# Re; Uncertainty of gravitational constant

2 views

### Jim Cobban

Nov 20, 1998, 3:00:00 AM11/20/98
to
As pointed out by this discussion, the methodology of determination of
the masses of solar system objects is significantly different between
the two eras.

Prior to the space age all that could be determined was the angular
position of solar system objects. It was impossible to directly measure
distance. Assuming the applicability of Newton's laws it was possible
to calculate the absolute space position of various objects in terms of
astronomical units, that is setting the distance between the Earth-Moon
center of gravity and the center of gravity of the solar system to 1.0.

Once you have done this you can calculate, highly accurately, a
constant, traditionally called the Gaussian gravitational constant k, which
represents the gravitational
influence of the Sun on the objects in the solar system. Further, by
solving the system so as to minimize deviations between prediction and
future positions it is possible for each of the major planets to
calculate the ratio between their values of k and the value of k for the
Sun. It is NOT possible to calculate the "mass" of any of the objects
in this system. As an additional aid in reducing the massively parallel
calculations, observations of the motion of planetary satellites, in
angular terms, can provide independent measurements of the value of k
for those planets which have moons. That excludes Mercury, Venus,
Pluto, and even to some extent the Earth. That is because we cannot
trivially calculate the distance between the Earth and the Moon in
astronomical units because the Moon is the one object that we cannot
observe from different spots on the Earth's orbit.

I repeat: Using only angular measurements it is impossible to measure
the "mass" of any object. However you can measure the relative mass of
any two objects.

With spaceprobes it is possible to accurately measure their DISTANCE at
any instant in terms of the time it takes light to cross from them to
the observer. You could also measure their angular positions, for
example using a long baseline radio interferometer, but the accuracy of
the distance measurement, in terms of light time, is orders of magnitude
more accurate. Since the length of the SI metre is defined in terms of
the time it takes for light to cross it, or alternatively the speed of
light is now a defining constant of the SI system, we can accurately, to
a matter of centimetres in fact, determine the exact distance to any
spaceprobe in metric units. This permits us, for each object which a
probe passes relatively close to, to determine with significant
accuracy the value representing the strength of the gravitational field
of the object in terms of metric units.

But, once again, you cannot measure the "mass" of any of the objects.
Just as with the older methods, all you can measure is the strength of
the gravitational field. In gravitational theory the strength of the
gravitational field is proportional to the mass and the constant of
proportionality is labelled G. While the value of the field strength is
frequently known to 7 or 8 digits, the value of the constant of
proportionality (in metric units) is only known to about 4 digits.

Note that it is possible to close the loop to some extent. Since we
have now measured the length of the AU in metric units to about 9
digits, and since we know the strengths of the gravitational fields of
many of the solar system objects to 7 or 8 digits, it is possible to
plug this knowledge back into the traditional model. When we do so we
find that there is no significant change except for the orbits of Uranus
and Neptune. In the old model the predictions for these planets drifted
unless a fudge factor was introduced (called planet X). However once
the space probe determined gravitational field strengths are introduced,
that fudge factor disappears and the observed orbits of Uranus and
Neptune are accounted for over the last 200 years.

However any time you see a mass for any object published in terms of
kilograms (or Petatonnes as one source quotes) then you know that the
author is fudging his results to satisfy a semi-literate audience.
--
Jim Cobban | jco...@nortel.ca | Phone: (613) 763-8013
Nortel Networks (MED) | FAX: (613) 763-5199

### Aleksandr Timofeev

Nov 25, 1998, 3:00:00 AM11/25/98
to
In article <734g05\$92h\$1...@bcarh8ab.ca.nortel.com>,

jco...@bnr.ca (Jim Cobban) wrote:
> As pointed out by this discussion, the methodology of determination of
> the masses of solar system objects is significantly different between
> the two eras.
>

What your judgement about " Timofeev's rule " (similar on Bode - Titius?)
for mass values of planets in Solar system?:

