Емпіричний аналіз гравітаційної хвилі Місяця та глобального потепління Землі
This research examines a possibility of a disturbance by Moon’s gravitational wave to the Earth’s global warming process in comparison with the increase of global volume of carbon dioxide. Because the general theory of relativity that predicts the gravitational wave of a planet has a dimension of 1/...
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| description | This research examines a possibility of a disturbance by Moon’s gravitational wave to the Earth’s global warming process in comparison with the increase of global volume of carbon dioxide. Because the general theory of relativity that predicts the gravitational wave of a planet has a dimension of 1/(distance)2, we analyzed the data sets of global temperature and global carbon dioxide, with this dimension of gravitational wave using Least Squares Estimation of Linear Classical Regression Model, Generalized Classical Regression Model, and Nonlinear Regression Model. The results suggest that there is a disturbance to the process of global warming by the Moon’s gravitational wave. However, there is uncertainty for this conclusion because the Moon’s rotational movement around Earth gives different type of distributions of its sample data, while global temperature and carbon dioxide increase proportionally accordingly to available time-series. |
| doi_str_mv | 10.20535/SRIT.2308-8893.2018.1.09 |
| first_indexed | 2025-07-17T10:23:29Z |
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Yoshio Matsuki, P.I. Bidyuk, 2018
Системні дослідження та інформаційні технології, 2018, № 1 107
TIДC
МАТЕМАТИЧНІ МЕТОДИ, МОДЕЛІ,
ПРОБЛЕМИ І ТЕХНОЛОГІЇ ДОСЛІДЖЕННЯ
СКЛАДНИХ СИСТЕМ
UDC 519.004.942
DOI: 10.20535/SRIT.2308-8893.2018.1.09
EMPIRICAL ANALYSIS OF MOON’S GRAVITATIONAL WAVE
AND EARTH’S GLOBAL WARMING
YOSHIO MATSUKI, P.I. BIDYUK
Abstract. This research examines a possibility of a disturbance by Moon’s gravita-
tional wave to the Earth’s global warming process in comparison with the increase
of global volume of carbon dioxide. Because the general theory of relativity that
predicts the gravitational wave of a planet has a dimension of 1/(distance)2, we ana-
lyzed the data sets of global temperature and global carbon dioxide, with this dimen-
sion of gravitational wave using Least Squares Estimation of Linear Classical Re-
gression Model, Generalized Classical Regression Model, and Nonlinear Regression
Model. The results suggest that there is a disturbance to the process of global warm-
ing by the Moon’s gravitational wave. However, there is uncertainty for this conclu-
sion because the Moon’s rotational movement around Earth gives different type of
distributions of its sample data, while global temperature and carbon dioxide in-
crease proportionally accordingly to available time-series.
Keywords: global warming, Moon and Earth, global carbon dioxide, gravitational
wave.
INTRODUCTION
Einstein’s theory of gravitational wave predicts that it contains a factor of ,
which has the dimension of
2
1
r
, where r is the distance (kilometers), to where
the gravitational wave reaches from a planet. Therefore, in this research,
2
1
r
is
considered as a surrogate of the intensity of the gravitational wave, and its rela-
tion to the global temperature is analyzed, together with the global carbon diox-
ide, in time-series.
THEORY
In the general theory of relativity [1], gravity is described by the derivatives, g ,
of the scalar potential, rmV / , where and are 0, 1, 2, 3, which indicate the
coordinates of the empty curved-space in 4 dimensions, where x0 is for time, x1,
x2 and x3 for space, and m is mass of a planet, and r is the distance from the cen-
Yoshio Matsuki, P.I. Bidyuk
ISSN 1681–6048 System Research & Information Technologies, 2018, № 1 108
ter of the planet. The gravitational field in the empty space is described by Ricci
tensor:
0R , (1)
while gravitational wave is described by the solutions of 0, g in har-
monic coordinates, where the condition of harmonic coordinates is
0,
2
1
,
ggg , where each of g satisfies the d’Alambert equation,
0),,(
VVg , where each of , , , and indicates each of the
coordinates, 210 ,, xxx and 3x . Here, g
dx
d
g , , and g
dxdx
d
g
2
, .
