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Journal of Applied Mathematics and Physics, 2018, 6, 2397-2401
http://www.scirp.org/journal/jamp
ISSN Online: 2327-4379
ISSN Print: 2327-4352
DOI:
10.4236/jamp.2018.611202 Nov. 27, 2018 2397 Journal of Applied Mathematics and Physics
The Sun and Big G Measurements
Jose L. Parra
Department of Physics, Florida International University, Miami, FL, USA
Abstract
On August 29th, 2018, a scientific team reported a measure of the Universal
Gravitational Constant G with the highest precision ever. The team com-
pleted three experimental campaigns in the same city
over the course of a
year. That work provided a complete data set
useful analyzing the values of
Big G change with the distance to the Sun, as is claimed by the author of this
paper.
Keywords
Gravitational Constant G, Rotation, Precession, Solar Cycles
1. Introduction
This note is not exactly an independent paper. The original intention was to
create a brief communication to show the correlation between the experimental
data from two different experimental works. The author apologizes for lack of
details on this communication about the Big G issue and recommends that in-
terested readers check the reference for a complete overview on this point.
On August 29th, 2018, a scientific team reported a measure of the Universal
Gravitational Constant, also known as Big G, with the lowest error ever. In this
journal, Li
et al.
[1] announced two new values for Big G using two independent
settings. The values for G were determined to be 6.674184(12) × 10−11 m3∙kg−1∙s−2
using a technique called TOS and 6.674484(12) × 10−11 m3∙kg−1∙s−2 using another
technique called AAF. The physical nature of Big G is so goosy that after more
than two years of science-art work, Li
et al.
exceed the precision reported in the
work by Gundlach
et al.
[2] in the year 2000 [6.674215(92) × 10−11 m3∙kg−1∙s−2] by
only ninety parts in a million. Many technological advances have occurred
within the last 18 years, but the increment in precision between both studies is
not well correlated with those advances. Another intriguing situation appears
after comparing the numbers in red in the values reported by Li
et al.
The errors
in both values cannot cover the 300th of a million separations between them. It is
How to cite this paper:
Parra, J.L. (2018
)
The Sun and Big G
Measurements.
Journal
of Applied Mathematics and Physics
,
6,
2397
-2401.
https:
//doi.org/10.4236/jamp.2018.611202
Received:
October 30, 2018
Accepted:
November 24, 2018
Published:
November 27, 2018
Copyright © 201
8 by author and
Scientific
Research Publishing Inc.
This work is licensed under the Creative
Commons Attribution International
License (CC BY
4.0).
http://creativecommons.org/licens
es/by/4.0/
Open Access
J. L. Parra
DOI:
10.4236/jamp.2018.611202 2398 Journal of Applied Mathematics and Physics
not hard to imagine that this situation indicates that something is missing or
hidden.
Schlamminger [3] published a comment in Nature on August 29th, 2018, call-
ing attention to the fact that the TOS and AAF experiments were done by the
same people, in the same place, and close in time. He thinks this could be a good
combination to solve the G puzzle and proposes that Li
et al.
carry out a study
explaining why they observe two non-overlapping values. He clarifies that the
explanation can help to guide future research. Schlamminger moves as far as
proposing to all the scholars to keep an open mind in regards to this problem.
He wrote “
A second possibility is that some unknown physics could explain the
scatter in the published values
.
Although this possibility is
,
of course
,
the more
exciting
,
it is also the less likely
.
Nevertheless
,
it should not be dismissed lightly
”.
Moreover, I published papers in 2017 [4] and 2018 [5] covering the Big G is-
sue both theoretically and experimentally. Therein, I mentioned that an unno-
ticed correlation exists between the best G values reported in the last 30 years
and the distance to the Sun. Thirty years is a long period, which made it more
difficult to draw a comparison between the studies carried out in so many labs
throughout the world. Li
et al.
’s work enabled a facilitated analysis because their
work and my work were produced during the same period.
I used a modified Cavendish’ balance with two strings instead of the original
single string balance. The length and separation of the strings act as a mechani-
cal filter allowing only microscopic oscillations. Nothing is moved by human de-
cision in this setting. This dynamic permits a precise reading of any variation in
the separation between the masses on the balance and the masses fixed to the
ground. Thus, 650 variations were collected, one per day, due to the apparent at-
traction between the masses. Unfortunately, it was not possible to calculate the
value for Big G with this setting because two new variables appeared, as shown
in Equation (1) (For details, see Equation (3) in [5]). The effect of the angular
variable was cancelled out in regular gravitational experiments by alternating the
position of the attractor masses. The other effect created by the distance to the
Sun cannot be neutralized completely because of non-linear effects. Li
et al.
have
obtained 29 precise values for Big G; however, they failed to study the systematic
variations of those values throughout the years. Every team has plenty of infor-
mation on one type but lack information on the other. An intelligent combina-
tion of both types of experimental information can produce a clear and precise
pattern for this gravitational problem.
