The gravitational constantBased on the gap space theory

SHOGO NIIMI
shogo-ni@sk2.aitai.ne.jp
February 21th, 2006

- Contents ////[1] /Substantiality with mass///////////////////P2////[2] /Gravitational constant GN//////////////////P4////[3] /Correction of GN by the gravitational field////P7-１-[1] /Substantiality with mass
I got electronic mass expression mq in <The creation of the electron>.
nmq = βsin⊿ωτ

A j dτ

[1-1]

j=1
/////
First, confirm that j has the area as ambiguous in that paper.
Adapting that I got the limitation from the <Gap space theory> to j.
Therefore, ω1τ equivalent to j = 1 is

(2.06099×10‑05)/////////////////[1-2]/////ω1τ = 0.0001312066853π/2
Also, ωnτ equivalent to j = n is(≒π/2)///////////////////////[1-3]/////ωnτ = 0.999999999890292π/2
Taking them, I got/////sin⊿ωτ = sin (⊿wτsin⊿θ)//////////////= 8.1057195×10-4///////////////⊿wτ= 0.025235,⊿θ= 0.032126471/////////////[1-4]β is expressed by fine-structure constant α, as follows.
β=
/////

1
4πε0α

[1-5]

ε0 is the dielectric constant of the vacuum.
by j has the area from 1 to n.

The value of β that has width/////1.3698229×10‑05≦β≦1.3712259×10‑05/////////////////////////[1-6]A j is the electric current, as follows.
n

⊿q =

Aj
j=1

/////

= 8.2×10‑23

[1-7]

-２-

The value of electronic mass mq has width by above/////9.1047882×10‑31≦mq≦9.1141134×10‑31/////////////////////////[1-8]The measurement value of electronic mass me has/////me = 9.1093897×10‑31/////[V1A1m-2s3]//////////////////////////[1-9]
It is almost average value of mq. However, the width of mq is caused by thecurvature that it has. Actually, here is an important concept for the
essence of the g-factor.
By the way, will be possible to the generalization of the mass? Here, I
pay attention to the β and sin⊿ωτ. The average of the product of both is/////βsin⊿ωτ = 1.1107753×10‑08///////////////////////////////[1-10]
Actually, round twice of this value equivalent to Planck mass MPL.
However, it is difficult to give this 2 to [1-10] under the logical limitation.
Also, it is difficult to give spin 2 to the expression, then I consider of theconsistence with the electronic mass.
/////MPL = 2Aβsin⊿ωτ//////// = 2.1767×10‑08//////A = 0.97981//(≒1)///////////////////[1-11]
I have an idea that - Must be dwell on Planck mass? -. However, put ahigh valuation that electronic mass mq and Planck mass MPL are expressed byβ sin ⊿ ω τ for it approaches essence and substantiality with mass.
Incidentally, the elementary function has a positive, negative mark fromthe history. The positive, negative electric charges appear by this meaning.
Also, β has the positive, negative value, in the same way. In this case,the positive, negative masses exist in whole space H 9. Will this be anegative solution? If the discussion of here is right, the mass expression of
all elementary particles will be shown using βsin⊿ωτ. In any case, I
need more consideration, including the approach from the manifoldness.