When the gravitational waves are all moving in the same direction, for ex-
ample 3x , g are functions of only one variable, 3x in time-series. And, in more
general case, lug , when g are all functions of the single variable
xl , while l are the constants that satisfy 0
llg , and u is the derivative,
g , of the function
xl . And, then, after the transformation of the tensors, we get:
ullu
2
1
. (2)
And, then,
ul
2
1
. Now, the gravitational wave moves in the direction
l of the form, bxx ' , where b is a function only of
xl with the re-
striction that wave moves only in one direction. And, then, the equation (2) indi-
cates the flow of the energy in the direction of 3x :
2
12
2
2211
0
0 )(
4
1
16 uuut .
Here,
t is a pseudo-tensor, which means a quantity, given by
Lgg
g
L
t
~
,
,
~
, while )(
gL ,
RgR
LR * , ),,(*
gR , LL
~
, g , and 00gg .
The gravitational field equation of the empty space (1) is generalized to
a tensor equation:
gR , (3)
where is a constant. The values of R contain second derivatives of the g ,
because
,,R ; so, must have the dimension of
(distance)-2. Where the planet exists, this constant coefficient must be small
enough, so that the flow of energy does not disturb the coordinate that the planet
makes, as shown in the tensor equation (1).
There is a comprehensive action principle:
0)( II g , (4)
Empirical analysis of moon’s gravitational wave and earth’s global warming
Системні дослідження та інформаційні технології, 2018 № 1 109
where gI is the gravitational action, and I is the action of sum of all the other
fields; while, xdggRgRI g
4)
2
1
(
, and xdgRI 4 .
For the cosmological theory, an extra term is added, such as:
xdgcIc
4 , where c is a suitable constant. And, then, cI
xdgggc 4
2
1
, and the action principle (equation (4)) gives:
0
2
1
2
1
)16(
cgRgR . (5)
Then, the equation (3) gives 4R , and hence: gRgR
2
1
.
And, if c8 , it satisfies the equation (5).
This theory suggests that Moon emits gravitational wave to Earth, which is a
flow of energy; and its intensity includes a dimension, related
to
2
1
84
r
cR , where r is the distance between two planets. In this re-
search, we use
2
1
r
as an indicator of the gravitational wave. In the following sec-
tions, we report the methods and the results of the analysis. It is assumed that the
global temperature is an indicator of the energy, which is given by the indicator of
Moon’s gravitational wave. The global carbon-dioxide is analyzed together in the
mathematical models for the data analysis, in order to evaluate the importance of
Moon’s gravitational wave.
METHOD OF THE RESEARCH
The descriptive statistics of the data, from 1987 till 2009, of the global tempera-
ture (increased degree Celsius since 1978) [2], the global carbon dioxide (million
metric tons) [3], the distance between Moon and Earth ( r : kilometers) [4], and
calculated
2
1
r
((kilometers)22)) ,, are shown in Table 1.
T a b l e 1 . Descriptive statistics
Variable
Global
Temperature
(oC) *
Carbon-gas
(million
metric tons) **
Distance between
Moon and Earth
(r: kilometers)
2/1 r
((kilometers)--22))
Mean 0,29130 1,25165103 3,62618105 7,6050910-12
Standard
deviation 0,12125 2,14245102 5,98411102 2,5109710-14
Minimum 0,10000 8,92000102 3,61583105 7,5699910-12
Maximum 0,43000 1,62600103 3,63483105 7,6486510-12
Skewness –0,21063 0,14292 –0,15249 0,15787
Kurtosis 1,29401 1,82491 1,67498 1,67879
Valid number
of observations 23 23 23 23
Yoshio Matsuki, P.I. Bidyuk
ISSN 1681–6048 System Research & Information Technologies, 2018, № 1 110
* Increased degree Celsius since 1978
** To convert these estimates to units of carbon dioxide (CO2), simply multiply these es-
timates by 3,667 [2]
Regression analysis is made on the global temperature, the global carbon-
dioxide and
2
1
r
, with the models, considered below.