See http://solar.cini.utk.edu/~russeds/unknown/astrochem/

This theory is basing on Henri Poincare physical concepts.
The reliable experimentally received mass values are available for
the following planets:
Integer
Planet Notations Mass | Ratio Experemental number
of mass value | value commensur-
value | ability
|
Jupiter MJU or 1 317.735 |(MJU+MSA)/(MUR+MNE)= 12.995971 ~ 13
Saturn MSA or 2 95.147 | MJU/(MUR+MNE) = 10.001011 ~ 10
Neptune MNE or 3 17.23 | MSA/(MUR+MNE) = 2.994869 ~ 3
Uranus MUR or 4 14.54 | (MJU+MSA)/MNE = 23.9630 ~ 24
Earth MTE or 5 1.000 | MUR/(MTE+MVE) = 8.011019 ~ 8
Venus MVE or 6 0.815 | (MNE+MUR)/MVE = 38.9816 ~ 39
Mars MMA or 7 0.108 | (MTE+MVE)/MME = 33.0000 ~ 33
Mercury MME or 8 0.055 | MVE/(MMA+MME) = 5.0000 ~ 5

Hense it follows - the periodic chain of discrete
commensurabilities between values of planetary masses
in Solar system.
. 10
I<----------->|
I 13 |
I<==============>I
I | I
? 39 I | I
|<--------------------->I 33 |<---------------->I 24 | I
| |<------------------>I |<----------------->I
| | I ? | | I 5 | | I 8 | | I 3 | | I
| | I<====>| | I<====>| | I<====>| | I<====>| | I
| | I | | I | | I | | I | | I
10 9 I 8 7 I 6 5 I 4 3 I 2 1 I
I | | I | | I | | I | | I
I Mercury MarsI Venus EarthI Uran NepI Saturn JupiterI
I I I I I
10+9 8+7 6+5 4+3 2+1
ln(mass)
- - ---------------------------------------------------------------->

The following disignations are used:
MSA+MJU <--> 2+1 ; MUR+MNE <--> 4+3 ;
MVE+MTE <--> 6+5 ; MME+MMA <--> 8+7 ;
MJU <--> 1 ; MSA <--> 2 ; MNE <--> 3 ; MUR <--> 4 ;
MTE <--> 5 ; MVE <--> 6 ; MMA <--> 7 ; MME <--> 8
5 10
Direct relations - <====> ; Reverse relations - <----------->

The chain of relations of body couples mass values is of
periodic type. It has a mirror reflection for direct and reverse
relations.
We have not breaks the symmetry of the chain of relations.
Direct and reverse relations of body couples mass values show
that there exists mechanisms inside gravitation System providing for the
maintenance of corresponding correlations of mass values which are
responsible for stability and stationary condition of the Solar system.
The chains of relations of body mass values embraces whole
Universe (Gravitation chemistry).

Regards,
Aleksandr

P.S. This work was made for a long time, therefore in it the old values of
masses are used.

-----------== Posted via Deja News, The Discussion Network ==----------

### Aleksandr Timofeev

Nov 25, 1998, 3:00:00 AM11/25/98
to

### Hoffman, Nick N

Nov 27, 1998, 3:00:00 AM11/27/98
to Jim Cobban
Jim Cobban wrote:

> Prior to the space age all that could be determined was the angular
> position of solar system objects. It was impossible to directly
> measure
> distance.

---snip---

We had radar measurements of the distance to the moon before the first
Sputnik. Major planets are regularly radar and laser ranged,
independently of sending space junk there.

The Moon is also close enough to calculate its distance from the
parallax of two observers across the baseline of the Earth.

>
>
> But, once again, you cannot measure the "mass" of any of the objects.
> Just as with the older methods, all you can measure is the strength of
>
> the gravitational field. In gravitational theory the strength of the
> gravitational field is proportional to the mass and the constant of
> proportionality is labelled G. While the value of the field strength
> is
> frequently known to 7 or 8 digits, the value of the constant of
> proportionality (in metric units) is only known to about 4 digits.
>

Don't forget the Cavendish torsion balance experiment where known masses
were used to measure their mutual gravitational attraction.

