a new definition of "hour". Problems occur only when comparing the time shown by such a clock to the time shown by other timekeeping devices such as an Earth-based pendulum clock or a battery-powered digital wristwatch.
-- Regards, Doug Miller (alphageek-at-milmac-dot-com)
For a copy of my TrollFilter for NewsProxy/Nfilter, send email to autoresponder at filterinfo-at-milmac-dot-com You must use your REAL email address to get a response.
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wrote:

I think maybe the terms "accuracy" and "precision" would be helpful here. You could say the clock has excellent precision, in that it will measure an hour almost the same exact way every time. However, its accuracy is poor, because it will not measure an Earth hour very well at all. Precision signifies how repeatable or closely matched measurements are to an average. Accuracy signifies how close those measurements are to the true value.
dwhite
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Dan White wrote:

I like consistency and precision equally, each in their own way. But I vote Republican anyway!
Hoyt W.
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wrote:

Ditto here, Hoyt, but the terms "accuracy" and "precision" are more than just my idea. These are the scientifically "accepted" terms to describe how close data are to each other (precision), and to the true value (accuracy).
dwhite
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You know, there was a *reason* I described things the way I did, in the original posting.
I'll repeat:
1) The 'stability', aka 'repeatability', is essentially unchanged.
John Martin contests that , claiming that 'outside influences'-- claimed to be comparatively larger on the moon -- beyond the local gravitational constant, will degrade the stability. I disagree. Because: (a) at a fixed location on the Moon, the effect of the Earth's gravitational pull is a constant -- both in magnitude and direction -- because the moon is in a 'tidal lock' with the same face constantly towards the earth. and (b) the gravitational effect of any other solar body is essentially identical, as the distance from Earth, or the Moon, to that solar body is 'for all practical purposes' identical. (gravitational attraction is inversely proportional to the square of the distance between the bodies. considering the Sun, as felt from the Earth and the Moon, there is a maximum difference of about 2.688/1000ths of the Earth-Sun distance. which means the relative difference in gravitational effect is 1/(1.002688^2), since period of a pendulum is proportional to the sqrt of the gravitational constant, you've got a variance +/- 0.2688% of the Sun-Earth gravitational effect at the Moon. On Earth, The Sun's gravitational effect varies the local gravitational constant every 24 hours. (maximum it the middle of the night, when it adds to the earth effect, and minimum at noon, when it is in the opposite direction). Exactly the same thing occurs on the Moon, albeit on a circa 28-earthday cycle. Solar gravitational constant, at the moon's surface, is about 1/12,750,000th of the moons gravity. On the Earth's surface, the solar effect is about 1/4,900,000th the Earth's gravity. This *is* counter-intuitive, but true, nonetheless -- it works out that way because the Moon is much smaller in diameter than the Earth, and thus, the surface is closer to the 'center of mass'.
What all these gyrations show is that the 'outside influence' effect of other solar bodies, measured on the surface of the Moon, will be _less_ than the effect from the same source, measured on the surface of the Earth.
And, as mentioned, the effect of the Earth does _not_ affect the stability of the tick because it is constant in both magnitude and direction.
Overall, the clock tick will be _more_ stable on the Moon than it is on Earth. By _maybe_ "one part in a ten million". <grin>
2) The _frequency_ of the tick -- also known as the 'period' of the pendulum -- *IS* lower. By the square-root of the ratio of the local gravitational constant. On the surface of the Moon, it is 0.1645g (I looked it up! :) this means that the pendulum will be slower by a factor of 2.4655. Or it will take 2 hrs, 27 minutes 55+ seconds for the clock to show the passage of one hour.
And, finally, it will take a little over 17-1/4 'earth' days for that 7-day mechanism to get to the point of requiring raising the weights. (which _will_ still be at the passage of '7 days' as "indicated* by the clock.)
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On Mon, 17 May 2004 21:33:59 +0000, snipped-for-privacy@host122.r-bonomi.com (Robert Bonomi) wrote:
<snip>