Least Squares Estimation of Linear Classical Regression Model
The global temperature Y { 1y , …… ny }, the constant value 1, 1x , the meas-
ured global carbon-dioxide , 2x , and the inverse of the squared distance between
Moon and Earth, 3x , are transformed into the forms of 1n vectors, y , 1x , 2x ,
3x , where n is the number of observation, 23. Then kn matrix },,{ 321 xxxX
is defined, where )(Xrankk .
We assume that: XyE )( , IYV 2)( , X non-stochastic, and
kX )(rank =3, where )(yE is the mean of y , )(yV is the variance of Y , and
)(2 yV . I is nn matrix, in which all diagonal elements are 1, and other ele-
ments are 0. In the Classical Regression Model, it is assumed that the diagonal
elements of IYV 2)( are all of the same value, 2 . And, all covariances are
assumed to be zero. With the following algebra, b (estimated coefficient from
the sampled data) and 2 are calculated:
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 square-root of the diagonal elements of )(bV are the standard errors of
elements of the estimated coefficient-vector b .
Time Series
After applying the Classical Regression Model to this problem, we examine the
time-series of the sampled data of global temperature, carbon-dioxide and
2
1
r
, in
order to estimate the independency (or dependency) and the distribution patterns
of these variables. For this purpose, we calculate the autocorrelation of each of the
sampled data of these three variables, with the following algebra:
From n consecutive observations, nyy ,,1 , we make a vector
T
1 ),,( nyyy , where ‘ T ’ transposes a vector. And then we calculate: sample
mean:
n
t
t
n
ym
1
, sample autovariance: nmyc
n
i
i
2
1
0 )(
, the first sample
Empirical analysis of moon’s gravitational wave and earth’s global warming
Системні дослідження та інформаційні технології, 2018 № 1 111
autocovariance: )1())((
2
11
nmymyc
n
i
ii , and then similarly, the second
sample autocovariance: )2())((
3
22
nmymyc
n
i
ii , and so forth.
Then we calculate the sample autocorrelations: 0ccr jj .
Generalized Classical Regression
In general, the autocorrelation suggests whether, or not, changes in time-series of
each of the variables are related to its own past; or it suggests whether or not, the
variable in the past is independent from the present time with the same pattern of
the distribution of the variable as it currently has. By comparing three autocorrela-
tions for three variables of global temperature, carbon-dioxide and
2
1
r
, we will
be able to estimate the distribution pattern of the standard deviations of the kn
matrix },,{ 321 xxxX , to see if the diagonal elements of the assumed matrix of
variances (square-root of standard deviation) IYV 2)( are all equal and/or
if the covariances are zero, or not. If not, the Classical Regression Model is not
applicable; but, instead, we need Generalized Classical Regression Model, in
which IYV 2)( , and/or the matrix contains non-zero covariances.
In this research, we examine two possibilities:
a) Pure Heteroskedasticity, in which diagonal elements of are all dif-
ferent; and,
b) First-Order Autoregressive Process, in which the first-order autocovari-
ance, )1())((
2
11
nmymyc
n
i
ii is not zero.
In case of Pure Heteroskedascity, the iy ’s are uncorrelated, but have dif-
ferent variances: the matrix is diagonal, with diagonal elements
222
1 ,,,, ni . Here we assume an nn matrix H that makes IHH .
H is the diagonal matrix that has the i1 ’s on its diagonal. If the i ’s are
known, then we can transform the data by dividing all variables at the i th obser-
vation by i to get
i
i
i
yy * ,
i
ij
ij
x
x * , where 23,,2,1 i ; 3,2,1j .
Then Classical Regression Model will apply to the new data and the regres-
sion of *Y on *X will produce the Least-Squares Estimation of Generalized
Classical Regression Model of *b with the same procedure shown in the analysis
of the Least Squares Estimation of Linear Classical Regression Model.
When we assume that the time-series of the global temperature is First-Order
Autoregressive Process, a common practice is: at first, run Least Squares Estima-
tion of Linear Classical Regression Model of y on X to get the residuals
YYe ˆ .