We can also get a reasonable measure of G by measuring the gravity
anomaly of a mountain of known rock type. The errors are appreciable,
but we can get 3 digits most days. Similarly, borehole gravimeters
mesure changes in gravity with depth as we pass rocks of measured
density, and gravity measurements at high and low tide or in reservoirs
at different charge level permit us to measure the gravitational effect
of quite large masses.

--

-------./\/^·._,·´`·.,··=-----------------

Nick Hoffman Geophysicist Extraordinaire

-------´\/\_.´`·._.·´`··=-----------------

### Aleksandr Timofeev

Nov 27, 1998, 3:00:00 AM11/27/98
to
In article
<Pine.A41.4.05.981125...@dante04.u.washington.edu>, "C.
Hillman" <opti...@u.washington.edu> wrote:

>
>
> On Wed, 25 Nov 1998, Aleksandr Timofeev, who ought to know better by now,

>
> > What your judgement about " Timofeev's rule " (similar on Bode - Titius?)
> > for mass values of planets in Solar system?:
> >
> > See http://solar.cini.utk.edu/~russeds/unknown/astrochem/
> >
> > This theory is basing on Henri Poincare physical concepts.
>

> [snip]
>

Dear sir Chris Hillman.

I am very grateful to you for advertising of my theory.
Please, give my person more and more attentions and hereafter.

Sincerely your,
Aleksandr

P.S. It would be little bit better, if you were acquainted with the
law of conservation of mass and some statistical distributions
used in physics.

I assume, that you have outstanding mathematical talent and can
physically and mathematically correctly to put and to decide this
problem.

Symmetry, you constantly overlook a symmetry.
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Do not overlook a symmetry now.

For your convenience I again bring the necessary data:

Quantization of a gravitational charge

A.N. Timofeev, V.A. Timofeev, L.G. Timofeeva

The experience shows, that the electrical charges of all elementary
particles exactly are identical. Probably anybody does not understand yet,
why their electrical charges are equal with a fancy degree of an exactitude.
Obviously, that the quantization of an electrical charge is the mysterious
and universal law of a Nature.
being based on experimental data for magnitudes of masses of planets
of a Solar system.

See http://solar.cini.utk.edu/~russeds/unknown/astrochem/

This theory is basing on Henri Poincare physical concepts.
The reliable experimentally received mass values are available for
the following planets:
Integer
Planet Notations Mass | Ratio Experemental number
of mass value | value commensur-
value | ability
|
Jupiter MJU or 1 317.735 |(MJU+MSA)/(MUR+MNE)= 12.995971 ~ 13
Saturn MSA or 2 95.147 | MJU/(MUR+MNE) = 10.001011 ~ 10
Neptune MNE or 3 17.23 | MSA/(MUR+MNE) = 2.994869 ~ 3
Uranus MUR or 4 14.54 | (MJU+MSA)/MNE = 23.9630 ~ 24
Earth MTE or 5 1.000 | MUR/(MTE+MVE) = 8.011019 ~ 8
Venus MVE or 6 0.815 | (MNE+MUR)/MVE = 38.9816 ~ 39
Mars MMA or 7 0.108 | (MTE+MVE)/MME = 33.0000 ~ 33
Mercury MME or 8 0.055 | MVE/(MMA+MME) = 5.0000 ~ 5

Hense it follows - the symmetrical chain of discrete

relations. A.N.

We have not breaks the symmetry of the chain of relations.
Direct and reverse relations of body couples mass values show
that there exists mechanisms inside gravitation System providing for the
maintenance of corresponding correlations of mass values which are
responsible for stability and stationary condition of the Solar system.
The chains of relations of body mass values embraces whole
Universe (Gravitation chemistry).