-３-[2] Gravitational constant GN
We cannot find the gravitational constant by the concept, function that is
known same as the mass. Therefore, I take <Kármán Vortex Street> on thehydrodynamics as you know(★Photo collection [Flow]/The Mechanics Society of Japan/Maruzen Co.
Ltd./JPN. ★ Study of the Flow science by PC/Genki Yagawa/BLUE BACKS/B-1337/Kodansha/JPN.).
Why<Kármán whirlpool>? Because, I think that situation of electron is born inthe gap space resembles situation of Kármán whirlpool is born. In this way,electron can be supposed to Kármán whirlpool itself. I 3 shows imaginary
space, G 3 shows gap space and R 3 shows real space in [Fig‑g1]. q is
Kármán whirlpool electron and resistance object G is equivalent to theisolate isle in the natural world. The vertical line in G 3 expresses thetransverse wave. The arc in R 3, I3 expresses the diffracted wave, I can
suppose that they are the electromagnetic wave. [Fig‑g2] is the figure that
adapted the value that was gotten from the gap space theory to Kármán
whirlpool. Here, I give the direction of x ωτ and give the direction of yθ. Make width to the Kármán whirlpool direction of x ⊿ωτ and makewidth to the direction of y ⊿θ. Give isolate isle G width ⊿wτ. The wayof giving these values does not have logical limitation, only convenience as
visual thinking.
The issue is that do I replace resistance object G to something of the gap
space theory. I consider about this. Generally, seem to be that the massdoes not born in resistance-less. The standard theory (the G-W-S theory)
authorizes that the mass exists there by the Higgs mechanism(★Physics of theelementary particles/Modern Sciences/Totsuka Yoji/ Iwanami Shoten).
In the same way, somemechanism will exist here. For example, it is following one. The Light
velocity was decision by that the vacuum has the dielectric constant andmagnetic permeability. Therefore, seem to be that the vacuum has
viscosity. I think that this viscosity becomes resistance and generates
mass.
Therefore, I accept that this resistance was generated by whole9
space H has the curvature. Resistance object G has this meaning in[Fig‑g1], [Fig‑g2]. Also, I can explain that G relates to the gravitational
constant by accept that the curvature generates gravitation. By the way, G
is expressed the reverse of resistance Ω[V1A-1] on the electromagnetism.
As described on the <The creation of the electron>, the unit of the resistance is-４-equal to unit [m1s-1] with velocity.
/////[V1A-1] ≡[m1s-1]/////////////////////////////////////////////[2-1]
Therefore, the key point is “ velocity v j” and “the product of time τsinθj toacceleration a j”. The relation of both is as follows.
/////w jτv j = a jτsinθj///////////////////////////////////////////[2-2]
In this result, the relational expressions of resistance object G areGj=1
w jτv j=1
a jτsinθj

////

[2-3]

I get gravitational constant GN approximately by numerical calculation of[2-3] at two points of “j = 1” and “j = n”.
/////G 1 = 6.8246×10‑11///////////////////////////////////////////[2-4]/////G n = 6.8211×10‑11///////////////////////////////////////////[2-5]Do these results have reliability? By the way, the value of gravitational
constant GN is as follows(★Chronological Scientific Tables/National Astronomical Observatory/Maruzen Co.
Ltd./JPN).
/////G N = 6.67259×10‑11//////[V-1A-1m5s-5]//////////////////////////[2-6][2-3] has w jτ that appears the curvature of H 9 indirectly is an advantage.
In the other hand, I cannot miss the expression that is assembled byacceleration a j. Product G j j has constant approximately in the given areathat is more important.
/////7.19331×10‑45 ≦ G j

j≦ 7.19703×10‑45////////////////////////[2-7]It has the important meaning that is the same as ratio
/////

j

/v j = 3.51767×10‑43//////////////////////////////////////[2-8]that is constant. The width of [2-7] is same as the electric charge.
at [Sheet‑g1]. Therefore, I accept

-５-

Look

///// G N ≒G j///////////////////////////////////////////////////[2-9]By the way, they have A that is the difference about 2% between G N andG j.
/////0.97823≦A ≦0.97773////////////////////////////////////////[2-10]
This is equal to A with Planck mass in the front-chapter approximately.
/////A ≒ A /////////////////////////////////////////////////////[2-11]
However, I do not accept that these differences came out from the sameplace.
Incidentally, theoretical gravitational constant G j has the positive,
negative solutions in here.

