Емпіричне дослідження впливу гравітаційного поля Місяця на глобальну температуру Землі
This research examined a possibility of the Moon’s gravitational-wave that may influence Earth’s global temperature, with a mathematical method of empirical analysis with the data of the global temperature, global carbon dioxide, and the distance between Moon and Earth. We made the regression analys...
Saved in:
| Date: | 2019 |
|---|---|
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute"
2019
|
| Subjects: | |
| Online Access: | https://journal.iasa.kpi.ua/article/view/175551 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | System research and information technologies |
| Download file: |  |
Institution
System research and information technologies| _version_ | 1867334388272857088 |
|---|---|
| author | Matsuki, Yoshio Bidyuk, Petro I. |
| author_facet | Matsuki, Yoshio Bidyuk, Petro I. |
| author_institution_txt_mv | [
{
"author": "Yoshio Matsuki",
"institution": "The Laboratory for Econometrics and Forecasting at the World Data Center for Geoinformatics and Sustainable Development, the National Technical University of Ukraine \"Igor Sikorsky Kyiv Polytechnic Institute\", Kyiv"
},
{
"author": "Petro I. Bidyuk",
"institution": "Educational and Scientific Complex \"Institute for Applied System Analysis\" of the National Technical University of Ukraine \"Igor Sikorsky Kyiv Polytechnic Institute\", Kyiv"
}
] |
| author_sort | Matsuki, Yoshio |
| baseUrl_str | http://journal.iasa.kpi.ua/oai |
| collection | OJS |
| datestamp_date | 2019-08-27T22:12:50Z |
| description | This research examined a possibility of the Moon’s gravitational-wave that may influence Earth’s global temperature, with a mathematical method of empirical analysis with the data of the global temperature, global carbon dioxide, and the distance between Moon and Earth. We made the regression analysis of the global temperature over the factors of Moon’s gravitational field taken from the General Theory of Relativity and from the Newton’s gravity theory, with the data of the carbon-dioxide. The result shows that Newton’s gravitational field is related to Earth’s global temperature, while the influence of Moon’s gravitational wave is negligible. However, we also found a possibility that the gravitational wave could contribute to Moon’s gravitational-field upon the analysis of multicollinearity of two factors taken from Newton’s theory and the General Theory of Relativity. |
| doi_str_mv | 10.20535/SRIT.2308-8893.2019.2.02 |
| first_indexed | 2025-07-17T10:26:04Z |
| format | Article |
| fulltext |
Yoshio Matsuki, Petro I. Bidyuk, 2019
18 ISSN 1681–6048 System Research & Information Technologies, 2019, № 2
UDC 519.004.942
DOI: 10.20535/SRIT.2308-8893.2019.2.02
EMPIRICAL INVESTIGATION ON INFLUENCE
OF MOON’S GRAVITATIONAL-FIELD TO EARTH’S
GLOBAL TEMPERATURE
YOSHIO MATSUKI, PETRO I. BIDYUK
Abstract. This research examined a possibility of the Moon’s gravitational-wave
that may influence Earth’s global temperature, with a mathematical method of em-
pirical analysis with the data of the global temperature, global carbon dioxide, and
the distance between Moon and Earth. We made the regression analysis of the global
temperature over the factors of Moon’s gravitational field taken from the General
Theory of Relativity and from the Newton’s gravity theory, with the data of the car-
bon-dioxide. The result shows that Newton’s gravitational field is related to Earth’s
global temperature, while the influence of Moon’s gravitational wave is negligible.
However, we also found a possibility that the gravitational wave could contribute to
Moon’s gravitational-field upon the analysis of multicollinearity of two factors taken
from Newton’s theory and the General Theory of Relativity.
Keywords: global temperature, Moon’s gravitational field, gravitational wave, mul-
ticollinearity.
INTRODUCTION
Our previous research [1, 2] investigated the influence of Moon’s gravitational-
wave to the process of Earth’s global warming with the methodology of empirical
analysis with the database of Earth’s global temperature and global carbon diox-
ide as well as the distance between Moon and Earth. Then, the result of the analy-
sis suggested that there was a possibility, such that Moon’s gravitational-wave
influenced Earth’s atmospheric temperature than global carbon dioxide could do.