We extract mass value data from book of William B. Hubbard
"PLANETARY INTERIORS" (Professor of Planetary Sciences University
of Arisona Van Nostrand Reinhold Company 1987)

Please, Do not overlook a symmetry now.

See http://solar.cini.utk.edu/~russeds/unknown/astrochem/

-----------== Posted via Deja News, The Discussion Network ==----------

### Aleksandr Timofeev

Nov 27, 1998, 3:00:00 AM11/27/98
to
In article <734g05\$92h\$1...@bcarh8ab.ca.nortel.com>,
jco...@bnr.ca (Jim Cobban) wrote:
> As pointed out by this discussion, the methodology of determination of
> the masses of solar system objects is significantly different between
> the two eras.
>
Your account of a problem is characterized by sharp clearness.
The following problems could you make clear:

1. What role play the empirical corrections inside the theories of a
celestial mechanics from a physical point of view?

In chapter: 3.The reliability of the input data
3.1 Inner precision of celestial mechanics
I wrote:
"... Without any exception all theories of celestial bodies motions
contain empirical assumptions with a purpose to match the past and
future observation data. Empirical corrections (depending exclusively
on the intuition of those who elaborate such theories) is an
inevitable evil connected with the imperfection of the mechanical
model of the system under consideration and an influence of
unaccounted and unknown phenomena which affects the system. ..."
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

2. What influence render the empirical corrections on values of computed
parameters in a celestial mechanics?

3. What " power weight " of the empirical corrections now and earlier?

Me interest evaluations of the attitude of values of energy come on
the empirical correction to full energy of a system.

4. What influence have rendered the measured values of planetary masses
on the empirical corrections?

Regards, Aleksandr

### s...@microtec.net

Nov 29, 1998, 3:00:00 AM11/29/98
to

[maga-snip]

> And oh yes, one more thing, Timofeev's "ideas" are about as closely
> related to Poincare's ideas about dynamical systems as the length of my
> toenail clippings are related to the fine structure constant.
>

André Michaud

Service de Recherche Pédagogique http://www.microtec.net/~srp/

### Duncan A. McDonald

Nov 29, 1998, 3:00:00 AM11/29/98
to
Good morning Mr. Hoffman:

I know this is off the topic at hand but, what is the strongest
Gravitation source in our Galaxy. The Center of it is suppose to
contain
a Black Hole. Can this source (black hole at the center of our galaxy)
of gravity be measured or calculated.

Cheers

Duncan.

____________________________________

### Steve Willner

Nov 30, 1998, 3:00:00 AM11/30/98
to
In article <734g05\$92h\$1...@bcarh8ab.ca.nortel.com>, jco...@bnr.ca (Jim
Cobban) writes:
> Prior to the space age all that could be determined was the angular
> position of solar system objects. It was impossible to directly measure
> distance. Assuming the applicability of Newton's laws it was possible
> to calculate the absolute space position of various objects in terms of
> astronomical units [AU]

True, but this didn't prevent indirect measurements of distance. The
size of the AU was reasonably well known long before the space age.

As far as I can tell, there were basically two categories of methods.
One was based on measurements of horizontal parallax, but it took
special conditions for such measurements to be accurate.
Opportunities arose only infrequently, for example with transits of
Venus or a near approach of an asteroid. I believe one example was
Eros in the 1930's, but the name or date might be wrong.

The second category of measurement was based on the speed of light.
Orbits of Jupiter's moons provide a clock, and seeing how the clock
varies with computed distance in AU) combined with the known speed of
light gives the true distance (in meters). Timing of eclipsing
binaries and accurate measurements of the aberration of starlight are
variations on the same method.

Historically, I believe measurements of the first type were more
important, but I could be wrong.

Of course nowadays the size of the AU is known quite accurately by
means of spacecraft and planetary radar observations.