-６-[3] /Correction of GN by the gravitational field
Here, I explain that the difference between G N and G j. Therefore, I use thegeneral theory of relativity by Albert Einstein (1879-1955). The equation ofgravitational field R ik has
R ik ////

1
8πG N
g ik R =
Tik
2
c4

[3-1]

R ik expresses the Ricci tensor, g ik expresses the metric tensor in the spacetime and Tik expresses the energy-momentum tensor, as you know. We get
R=-

8πG N

////

c4

T

[3-2]

by operate the contraction about i and k.
By the above, we get ⊿ψ that the equation of the gravitational fieldon the un-relativity, as follows.
////⊿ψ = 4πG ND///////////////////////////////////////////////[3-3]
D is the mass density of material in here.

Potential ψ in the field of aparticle has
ψ= ////

GNm
R

[3-4]

(★Classical field theory/Curriculum of Theoretical Physics/ L. D. Landau, E. M. Lifusit/Л. Д. Ландау и Е. М. Лифшиц
/ТЕОРИЯ ПОЛЯ/Издание шестое, исправленное и дополненное, Издательство <m is the mass of particle.
Therefore, I rewrite it is as follows.

Н а у к а >, М о с к в а ,1973).

ψ has unit [m1s-1]2.

////ψ = - vj2/////////////////////////////////////////////////////[3-5]Of course, this solution is approximation.
correction to it for the relativity.
First, I rewrite G j in [2-3] use [3-5].

-７-Consequently, I must be1
w jτv j
vj
=
w jτψ

Gj=

////

[3-6]

This expression shows us that G j need correction for adjust to the actual
space because it is the gravitational constant on the un-relativity.
Incidentally, the positive negative symbol can be omitted because velocity vj
has both. So, is the gap space theory the one to get merely approximate
solution? The conclusion is rashness. I should consider why the equationof gravitational field on the relativity is a nonlinear. In other words, thegap space theory shows an ideal condition in the moment that whole space H 9
was born; on the other hand, the theory of relativity and the quantum
theory express the condition that the influence of the self must be considered.
Consequently, I should accept that the theory of relativity, the quantum
theory and the gap space theory also the value of experiment are correct.
Therefore, for example, I give potential ψ ι (iota) that is the selfcorrection by the gravitational field, as follows.
∞ι=nΠ(1- (w τ)
)
n

j

n=1

////

≒ - sinwjτ

[3-7]More approximation of self correction ο(omicron) has
∞

ο=
////

Π(
n=1

)

n2
1(wjτ) n[3-8]

In this connection, the width of ο is as follows [Sheet‑g2].
////0.977822005≦ο≦0.977834359/////////////////////////////////[3-9]As the result, the expression of gravitational constant GNj after thecorrection has

-８-

GNj=
=
////

v jο
w jτψ
ajτsinθjο(w jτ)2ψ

(
(

)
)

ο
wjτvj
ο
=
ajτsinθj=[3-10][3-11]

Finally, theory value GN j will be convergence to experiment value GN.
////G N = G N j////////////////////////////////////////////////////[3-12]
By the way, I have ever been had doubt that light velocity c may be notmaximum speed vmax in the whole space. vmax may be faster than c about 2%
as the correction of gravitational constant G j is unnecessary by the fact of thephoton is dominated in the gravitation. In this case, vmax is the velocity thathas the relation in the expending universe (C. H. Lineweaver, T. M. Davis/Misconceptions about the
Big Bang/SCIENTIFIC AMERICAN/March 2005).
Actually, it is possible to say that
self-correction ι, ο is the correction with the velocity by [3-5]. This idea
is in consistency with other quantum constant even if considering that theacceleration of the expending universe. On the other hand, the cause of
the doubt may be consequence in the change of gravitational constant GN j by
I admit c is maximum speed in the space persistently. The gravitational
constant changes by about 2% in 1.37×1010 years after the space was bornthat is the big problem.