( )
( )
3
exp ,
NE torus
a
a
G G G Cos
r
α
θ
= +
(1)
2. Li et al. [1] Chronological Data
The team of Li
et al.
failed to report any possible variations of their data by tak-
ing into account other variables that might affect the results such as time or the
distance from the Sun. Figure 1 included only the AAF data for reasons
J. L. Parra
DOI:
10.4236/jamp.2018.611202 2399 Journal of Applied Mathematics and Physics
Figure 1. AAF error bars from three different campaigns with different color. The
2014-2015 campaign is shown in blue; the 2016 campaign is shown in orange, and the
2017-2018 campaign is shown in green.
explained later. A pattern is clear in Figure 1, despite only having 29 G values.
The figure included a dashed line representing the Earth’s path, an offset yellow
spot representing the Sun and a fitting curve. The red side of the fitting curve
corresponds to the January-December period.
Figure 2 was created using the main values from AAF to introduce a fitting
function. Figure 2 included only the 29 G values obtained from the AAF expe-
riments versus a unit-less parameter
x
correlate with the distance to the Sun. The
x
is the ratio between the instantaneous distance to the Sun and the average to
that distance, also called the Astronomical Unit. Every value from AAF was de-
termined after an average of three days. However, every value from TOS re-
quired an average of 132 days. That is an exclusionary condition in this analysis
because such a large period hides progressive variations. This lengthy variation,
which was not taken into account, can be used to explain why the final G value
determined using TOS is closer to the average G recommended by standard
government departments.
Figure 1 also includes the regression function that corresponds to the theo-
retical model proposed by the author.
( )
11
e
3 12
3
xp.
0.00228 0.00036
6.67218 0.00037 10 m kg s
x
G− −−
±
±+ ×
=
(2)
In Equation (2), the value of 6.67218 × 10−11 m3∙kg− 1∙s−2 corresponds to the
constant Big G. According to the author, the 0.00228(36) × 10−11 m3∙kg−1∙s−2 val-
ue is due to the dragging effect arising from the nucleus of the Sun.
Now, it is possible to integrate the Big G data obtained by Li
et al.
with the
variations recorded by the author.
J. L. Parra
DOI:
10.4236/jamp.2018.611202 2400 Journal of Applied Mathematics and Physics
Figure 2. 29 values obtained by Li
et al.
using the AAF technique. The high
vertical dispersion of the points should not impress negatively the reader
because the precision on that axis is huge.
Figure 3. “Variations” of the attractive forces between the masses on a modified Caven-
dish’ balance versus the distance to the Sun. The 24 Solar Cycle (SC) is shown in blue; the
transition to the 25 SC (High oscillations) is shown in green, and the 25 SC is shown in
orange.
3. Mixing Big G Determinations and Its Variations
The pattern in Figure 3 matches very well with Equation (1). The observed
peaks are due to nutation’ effects. Figure 3 includes a ribbon-like feature that is
correlated to the fitting of Equation (2) but with new errors. The width of the
ribbon is a visual representation of the new heightened precision. The ribbon
was created using Equation (3) to contain the main sequence of the author’s ex-
perimental data.
J. L. Parra
DOI:
10.4236/jamp.2018.611202 2401 Journal of Applied Mathematics and Physics
( )
11
e
3 12
3
xp.
0.00228 0.00020
6.67218 0.00020 10 m kg s
x
G− −−
±
±+ ×
=
(3)
4. Conclusion
The average of the available experimental values of Big G can create confidence
on its real value only to the third significant figure (6.67). Any researcher look-
ing for more precise information about Big G requires considering the experi-
mental variation of its value with the distance to the Sun. This is experimentally
justified by all the research conducted since Cavendish. Any art of science work
in the modern time ought not aim or attempt to overcome this constraint. Many
scholars may disagree with the assertion made in the author’s initial hypothesis,
but any argument can be brought in future work. In order to assert a different
position on the hypothesis future work and research would have to be con-
ducted; however, a six-significant figure on the value of Big G is due by now.
Conflicts of Interest
The author declares no conflicts of interest regarding the publication of this pa-
per.
References
[1] Li, Q.,
et al.
(2018) Measurements of the Gravitational Constant Using Two Inde-
pendent Methods.
Nature
, 560, 582-588. https://doi.org/10.1038/s41586-018-0431-5
[2] Gundlach, J.H. and Merkowitz, S.M. (2000) Measurement of Newton’s Constant
Using a Torsion Balance with Angular Acceleration Feedback.
Physical Review Let-
ters
, 85, 2869-2872. https://doi.org/10.1103/PhysRevLett.85.2869
[3] Schlamminger, S. (2018) Gravity Measured with Record Precision.
Nature
, 560,
562-563. https://doi.org/10.1038/d41586-018-06028-6
[4] Parra, J.L. (2017) The Implications of the Sun’s Dragging Effect on Gravitational
Experiments.
International Journal of Astronomy and Astrophysics
, 7, 174-184.
https://doi.org/10.4236/ijaa.2017.73014
[5] Parra, J.L. (2018) Toward a Common Ground for Gravity and Optics.
Journal of
Applied Mathematics and Physics
, 6, 1896-1906.
https://doi.org/10.4236/jamp.2018.69161