> Once you have done this you can calculate, highly accurately, a
> constant, traditionally called the Gaussian gravitational constant
> k, which represents the gravitational influence of the Sun on the
> objects in the solar system.

Yes, this is equivalent to the length of the year in seconds. (The
actual definition is slightly different.) As the poster said, you
don't need to know the size of the AU in physical units.

> I repeat: Using only angular measurements it is impossible to measure
> the "mass" of any object. However you can measure the relative mass of
> any two objects.

True. You can measure masses for the planets in units of solar (or
earth) masses by motions of their satellites or by perturbations of
one planet on the motion of other objects. Since Mercury and Venus
have no natural satellites, their masses were poorly known. I
believe the best measurements came from their small perturbations of
Earth's orbit, but I could be wrong. (The alternative would be a
near asteroid passage.) Pluto's mass was wild guesswork until its
satellite Charon was discovered.

In order to get the mass in physical units, you have to know the
usual gravitational constant G. This is measured via terrestrial
experiments, typically ("the Cavendish experiment") involving lead
balls and a torsion balance. Demonstrations are common staples of
introductory physics courses and science museums, although an
accurate experiment is quite difficult because there are many
perturbations. Other methods have also been used.

--
Steve Willner Phone 617-495-7123 swil...@cfa.harvard.edu
Cambridge, MA 02138 USA
email may be sent to your ISP.)

### Aleksandr Timofeev

Dec 2, 1998, 3:00:00 AM12/2/98
to
In article <3662e...@cfanews.harvard.edu>,
wil...@cfa183.harvard.edu (Steve Willner) wrote:
[snip]

>
> True. You can measure masses for the planets in units of solar (or
> earth) masses by motions of their satellites or by perturbations of
> one planet on the motion of other objects. Since Mercury and Venus
> have no natural satellites, their masses were poorly known. I
> believe the best measurements came from their small perturbations of
> Earth's orbit, but I could be wrong. (The alternative would be a
> near asteroid passage.) Pluto's mass was wild guesswork until its
> satellite Charon was discovered.
>
> In order to get the mass in physical units, you have to know the
> usual gravitational constant G. This is measured via terrestrial
> experiments, typically ("the Cavendish experiment") involving lead
> balls and a torsion balance. Demonstrations are common staples of
> introductory physics courses and science museums, although an
> accurate experiment is quite difficult because there are many
> perturbations. Other methods have also been used.
>
> --
> Steve Willner Phone 617-495-7123 swil...@cfa.harvard.edu
> Cambridge, MA 02138 USA

I wrote in article:
===========================================================================
Re: Uncertainty of gravitational constant
Author: Aleksandr Timofeev
Date: 1998/11/29
Forums: sci.physics.research

In article <367770bb...@kcbbs.gen.nz>,
rto...@kcbbs.gen.nz (Ray Tomes) wrote:
> j...@ibms48.scri.fsu.edu (Jim Carr) wrote:
> > That problem can be summarized by noting that measurements claiming
> > four sig.fig. accuracy disagree in the third sig.fig.
>
> Yes, something strange is going on. The following is from a CIFA
> newsletter from ~1995 I think.
>
> HELIOGEOPHYSICAL DISTURBANCES INFLUENCE UPON THE RESULTS OF THE
> MEASUREMENTS OF GRAVITATION CONSTANT
>
> Crimean Astrophysical Observatory
> 334413, p/o Nauchny, Crimea, Ukraine
>
> The value of gravitational constant as measured by classic
> instrument - torsion pendulum,- is not defined more precisely over a
> long time. It's known that inexplicable variations of these results
> are observed at the same apparatus [1]. So it's possible that partial
> non-reproducibility of the measurements are caused by unidentified
. ^^^^^^^^^^^^^^^^^^^^^^^^^^
> external agent. Probably this enigmatic factor correlates with ...
. ^^^^^^^^^^^^^^^
[snip]
Without any exception all theories of celestial mechanics

contain empirical assumptions with a purpose to match the past and
future observation data. Empirical corrections (depending exclusively
on the intuition of those who elaborate such theories) is an
inevitable evil connected with the imperfection of the mechanical
model of the system under consideration and an influence of
unaccounted and unknown phenomena which affects the system. ..."

. ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
See my homepage chapter: 3.The reliability of the input data

3.1 Inner precision of celestial mechanics

===========================================================================

From your point of view. What role play the empirical suppositions
(assumptions) in a celestial mechanics?

Aleksandr Timofeev
--
homepage http://solar.cini.utk.edu/~russeds/unknown/astrochem/
Boundaries of Science http://www.kcbbs.gen.nz/users/af/scienceb.htm

### Aleksandr Timofeev

Dec 7, 1998, 3:00:00 AM12/7/98
to
I wrote in article:
===========================================================================
Re: Uncertainty of gravitational constant
Author: Aleksandr Timofeev
Date: 1998/11/29
Forums: sci.physics.research

Without any exception all theories of celestial mechanics

contain empirical assumptions with a purpose to match the past and
future observation data. Empirical corrections (depending exclusively
on the intuition of those who elaborate such theories) is an
inevitable evil connected with the imperfection of the mechanical
model of the system under consideration and an influence of
unaccounted and unknown phenomena which affects the system. ..."
. ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

chapter: 3.The reliability of the input data
3.1 Inner precision of celestial mechanics
=======================================================================
=======================================================================

From your point of view. What role play the empirical suppositions
(assumptions) in a celestial mechanics?

=======================================================================
=======================================================================

=======================================================================
. Appendix 1

In article <367770bb...@kcbbs.gen.nz>,
rto...@kcbbs.gen.nz (Ray Tomes) wrote:
> j...@ibms48.scri.fsu.edu (Jim Carr) wrote:
> > That problem can be summarized by noting that measurements claiming
> > four sig.fig. accuracy disagree in the third sig.fig.
>
> Yes, something strange is going on. The following is from a CIFA
> newsletter from ~1995 I think.
>
> HELIOGEOPHYSICAL DISTURBANCES INFLUENCE UPON THE RESULTS OF THE
> MEASUREMENTS OF GRAVITATION CONSTANT
>
> Crimean Astrophysical Observatory
> 334413, p/o Nauchny, Crimea, Ukraine
>
> The value of gravitational constant as measured by classic
> instrument - torsion pendulum,- is not defined more precisely over a
> long time. It's known that inexplicable variations of these results
> are observed at the same apparatus [1]. So it's possible that partial
> non-reproducibility of the measurements are caused by unidentified
. ^^^^^^^^^^^^^^^^^^^^^^^^^^
> external agent. Probably this enigmatic factor correlates with ...
. ^^^^^^^^^^^^^^^
[snip]

=======================================================================
. Appendix 2

In article <3662e...@cfanews.harvard.edu>,
wil...@cfa183.harvard.edu (Steve Willner) wrote:
[snip]
>
> True. You can measure masses for the planets in units of solar (or
> earth) masses by motions of their satellites or by perturbations of
> one planet on the motion of other objects. Since Mercury and Venus
> have no natural satellites, their masses were poorly known. I
> believe the best measurements came from their small perturbations of
> Earth's orbit, but I could be wrong. (The alternative would be a
> near asteroid passage.) Pluto's mass was wild guesswork until its
> satellite Charon was discovered.
>
> In order to get the mass in physical units, you have to know the
> usual gravitational constant G. This is measured via terrestrial
> experiments, typically ("the Cavendish experiment") involving lead
> balls and a torsion balance. Demonstrations are common staples of
> introductory physics courses and science museums, although an
> accurate experiment is quite difficult because there are many
> perturbations. Other methods have also been used.
>
> --
> Steve Willner Phone 617-495-7123 swil...@cfa.harvard.edu
> Cambridge, MA 02138 USA