However, the presence of the gravitational-wave is not yet proven. In this re-
search, we investigated the Moon’s gravitational-field, in relation to the theory of
4-dimensional space that could include the gravitational-wave.
THEORY
The General Theory of Relativity [3] describes the actions of materials and en-
ergy flows in the gravitational field; while the gravitational wave is one of those
flows of energy. At first, the actions of materials in the empty space, where only
gravitational field exists, are described by the time-integral of the Lagrangian,
xdgLI g
4 , where gL is the action density for the gravitational field.
According to Einstein’s law, 0)2/1(16 4
xdggRgRI g ,
where g is a covariant fundamental tensor that describes the 4-dimensional
curved space (of coordinates x , where 3,2,1,0 ), g is the determinant of
g , R is a Ricci Tensor that describes the curvature of the 4-dimensional
Empirical Investigation on Influence of Moon’s Gravitational-Field to Earth’s …
Системні дослідження та інформаційні технології, 2019, № 2 19
curved space,
RR ,
,,R ,
g , )(
2
1
,,, ggg ,
x
g
g , and v
vRR
Rg . And, then, when an additional energy flow, such as gravitational
wave is included one more extra Lagrangian, xdgcIc
4 is added to gI .
Here, xdgggcIc
4
2
1
, and 0)( cg II . Hence,
0
2
1
2
1
16
cgRgR , and then, 4R . Hence,
RgR
2
1
g . Here, is a constant, and it must have the dimensions of (distance)-2,
because R contains the second derivatives of g in the 4-dimensional curved
space. However, in the General Theory of Relativity, energy of the gravitational
field can be integrated only in a large 3-dimensional volume at a certain time,
which tends to be infinity, so that the energy densities can be integrated in the
4-dimensinal curved coordinate system.
On the other hand, Newton’s theory of gravity assumes weak and static grav-
itational field, and therefore the space is nearly flat, not with curvature; therefore,
the energy of the gravitational field has the dimensions of (distance)-1. And,
Newton’s gravitational field is independent from other energy fields. For
example, the gravitational wave cannot be integrated within Newton’s gravita-
tional field.
In this research, we tried to find how Moon’s gravitational wave can be re-
lated to the gravitational field, by using the mathematical method for empirical
analysis with the database. For this purpose, we analyzed the relation between
(distance)-2 and (distance)-1, where (distance) is the distance between Moon and
Earth, within the system of Earth’s global temperature. The research question is,
“Are (distance)-2 and (distance)-1 related?” If there is a relation, we have a possi-
bility to assume the 4-dimensional curved space which allows the curvature and
the second derivatives of the energy.
METHOD
In order to examine the above research question, we made the regression analysis
of (distance)-2 and (distance)-1 over the global temperature of Earth. And, then, we
analyzed the multicollinearity of (distance)-2 and (distance)-1. We followed the
steps bellow:
1. We assumed the regression model:
243221
11
CO
r
c
r
ccct in ad-
dition to the model which we used in our previous research [1, 2]:
23221
1
CO
r
ccct , and then, we examined the coefficients and other charac-
ters of the models, which indicate the adequacy of the models. Here, t : Earth’s
global temperature, 2CO : Earth’s carbon dioxide, r : distance between Moon and
Earth, and 1c , 2c , 3c , and 4c : constant coefficients.
Yoshio Matsuki, Petro I. Bidyuk
ISSN 1681–6048 System Research & Information Technologies, 2019, № 2 20
2. We investigated the multicollinearity of )/(1 2r and r/1 , by the following
steps:
a) regress )/(1 2r on r/1 , and obtain the residuals, *)/(1 2r ;
b) regress t (temperature) on r/1 and *)/(1 2r to estimate the parameters of
the global temperature function;
c) Denote the results of the second step by *)/(1*)/1( 2
21 rcrct ;
d) Investigate the change of the value from 2c to *2c .