Yoshio Matsuki, P.I. Bidyuk
ISSN 1681–6048 System Research & Information Technologies, 2018, № 1 112
Then regress ie on 1ie (across 23,,2 i in the time-series) to estimate
011 ccr : as
23
2
2
1
23
2
1ˆ
i
i
i
ii eee . No intercept is required when the sum of
the residuals
23
1i
ie is zero. And then transform the data as bellow, using ̂ :
1ˆ* iii yyy and 1ˆ* ii XXX , where },,{ ,3,2,1 iiii xxxX and 1iX
},,{ 1,31,21,1 iii xxx ; and then run Least Squares Estimations of Linear Classi-
cal Regression Model of *y over *X .
Nonlinear Regression Model
In this research, we try to analyze the database also with Nonlinear Regression
Model, with Cobb-Douglas function, 32
321
bb xxby . Not like as Least Squares Es-
timation of Classical Regression Model, we cannot calculate the coefficients, 1b ,
2b , 3b , algebraically; but, we can calculate them only numerically:
Now ),,,,( 32321 xxbbbhh ;
),,,,( 32132
321
bbbxxzb
h
b
h
b
hz
;
),,,,,( 32132 bbbxxyuhyu .
We seek the values of 1b , 2b , 3b that make 0uz . We assume that 0
1b ,
0
2b , 0
3b are the initial guessed values for 1b , 2b , 3b . Then, ),,,,( 32
0
3
0
2
0
1
0 xxbbbhh ,
),,,,( 0
3
0
2
0
132
0 bbbxxzz , ),,,,,( 0
3
0
2
0
132
00 bbbxxyuhyu . The linear ap-
proximation to h at the point ( 0
3
0
2
0
1 ,, bbb ) is ))()(( 0
33
0
22
0
11
00 bbbbbbzhh ,
so that order of approximation,
)])()(([ 0
33
0
22
0
11
00 bbbbbbzhyhyu
))()(( 0
33
0
22
0
11
00 bbbbbbzu ;
000
33
0
22
0
11
00
321 '))()(('),,( zzbbbbbbuuuubbb
000
33
0
22
0
11 '))()((2 uzbbbbbb ;
00000
33
0
22
0
11
321
321 '2'))()((2),,( uzzzbbbbbbbbbbbb
.
Set 0),,( 321 bbb , and solve for ))()(( 0
33
0
22
0
11 bbbbbb
0000 '/' zzuz .
And then take the resulting ))()(( 0
33
0
22
0
11 bbbbbb as the new
0
3
0
2
0
1 ,, bbb and restart the calculation. Continue until the result converge, that is
until 0))()(( 0
33
0
22
0
11 bbbbbb .
Empirical analysis of moon’s gravitational wave and earth’s global warming
Системні дослідження та інформаційні технології, 2018 № 1 113
In practice, the derivative 0
3
0
2
0
1 b
h
b
h
b
hz
can be approximated
numerically as
]222/[)( 321
))((
2
0
1
))((
2
0
1
0 33223322 pppxbxbz pbpbpbpb ,
where 1p , 2p , and 3p are small steps.
RESULT
The results of Least Squares Estimation of Classical Regression Model are shown
from Table 2 to Table 6.
T a b l e 2 . Matrix XXQ in Classical Regression Model
23,00000 2,87880104 1,7491710-10
2,87880104 3,70424107 2,1893010-7
1,7491710-10 2,1893010-7 1,3302710-21
T a b l e 3 . Matrix YX ' in
Classical Regression Model
T a b l e 4 . Matrix YXQb '1 in * Classical
Regression Model
6,70000 for 1 ( 1x ) -1,17863
8,92389103 for Carbon dioxide ( 2x ) 5,3315010-4
5,0952710-11 for )1( 2r ( 3x ) 1,055371011
* With this model, R2 = 0,88602.
