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.
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.
Doug Miller (alphageek-at-milmac-dot-com)
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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.
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).
You know, there was a *reason* I described things the way I did, in the
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
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.)
On Mon, 17 May 2004 21:33:59 +0000, email@example.com (Robert Bonomi) wrote:
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
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). ;-)
Wichita, KS USA
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,
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
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>
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;
#define GRAV_CONST 6.672e-11 /* Constant of gravitation;
#define LMASS_RATIO 0.01230002 /* Ratio of mass of Moon to mass of
#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
#define S_E_RATIO 332946.0 /* Ratio of mass of Sun to mass of
#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
#define SID_SOLAR 1.002737909350795 /* Ratio of Sidereal time interval
to Solar time interval at
#define ACCEL_GRV 9.78031846 /* acceleration of gravity at the
* earth's surface (m)(s^-2) */
#define GRAV_MOON 4.90279750e12 /* Lunar-centric gravitational
#define ETIDE_LAG 0.0 /* Earth tides: lag angle
#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) */
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.
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
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.
Reply to jclarke at ae tee tee global dot net
"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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