3. Database. The descriptive statistics of the data, from 1987 till 2009, of the
global temperature (increased degree Celsius since 1978) [4], the global carbon
dioxide (million tons) [5], the distance between Moon and Earth ( r , km) [6], cal-
culated )/(1 2r ((km--––22)),, and calculated r/1 (km)) are shown in Table 1, and the
distance between Moon and Earth is shown in Figure.
T a b l e 1 . Descriptive statistics
Variable
Global
Tempera-
ture (oC)*
CO2
(million tons)
**
Distance
between Moon
and Earth (r, km)
2
1
r
(km--22))
r
1
(km--11))
Mean 0,29130 1,25165103 3,62618105 7,6050910-12 2,7577310-6
Standard
deviation 0,12125 2,14245102 5,98411102 2,5109710-14 4,5520010-9
Minimum 0,10000 8,92000102 3,61583105 7,5699910-12 2,7511610-6
Maximum 0,43000 1,62600103 3,63483105 7,6486510-12 2,7656210-6
Skewness –0,21063 0,14292 -0,15249 0,15787 0,15604
Kurtosis 1,29401 1,82491 1,67498 1,67879 1,67771
Valid number
of observations 23 23 23 23 23
* Increased degree Celsius since 1978.
** To convert these estimates to units of carbon dioxide (CO2), simply multiply these es-
timates by 3,667 [3].
Distance between Moon and Earth [1].
D
is
ta
nc
e,
k
m
Empirical Investigation on Influence of Moon’s Gravitational-Field to Earth’s …
Системні дослідження та інформаційні технології, 2019, № 2 21
RESULTS
Regression Analysis (by Least Squares Estimations of Linear Classical
Regression Model)
The global temperature },,{ 1 nyyY , the constant value 1, 1x , the measured
global carbon-dioxide, 2x , the inverse of the distance between Moon and Earth,
3x , and the inverse of the squared distance between Moon and Earth, 4x , are
transformed into the forms of 1n vectors, y , 1x , 2x , 3x , 4x , where n is the
number of observation, 23. Then, kn matrix },,,{ 4321 xxxxX is defined,
where )(rank Xk . Then, we calculated the following matrices to get the coeffi-
cients b and their standard error (the diagonal elements of )(bV ).
XXQ , where 'X is a transposed matrix of the matrix X ;
YXQb 1 , where 1Q is an inversed matrix of the matrix Q ;
XbY ˆ : expected global temperature Y ;
YYe ˆ ; 1)(
Q
kn
ee
bV .
And, the values of the square-root of the diagonal elements of )(bV are the
standard errors of elements of the estimated coefficient-vector b . The results of
the regression analysis are shown in Table 2.
T a b l e 2 . Result of Regression Analysis and Model Characterization (adequacy)
Parameter )/(1CO 2
3221 rcccY )/(1)/1(CO 2
43221 rcrcccY
1c –1,17863 –3,52065 310
Coefficient of
2CO 5,33150 410 5,31189 410
2c
Standard error of
2CO 4,27704 510 4,29964 510
Coefficient of r/1 --- 2,55211 910
3c Standard error of
r/1
--- 2,78543 910
Coefficient of
)/(1 2r 1,05537 1110 –4,62552 1410
4c
Standard error of
)/(1 2r 3,64932 1110 5,04955 1410
R2 (coefficient
of determination)
0,88602 0,89084
Durbin-Watson
Statistic
0,22092 0,40021
Sum of Squared
Residuals 3,68696 210 3,53096 210
Yoshio Matsuki, Petro I. Bidyuk
ISSN 1681–6048 System Research & Information Technologies, 2019, № 2 22
Multicollinearity
At first, we made the regression of
2
1
r
on
r
1
, and obtain the residuals *
1
2r
, by
calculating the following matrices:
2
1
,
1
rr
X , a matrix made of two vectors
r
1
and
2
1
r
;
XXQ , where, X is a transposed matrix of X ;
'
11
r
QA , where 1Q is an inversed matrix of Q ;
XAN ;
NIM , where, I is kk matrix, in which all diagonal element is 1, and
non-diagonal elements are ;
22
1
*
1
r
M
r
.