T a b l e 5 . Matrix 1)(
Q
kn
ee
bV in Classical Regression Model
7,71895 –7,67170 10-6 –1,01370 1012
–7,67170 10-6 1,82931 10-9 7,07689 105
–1,01370 1012 7,07689 105 1,33176 1023
T a b l e 6 . Coefficients and standard errors of the coefficients in Classical Re-
gression Model
Variable Coefficient Standard error
for 1 ( 1x ) –1,17863 2,77830
for Carbon dioxide ( 2x ) 5,3315010-4 4,2770410-5
for )1( 2r ( 3x ) 1,055371011 3,649331011
The coefficients of Table 6, which are calculated by Classical Regression
Model, show that 3x
2
1
r
influences y (global temperature) more than 2x (car-
bon-dioxide) does; however, the standard error of the estimated coefficient of 3x
is larger than 2x ’s. In order to investigate this large size of the standard error of
the coefficient of 3x , we analyzed the patterns of the changes of y , 2x , and 3x ,
Yoshio Matsuki, P.I. Bidyuk
ISSN 1681–6048 System Research & Information Technologies, 2018, № 1 114
in time-series, by calculating their autocorrelations. Fig. 1 shows the auto-
correlation of y , Fig. 2 of 2x and Fig. 3 of 3x .
Fig. 2. Calculated autocorrelation of global carbon dioxide ( 2x )
Fig. 1. Calculated autocorrelation of global temperature ( y )
Fig. 3. Calculated autocorrelation of 2/1 r , 3x
Empirical analysis of moon’s gravitational wave and earth’s global warming
Системні дослідження та інформаційні технології, 2018 № 1 115
The autocorrelation of y (sample data of global temperature) in Fig. 1 sug-
gests that all sample autovariance 0c of y are same over different i s, where
23,,2 i ; and, sample autocovariances ic s are becoming smaller when i be-
comes larger; so, this sample data of y suggests possibilities of both Heteroske-
dasticity and Autoregressive Process.
The autocorrelation of 2x (sample data of carbon dioxide) in Fig. 2 also
suggests possibilities of both Heteroskedasticity and Autoregressive Process.
However, the autocorrelation of 3x , 21 r , in Fig. 3 shows a different pattern of
its distribution, in comparison with Fig. 1 and Fig. 2. And, then, because of these
observations of autocorrelations, we further tested Generalized Classical Regres-
sion Model by regressing y over 2x and 3x , assuming the following: Pure Het-
eroskedacity, where the diagonal elements of have different variances,
2
23
2
2
2
1 ,,,, , and First Order Autoregressive Process, in which the first-
order autocovariance, 01ˆ cc is not zero, but the same value.
The results of the analysis with Generalized Classical Regression Model in
the assumed Pure Heteroskedasticity and the assumed First-Order Autoregressive
Process are shown from Table 7 to Table 11.
Here, it is noted that for b) First-Order Autoregressive Process, at first, we
calculated the residuals YYe ˆ , and
23
1i ie to see if the sum of the residuals
is zero. And, then, we knew 1123
1 1052104.4
i ie , which is small enough to
assume as it is zero. And, then, we regressed ie on 1ie (across 23,,2 i in
time-series), and then, we got 90997.0ˆ .
T a b l e 7 . Matrix XXQ in Generalized Classical Regression Model
Pure Heteroskedasticity First-Order Autoregressive Process
23,00000 1,34369102 6,96610103 0,17832 2,82472102 1,3561310-12
1,34369102 8,07005102 4,06960104 2,82472102 4,62382105 2,1454910-9
6,96610103 4,06960104 2,10987106 1,3561310-12 2,1454910-9 1,0335210-23
T a b l e 8 . Matrix YX ' in Generalized Classical Regression Model
Pure Heteroskedasticity First-Order Autoregressive Process
55,25547 7,9711510-2
3,43513102 1,26456102
1,67350104 6,0631910-13
T a b l e 9 . Matrix YXQb 1* in Generalized Classical Regression Model
Pure Heteroskedasticity* First-Order Autoregressive Process
for 1, 1x -9,72055 0,37507
for Carbon dioxide, 2x 0,94202 1,3650310-5
for )(1/ 2r , 3x 2,1855710-2 6,61708109
* With this model, R2 = 0,88602, which is as same as R2 of the classical regression model
in Table 4.