Strictly in the interest of precision, you are almost correct saying the Earth's gravitational pull is a constant vector in the"lunacentric" reference system, and would be precisely correct if the Moon's orbit was a perfect circle and both the Earth and the Moon were perfect homogeneous spheres. But, the orbit of the Moon about the Earth is Oh-So-Slightly Elliptical and both bodies are just a tad off from being perfectly spherical. Oh, hell, let's ignore variations in mass concentrations. I did mention "precision", didn't I? 8^)
As a result, there is a slight "back and forth" precession of the surface of the Moon as seen from Earth and an equivalent back and forth precession of the position of the Earth as seen from the Moon. This causes the direction of the vector to oscillate back and fourth with a period matching the Moon's orbital period. Likewise, the eccentricity of the orbit causes the distance between the centers of mass of the Earth and the Moon to oscillate with that same period. Ergo, the magnitude of the vector is also non constant.
Very much a higher order effect that can be, and rightfully was, ignored in your analysis. However, you might want to take it into account the next time you plan a Lunar Landing Mission.
Just trying to be "precise" (with maybe just a little "wise-assedness" thrown in). ;-)
Tom Veatch Wichita, KS USA
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The fact that the bodies are not perfectly spherical,and not perfectly homogeneous, and/or the mass concentration variations are NOT a factor. Two reasons -- first, the axis of rotation is the 'center of mass', and second, for gravitation calculations, _at_or_above_ the surface of the object, it can be treated as a 'point source', with the entire mass existent at the putative center of mass.
Eccentricity of the Lunar orbit does contribute some variance. its about +/- 0.015% in the gravitational constant. Which translates to a variance of about 74 parts in a million in the pendulum period.
Over the short term, this introduces a maximum effect of about 6 seconds per (earth) day.
Over a complete _lunar_ day, on the other hand, the effects cancel out, completely.

I don't have a quantitative figure on the precession. However, *IF* it is +/- 1 degree. then the effect is almost exactly the same as the orbital eccentricity. +/- 0.015%
Which raises the _very_ interesting situation that if the effects are 180 degrees out-of-phase, relative to each other, then they nullify each other almost perfectly.

For _that_, I d*mn well need better data than 4 sig-fig accuracy on the Lunar gravitational constant, 3 sig-fig accuracy on the mean Sun-Earth distance, and the Earth-Moon distance, and 2 sig-figs on the diameter of the Earth and the Moon.
I _do_ have 'pi' memorized to 20 decimal places, so precision is not restricted on _that_ basis. <grin>

We'll be sure to let you know, if you succeed. <snicker>
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[snip]
At work here we need to include gnat fart constants. Here is a sample of some constants to better pin down how accurate that darn moon clock is:

/* IAU (1976) System of Astronomical Constants * SOURCE: USNO Circular # 163 (1981dec10) * ALL ITEMS ARE DEFINED IN THE SI (MKS) SYSTEM OF UNITS * */ #define GAUSS_GRAV 0.01720209895 /* Gaussian gravitational constant */ #define C_LIGHT 299792458. /* Speed of light; m/s */ #define TAU_A 499.004782 /* Light time for one a.u.; sec */ #define E_EQ_RADIUS 6378137. /* Earth's Equatorial Radius, meters (IUGG value) */ #define E_FORM_FCTR 0.00108263 /* Earth's dynamical form factor */ #define GRAV_GEO 3.986005e14 /* Geocentric gravitational constant; (m^3)(s^-2) */ #define GRAV_CONST 6.672e-11 /* Constant of gravitation; (m^3)(kg^-1)(s^-2) */ #define LMASS_RATIO 0.01230002 /* Ratio of mass of Moon to mass of Earth */ #define PRECESS 5029.0966 /* General precession in longitude; arcsec per Julian century at standard epoch J2000 */ #define OBLIQUITY 84381.448 /* Obliquity of the ecliptic at epoch J2000; arcsec */ #define NUTATE 9.2025 /* Constant of nutation at epoch J2000; arcsec */ #define ASTR_UNIT 1.49597870e11 /* Astronomical unit; meters */ #define SOL_PRLX 8.794148 /* Solar parallax; arcsec */ #define ABERRATE 20.49552 /* Constant of aberration at epoch J2000; arcsec */ #define E_FLAT_FCTR 0.00335281 /* Earth's flattening factor */ #define GRAV_HELIO 1.32712438e20 /* Heliocentric gravitational constant (m^3)(s^-2) */ #define S_E_RATIO 332946.0 /* Ratio of mass of Sun to mass of Earth */ #define S_EMOON_RATIO 328900.5 /* Ratio of mass of sun to mass of Earth plus Moon */ #define SOLAR_MASS 1.9891e30 /* Mass of Sun; kg */ #define JD_J2000 2451545.0 /* Julian Day Number of 2000jan1.5 */ #define BES_YEAR 365.242198781 /* Length of Besselian Year in days at B1900.0 (JD 2415020.31352) */#define SOLAR_SID 0.997269566329084 /* Ratio of Solar time interval to Sidereal time interval at J2000 */ #define SID_SOLAR 1.002737909350795 /* Ratio of Sidereal time interval to Solar time interval at J2000 */ #define ACCEL_GRV 9.78031846 /* acceleration of gravity at the * earth's surface (m)(s^-2) */ #define GRAV_MOON 4.90279750e12 /* Lunar-centric gravitational constant (m^3)(s^-2) */ #define ETIDE_LAG 0.0 /* Earth tides: lag angle (radians) */ #define LOVE_H 0.60967 /* Earth tides: global Love Number H, IERS value (unitless) */ #define LOVE_L 0.0852 /* Earth tides: global Love Number L, IERS value (unitless) */
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BruceR wrote:

<big snip>
Gee whillerkers Bruce, how does "global Love Number H" and "global Love Number L" affect whether the clock will run slower or not? I have always been wanting to know and you are the first one to bring it up.
Hoyt W.
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Hoyt Weathers wrote:

Gee silly! Of course you have to consider horizontal displacement of the earths crust as the tidal forces move about, being different depending on the density of the body in question....
BTW, would a moon clock have a inset face that shows the phases of the earth?
-Bruce

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BruceR wrote:

The clock in question does not have an inset face, but that was not a "given" within my original questions. Therefore your question is N/A. Interesting though.
-Hoyt W.
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Ask the Addams family what they have on their moondial. <grin>
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Robert Bonomi wrote:

That's actually true only if the body is homogeneous. The Moon is not--Lunar mass concentrations were discovered by their effect on the motion of the Lunar Orbiter satellite, which orbit would not have been perturbed by them if your contention was correct.
However, if our clock is in a fixed location on the lunar surface then the effect of any nearby mass concentration would be accounted for when the clock was regulated--that would only be an issue if the clock was moved around, and even then I suspect it would be a very small effect.
Libration would have some effect--objects on the surface of a macroscopic body in orbit about the other (or to be pedantic about their common center of mass) are subject to tidal stresses which would affect the rate of a pendulum clock, however most of that would againb be accounted for when the clock was regulated, with libration being the only significant variable in that regard. But again I suspect that that would be a very small effect.

--
--John
Reply to jclarke at ae tee tee global dot net
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Doug Miller wrote:

Thanks for clearing that up Doug. Consistency is a good clarification, STS, to the use of the single word of accuracy. I learn something new every day - or try to.
Hoyt W.
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<snip>

Only if you are facing south.
Greg
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Nope. It'll rise in the South. Sets in the South, too.
Tom Veatch Wichita, KS USA
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Tom Veatch wrote:

South with respect to what, pray tell?
Hoyt W.
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wrote:

with respect to where you are standing, of course. all directions are due south from the north pole.....
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"Up", naturally. Take any map and look at it, there are 4 directions. 'East', 'West', 'South', and 'Up'. <snicker>
Seriously, at the North Pole, _every_ direction is South.
Thus, the entire horizon is 'South' of you. So _wherever_ the Sun comes over the horizon -- or goes under it -- _is_ South.
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