And, then, we made a regression analysis with the following steps:
*
1
,
1
*
2rr
X ;
2732
3210
1046866.31018316.5
1018316.51074017.1
*** XXQ ;
*** 1 XQA ;
YAb ** ;
*** AXN ;
** NIM ;
YMe ** ;
1*
**
*)(
Q
kn
ee
bV .
And, the values of the square-root of the diagonal elements of *)(bV are the
standard errors of elements of the estimated coefficient-vector *b . The calculated
coefficients and their standard errors are shown in the second column of Table 3
*
11
221
r
c
r
cY . The third column of Table 3
221
1
*
1
r
c
r
cY was calcu-
lated after the regression of
r
1
on
2
1
r
, to obtain the residuals *
1
r
; and, the first
column of Table 3
221
11
r
c
r
cY was calculated by making the regression of
Y on
r
1
and
2
1
r
.
Empirical Investigation on Influence of Moon’s Gravitational-Field to Earth’s …
Системні дослідження та інформаційні технології, 2019, № 2 23
T a b l e 3 . Comparison of Calculated Coefficients and Standard Errors
Parameter 221
11
r
c
r
cY *
11
221
r
c
r
cY
221
1
*
1
r
c
r
cY
Coefficient 7,68915 510 1,05630 510 7,68916 510
1c
Standard error 5,81004 610 9,38188 310 5,81005 610
Coefficient –2,40517 1110 –2,40519 1110 3,83024 1010
2c
Standard error 2,10681 1210 2,10681 1210 3,40201 910
ANALYSIS OF THE RESULTS
1. We added
r
1
to the Classical Regression Model of our previous analy-
sis [1]. The result shows more adequacy of the model in comparison with the pre-
vious model [1] in the coefficient of determination, Durbin-Watson Statistic and
Sum of Squared Residuals; however, the sign of the coefficient of
2
1
r
changed
from positive sign (plus) to negative sign (minus), in Table 2. It means that
r
1
is
an influential variable to Earth’s global temperature; while,
2
1
r
is not influential
in this system of Moon’s gravitational field and Earth’s global temperature.
2. We tested the multicollinearity of
r
1
and
2
1
r
, by changing
2
1
r
to *
1
2r
by auxiliary residual regression, and then made the regression of Earth’s tempera-
ture (Y ) over
r
1
and *
1
2r
. As the result, multicollinearity was found. In Table 3,
the coefficient of
r
1
changed from 7,68915 510 to 1,05630 510 . It means that
2
1
r
lowered the influence of
r
1
. On the other hand, we also changed
r
1
to *
1
r
by
auxiliary residual regression, and then made the regression of Earth’s temperature
(Y ) over *
1
r
and
2
1
r
. The result shows that the coefficient of
2
1
r
changed from
–2,40517 1110 to 3,83024 1010 . This result means that
r
1
increased the influence
of
2
1
r
in the system.
After these calculations, we conclude that
r
1
and
2
1
r
are related in the sys-
tem of Moon’s gravitational-field and Earth’s temperature. This finding also im-
plies that Moon’s gravitational-field may be mainly described in the flat space,
Yoshio Matsuki, Petro I. Bidyuk
ISSN 1681–6048 System Research & Information Technologies, 2019, № 2 24
although non-linear space (4-dimentional curved space in theory) could also
influence the gravitational field of this system where the gravitational wave
could interact.
CONCLUSION AND RECOMMENDATION
In the system of Earth’s global temperature with Moon’s gravitational field, the
effect of
2
1
r
is negligible in the presence of
r
1
. However, there is the multicol-
linearity between
r
1
and
2
1
r
, which suggests the existence of the gravitational
wave’s interaction to the gravitational field; therefore there is a possibility for as-
suming the 4-dimensional curved space, instead of flat space. Further simulation
is needed to model the system of flat space and curved space, which may explain
how the gravitational wave and the gravitational field are interrelated.