Yoshio Matsuki, P.I. Bidyuk
ISSN 1681–6048 System Research & Information Technologies, 2018, № 1 116
T a b l e 1 0 . Matrix 1'
*)(
Q
kn
ee
bV in Generalized Classical Regression Model
Pure Heteroskedasticity First-Order Autoregressive Process
5,24998102 -0,11178 -1,73122 0,62342 -3,4971010-5 -7,454131010
-0,11178 5,7109710-3 2,5892010-4 -3,4971010-5 1,3785610-8 1,72693106
-1,73122 2,5892010-4 5,7109610-3 -7,454131010 1,72693106 9,441811021
T a b l e 1 1 . Coefficients and standard errors of the coefficients in Generalized
Classical Regression Model
Pure Heteroskedasticity First-Order Autoregressive Process
Variable
Coefficient Standard error Coefficient Standard error
for 1 ( 1x ) -9,72055 22,91283 0,37507 0,78957
for Carbon
dioxide ( 2x ) 0,94202 7,5571010-2 1,3650310-5 1,1741210-4
for )(1/ 2r ( 3x ) 2,1855710-2 7,5570910-3 6,61708109 9,716901010
The adjusted coefficients of Table 11, which were calculated by the assump-
tion of Pure Heteroskedasticity in Generalized Classical Regression Model, sug-
gest that 3x
2
1
r
influenced y (global temperature) less than 2x (carbon-
dioxide) did; while, the standard error of the estimated coefficient of 3x is almost
equal to 2x ’s. On the other hand the assumption of First-Order Autoregressive
Process suggests that 3x
2
1
r
influenced y (global temperature) more than 2x
(carbon-dioxide) did; while, the standard error of the estimated coefficient of 3x
is larger than 2x ’s.
In order to further investigate the relation between 3x
2
1
r
and y (global
temperature), we also analyzed the same data set by Nonlinear Regression Model
of Cobb-Douglas function. The result is shown in Table 12.
T a b l e 1 2 . Coefficients of Cobb-Douglas model, 3
321
2 bb xxby
Coefficient Estimated coefficient Standard error
1b coefficient of 1 0,000103 0,02761
2b coefficient of 2x 2,126546 0,23431
3b coefficient of 3x 0,283107 10,62035
The estimated coefficients of nonlinear Cobb-Douglas function show that the
coefficient of 2x is larger than the coefficient of 3x . This result suggests that the
carbon dioxide is more influential to the global warming, than
2
1
r
, if the global
temperature is to be described by the Cobb-Douglas function.
Empirical analysis of moon’s gravitational wave and earth’s global warming
Системні дослідження та інформаційні технології, 2018 № 1 117
ANALYSIS OF THE CALCULATED RESULTS
We cannot measure Moon’s gravitational wave; while the general theory of rela-
tivity only suggests that it includes dimension of
2
1
r
, where r is a distance be-
tween Moon and Earth in kilometers. The result of the Least Squares Estimation
of Linear Classical Regression Model suggests that the influence of Moon’s
gravitational wave to the global warming is large; however, the standard error of
the estimated coefficient is also large. On the other hand, the autocorrelations of
the global temperature, in time-series, suggests that the process of the global
warming could be explained by its own history, which could be also influenced
by carbon dioxide and gravitational wave from Moon. However, as shown in
Fig. 4, the distribution of
2
1
r
is cyclic in time-series because Moon rotates on
oval orbit around Earth; while the distributions of global temperature and carbon
dioxide are proportional to the time-series as Fig. 1 and Fig. 2 show. And then we
assumed that Moon’s gravitational wave could disturb the process of the global
warming; and, then we tried to measure the order of magnitude of the assumed
disturbance by Moon to Earth (global temperature), with two assumptions in the
Generalized Classical Regression Models: Pure Heteroskedasticity and First-
Order Autoregressive Process, and one Nonlinear Model.
The results of First-Order Autoregressive Process of Generalized Classical
Regression Model suggests large disturbance of Moon to the process of global
warming, which is as same as the result of Least Squares Estimation of Classical
Regression Model; although, the results of the analysis with the assumptions of
Pure Heteroskedasticity and Nonlinear Model suggest the opposite.
The reasons of these differences, which are observed in analysis in these four
models, are supposed to be related to the nature of Moon’s movement on the oval
orbit, which gives larger variance and covariance, which are taken in different
ways by different models.
Fig. 4. Distance between Moon and Earth
Yoshio Matsuki, P.I. Bidyuk
ISSN 1681–6048 System Research & Information Technologies, 2018, № 1 118
CONCLUSION AND RECOMMENDATIONS
We assumed that the gravitational wave from Moon to Earth influenced the global
temperature of Earth; and, then, the result of the Least Squares Estimation of
Classical Regression Model suggested such effect to exist. However, we also
found that the calculated standard error of the estimated coefficient of the gravita-
tional wave was large.
And, then, we examined Generalized Classical Regression Model, to see if
the magnitude of standard error changes, by assuming Pure Heteroskedasticity
and First Order Autoregressive Process, which added more different variances
and covariances in the regression models. The results indicated that the expected
influence of Moon’s gravitational wave was large, while the standard-error was
large with the assumption of First Order Autoregressive Process; while, the ex-
pected influence was small and its standard error was also small when Pure Het-
eroskedasticity is assumed. However, we don’t know if the assumption of Pure
Heteroskedasticity is appropriate for modeling Moon’s rotational movement.
Also, we tested the nonlinear Cobb-Douglas function to simulate the impacts
from Moon’s gravitational wave and carbon dioxide to the global warming, and
the result showed more influence of carbon dioxide. However, we don’t’ know
any reasonable theory to justify the nonlinear function, yet, rather we examined it,
only to observe how the coefficients change in comparison with those of Least
Squares Estimation of Classical Regression Model.
Upon above observations, we cannot deny our assumption that Moon’s
gravitational wave could disturb the process of global warming, yet; while, the
results also suggest that uncertainty exists because of Moon’s rotational move-
ment, which is different from the processes of rising global temperature and car-
bon dioxide.
REFERENCES
1. Dirac P.A.M. General Theory of Relativity / P.A.M. Dirac. — New York: Florida
University, A Wiley-Interscience Publication, John Wiley & Sons, 1975. —
P. 69. — Available at: http://amarketplaceofideas.com/wp-content/uploads/2014/
08/P%2520A%2520M%2520Dirac%2520-%2520General%2520Theory%
2520Of%2520Relativity1.pdf
2. UK Department of Energy and Climate Change (DECC). — Available at:
http://en.openei.org/datasets/dataset/b52057cc-5d38-4630-8395-
b5948509f764/resource/f42998a9-071e-4f96-be52-
7d2a3e5ecef3/download/england.surface.temp1772.2009.xls
3. Boden T.A. Global Regional and National Fossil-Fuel CO2 Emissions / T.A. Boden,
G. Marland, R.J. Andres. — Available at: cdiac.ornl.gov/trends/emits/tre_
glob.html
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https://www.timeanddate.com/astronomy/moon/distance.html?year=1987&n=367.
Received 28.08.2017
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| id | journaliasakpiua-article-126683 |
| institution | System research and information technologies |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2025-07-17T10:23:29Z |
| publishDate | 2017 |
| publisher | The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" |
| record_format | ojs |
| resource_txt_mv | journaliasakpiua/67/4cff4019bd5a6390881e8340fbbbc467.pdf |
| spelling | journaliasakpiua-article-1266832018-04-12T11:42:34Z Empirical analysis of Moon’s gravitational wave and earth’s global warming Эмпирический анализ гравитационной волны Луны и глобального потепления Земли Емпіричний аналіз гравітаційної хвилі Місяця та глобального потепління Землі Matsuki, Yoshio Bidyuk, Petro I. global warming Moon and Earth global carbon dioxide gravitational wave глобальное потепление Луна и Земля глобальный углекислый газ гравитационная волна глобальне потепління Місяць і Земля глобальний вуглекислий газ гравітаційна хвиля This research examines a possibility of a disturbance by Moon’s gravitational wave to the Earth’s global warming process in comparison with the increase of global volume of carbon dioxide. Because the general theory of relativity that predicts the gravitational wave of a planet has a dimension of 1/(distance)2, we analyzed the data sets of global temperature and global carbon dioxide, with this dimension of gravitational wave using Least Squares