So far, our calculation has shown that the influence of Moon’s gravitational
field to Earth’s global temperature is significant than the influences of CO2.
REFERENCE
1. Matsuki Y. Empirical analysis of moon’s gravitational wave and Earth’s global
warming / Y. Matsuki, P.I. Bidyuk // System Research & Information Technol-
ogy. — N 1. — 2018. — P. 107–118.
2. Matsuki Y. Analysis of Moon’s gravitational-wave and Earth’s global temperature:
influence of time-trend and cyclic change of distance from Moon / Y. Matsuki,
P.I. Bidyuk // System Research & Information Technology. — N 3. — 2018. —
P. 19–30.
3. Dirac P.A.M. General Theory of Relativity / P.A.M. Dirac. — Florida University,
A Wiley-Interscience Publication, John Wiley & Sons, New York, 1975. — P. 69.
4. UK Department of Energy and Climate Change (DECC). — Available at: http://
en.openei.org/datasets/dataset/b52057cc-5d38-4630-8395-b5948509f764/ re-
source/f42998a9-071e-4f96-be52-7d2a3e5ecef3/download/england.surface.
temp1772.2009.xls
5. Boden T.A. Global Regional and National Fossil-Fuel CO2 Emissions / T.A. Boden,
G. Marland, R.J. Andres. — Available at: cdiac.orbl.gov/trends/emits/tre_
glob.html cdiac.ornl.gov/trends/emits/tre_glob.html (last access, 8 August 2017)
6. Moon Distance Calculator – How Close is Moon to Earth?. — Available at: https://
www.timeanddate.com/astronomy/moon/distance.html?year=1987&n=367
Received 15.11.2018
From the Editorial Board: the article corresponds completely to submitted manuscript.
|
| id | journaliasakpiua-article-175551 |
| institution | System research and information technologies |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2025-07-17T10:26:04Z |
| publishDate | 2019 |
| publisher | The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" |
| record_format | ojs |
| resource_txt_mv | journaliasakpiua/7f/c3cfaa159c021529ba75ac3017b9297f.pdf |
| spelling | journaliasakpiua-article-1755512019-08-27T22:12:50Z Empirical investigation on influence of Moon’s gravitational-field to Earth’s global temperature Эмпирическое исследование влияния гравитационного поля Луны на глобальную температуру Земли Емпіричне дослідження впливу гравітаційного поля Місяця на глобальну температуру Землі Matsuki, Yoshio Bidyuk, Petro I. global temperature Moon’s gravitational field gravitational wave multicollinearity глобальная температура гравитационное поле Луны гравитационная волна мультиколлинеарность глобальна температура гравітаційне поле Місяця гравітаційна хвиля мультиколінеарність This research examined a possibility of the Moon’s gravitational-wave that may influence Earth’s global temperature, with a mathematical method of empirical analysis with the data of the global temperature, global carbon dioxide, and the distance between Moon and Earth. We made the regression analysis of the global temperature over the factors of Moon’s gravitational field taken from the General Theory of Relativity and from the Newton’s gravity theory, with the data of the carbon-dioxide. The result shows that Newton’s gravitational field is related to Earth’s global temperature, while the influence of Moon’s gravitational wave is negligible. However, we also found a possibility that the gravitational wave could contribute to Moon’s gravitational-field upon the analysis of multicollinearity of two factors taken from Newton’s theory and the General Theory of Relativity. В исследовании изучается возможность гравитационной волны Луны, которая может влиять на глобальную температуру Земли с применением математического метода эмпирического анализа с учетом данных глобальной температуры, глобального углекислого газа и расстояния между Луной и Землей. Проведен регрессионный анализ глобальной температуры относительно гравитационного поля Луны, взятых из общей теории относительности, из теории тяготения Ньютона и