Estimation of Linear Classical Regression Model, Generalized Classical Regression Model, and Nonlinear Regression Model. The results suggest that there is a disturbance to the process of global warming by the Moon’s gravitational wave. However, there is uncertainty for this conclusion because the Moon’s rotational movement around Earth gives different type of distributions of its sample data, while global temperature and carbon dioxide increase proportionally accordingly to available time-series. Рассматрена возможность нарушения процесса глобального потепления Земли гравитационной волной Луны по сравнению с увеличением глобального объема углекислого газа. Поскольку общая теория относительности предсказывает, что гравитационная волна планеты имеет размерность 1/(расстояние)2, проанализирован набор данных о глобальной температуре и глобальном объеме углекислого газа с этой размерностью гравитационной волны с использованием метода наименьших квадратов и линейной классической регрессионной модели, обобщенной классической регрессионной модели и модели нелинейной регрессии. Полученные результаты свидетельствуют о том, что процесс глобального потепления возмущается гравитационной волной Луны, однако существует некоторая неопределенность, поскольку вращательное движение Луны вокруг Земли приводит к различным типам распределений выборочных данных, а глобальная температура и двуокись углерода увеличиваются пропорционально согласно имеющимся временным рядам. Розглянуто можливість порушення процесу глобального потепління Землі гравітаційною хвилею Місяця порівняно зі збільшенням глобального об’єму вуглекислого газу. Оскільки загальна теорія відносності передбачає, що гравітаційна хвиля планети має розмірність 1/(відстань)2, проаналізовано вибірки даних про глобальну температуру та глобальний об’єм вуглекислого газу з цією розмірністю гравітаційної хвилі із застосуванням методу найменших квадратів і лінійної класичної регресійної моделі, узагальненої моделі класичної регресії та моделі нелінійної регресії. Отримані результати свідчать, що гравітаційна хвиля Місяця збурює процес глобального потепління, однак є деяка невизначеність, оскільки обертальний рух Місяця навколо Землі приводить до різних типів розподілів вибірок даних, а глобальна температура і вуглекислий газ збільшуються пропорційно згідно з наявними часовими рядами. The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" 2017-03-20 Article Article application/pdf https://journal.iasa.kpi.ua/article/view/126683 10.20535/SRIT.2308-8893.2018.1.09 System research and information technologies; No. 1 (2018); 107-118 Системные исследования и информационные технологии; № 1 (2018); 107-118 Системні дослідження та інформаційні технології; № 1 (2018); 107-118 2308-8893 1681-6048 en https://journal.iasa.kpi.ua/article/view/126683/123514 Copyright (c) 2021 System research and information technologies |
| spellingShingle | глобальне потепління Місяць і Земля глобальний вуглекислий газ гравітаційна хвиля Matsuki, Yoshio Bidyuk, Petro I. Емпіричний аналіз гравітаційної хвилі Місяця та глобального потепління Землі |
| title | Емпіричний аналіз гравітаційної хвилі Місяця та глобального потепління Землі |
| title_alt | Empirical analysis of Moon’s gravitational wave and earth’s global warming Эмпирический анализ гравитационной волны Луны и глобального потепления Земли |
| title_full | Емпіричний аналіз гравітаційної хвилі Місяця та глобального потепління Землі |
| title_fullStr | Емпіричний аналіз гравітаційної хвилі Місяця та глобального потепління Землі |
| title_full_unstemmed | Емпіричний аналіз гравітаційної хвилі Місяця та глобального потепління Землі |
| title_short | Емпіричний аналіз гравітаційної хвилі Місяця та глобального потепління Землі |
| title_sort | емпіричний аналіз гравітаційної хвилі місяця та глобального потепління землі |
| topic | глобальне потепління Місяць і Земля глобальний вуглекислий газ гравітаційна хвиля |
| topic_facet | global warming Moon and Earth global carbon dioxide gravitational wave глобальное потепление Луна и Земля глобальный углекислый газ гравитационная волна глобальне потепління Місяць і Земля глобальний вуглекислий газ гравітаційна хвиля |
| url | https://journal.iasa.kpi.ua/article/view/126683 |
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