углекислоты. Результат свидетельствует о влиянии гравитационного поля Ньютона на глобальную температуру Земли; влияние гравитационной волны Луны незначительно. Однако обнаружена возможность влияния гравитационной волны на гравитационное поле Луны в четырехмерном неевклидовом пространстве согласно анализу мультиколлинеарности двух факторов, взятых из теории Ньютона и общей теории относительности. У дослідженні вивчається можливість гравітаційної хвилі Місяця, яка може впливати на глобальну температуру Землі із застосуванням математичного методу емпіричного аналізу з урахуванням даних глобальної температури, концентрації вуглекислого газу та відстані між Місяцем та Землею. Проведено регресійний аналіз глобальної температури стосовно гравітаційного поля Місяця, узятих із загальної теорії відносності, з теорії тяжіння Ньютона та вуглекислоти. Результат свідчить про вплив гравітаційного поля Ньютона на глобальну температуру Землі; вплив гравітаційної хвилі Місяця є незначним. Однак виявлено можливість впливу гравітаційної хвилі на гравітаційне поле Місяця у чотиривимірному неевклідовому просторі згідно з аналізом мультиколінеарності двох факторів, узятих з теорії Ньютона та загальної теорії відносності. The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" 2019-06-25 Article Article application/pdf https://journal.iasa.kpi.ua/article/view/175551 10.20535/SRIT.2308-8893.2019.2.02 System research and information technologies; No. 2 (2019); 18-24 Системные исследования и информационные технологии; № 2 (2019); 18-24 Системні дослідження та інформаційні технології; № 2 (2019); 18-24 2308-8893 1681-6048 en https://journal.iasa.kpi.ua/article/view/175551/175460 Copyright (c) 2021 System research and information technologies |
| spellingShingle | глобальна температура гравітаційне поле Місяця гравітаційна хвиля мультиколінеарність Matsuki, Yoshio Bidyuk, Petro I. Емпіричне дослідження впливу гравітаційного поля Місяця на глобальну температуру Землі |
| title | Емпіричне дослідження впливу гравітаційного поля Місяця на глобальну температуру Землі |
| title_alt | Empirical investigation on influence of Moon’s gravitational-field to Earth’s global temperature Эмпирическое исследование влияния гравитационного поля Луны на глобальную температуру Земли |
| title_full | Емпіричне дослідження впливу гравітаційного поля Місяця на глобальну температуру Землі |
| title_fullStr | Емпіричне дослідження впливу гравітаційного поля Місяця на глобальну температуру Землі |
| title_full_unstemmed | Емпіричне дослідження впливу гравітаційного поля Місяця на глобальну температуру Землі |
| title_short | Емпіричне дослідження впливу гравітаційного поля Місяця на глобальну температуру Землі |
| title_sort | емпіричне дослідження впливу гравітаційного поля місяця на глобальну температуру землі |
| topic | глобальна температура гравітаційне поле Місяця гравітаційна хвиля мультиколінеарність |
| topic_facet | global temperature Moon’s gravitational field gravitational wave multicollinearity глобальная температура гравитационное поле Луны гравитационная волна мультиколлинеарность глобальна температура гравітаційне поле Місяця гравітаційна хвиля мультиколінеарність |
| url | https://journal.iasa.kpi.ua/article/view/175551 |
| work_keys_str_mv | AT matsukiyoshio empiricalinvestigationoninfluenceofmoonsgravitationalfieldtoearthsglobaltemperature AT bidyukpetroi empiricalinvestigationoninfluenceofmoonsgravitationalfieldtoearthsglobaltemperature AT matsukiyoshio émpiričeskoeissledovanievliâniâgravitacionnogopolâlunynaglobalʹnuûtemperaturuzemli AT bidyukpetroi émpiričeskoeissledovanievliâniâgravitacionnogopolâlunynaglobalʹnuûtemperaturuzemli AT matsukiyoshio empíričnedoslídžennâvplivugravítacíjnogopolâmísâcânaglobalʹnutemperaturuzemlí AT bidyukpetroi empíričnedoslídžennâvplivugravítacíjnogopolâmísâcânaglobalʹnutemperaturuzemlí |