Footnote① We know that the gravitational lens refracts the photon. The photon
curves by about 1.74-second degrees with the sun. This value is sameas the theory value on the relativity. The solution of the “Newton
theory” has 0.87-second degrees ( ★ Tastuo Uctiyama/The general relativity/The physics
15/Shokabo/JPN).
There are 2 times of differences in both. This 2 may be
adapted to [1-11]. As for the reason, this 2 is a steady value, as thefollowing. As for the “Newton theory”, it considers only mass andgravitation, on the other hand, as for the relativity, it considers thegravitational field in addition to them (★Hermann Weyl/Space・Time・Material///Raum・Zeit・
Materie/Vorlesungen ber allgemeine Relativit tstheorie).
②

The acceleration of the space may have a positive symbol (★L.V.E.Koopmans,
R.D.Blandford/Gravitational Lenses/Physics Today/Vol.57-No.6).
This fact admits a result with-９-

the decreasing gravitational constant that is gotten by [3-10], [3-11].
③ The Hubble constant may have 70[Km1s-1Mps-1] by the latest observation.
The age of the space is 1.37×1010 years old by it (★Yoshiaki Tanigucti/ Mystery of thequasar/BLUE BACKS/B-1458/Kodansha/JPN).

- １０ -

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Sheet.g1/Gravitational constant
ωτ

j

wτ

ωτ= wτsinθ
1
2
3
・
・
・

value of [ωτ]0

π/2×0.00000000000553261063
π/2×0.0000000292757
π/2×0.00001312066853
π/2×0.00001326929
0.001
0.001001
0.001005
0.00101
0.001020.00105
0.00110.00120.0015
0.002
0.003
0.004
0.005
0.01
0.05
π/32

π/16

π/8

π/4

Θe
Θe×1.00000000000001

1
π/3

B

・
・
・
n-2
n-1 π/2×0.999999999887850(2)n π/2×0.999999999890292- π/2×0.999999999996476- π/2×0.999999999999999- π/2

08.6906E-12
4.59862E-08
2.06099E-05
2.08434E-05
0.001
0.001001
0.001005
0.00101
0.001020.00105
0.00110.00120.0015
0.002
0.003
0.004
0.005
0.01
0.05
0.09817477
0.12
0.15
0.17
0.196349541
0.25
0.3
0.35
0.392699082
0.47
0.49297955
0.55
0.63
0.71
0.785398163
0.81
0.84
0.87
0.9
0.93
0.935
0.94
0.945
0.95
0.955
0.95510.95520.955316618
0.955316618
0.96
0.97
0.98
0.99
1
1.047197551
1.07
1.1
1.12
1.15
1.170019129
1.23
1.23566095
1.27
1.351
1.37
1.47
1.48
1.49
1.5
1.51
1.52
1.53
1.54
1.55
1.56
1.570796327
1.570796327
1.570796327
1.570796327
1.570796327

θθ=asin(ωτ/wτ)48.8766796
48.8766796
48.8766796
48.87668
48.87668
48.8766801
48.8766801
48.8766801
48.8766801
48.8766801
48.87668011
48.87668011
48.87668012
48.87668015
48.8766802
48.8766803
48.8766804
48.8766805
48.876681
48.8767059
48.876779
48.876828
48.8769105
48.8769763
48.877075
48.877319
48.877601
48.877933
48.878258
48.87894
48.879166
48.879775
48.88074
48.881837
48.88299
48.883391
48.883898
48.884422
48.884965
48.885527
48.885622
48.885718
48.8858145
48.885911
48.8860085
48.8860108
48.8860128
48.886015
48.886015
48.886107
48.886305
48.886504
48.886706
48.886909
48.887897
48.888391
48.889057
48.88951
48.890207
48.890682
48.892155
48.8922973
48.893177
48.895348
48.895877
48.898781
48.899082
48.8993855
48.8996913
48.899999
48.900309
48.9006208
48.9009345
48.9012505
48.901569
48.901915
48.901915
48.9019151
48.9019151
48.9019151

01.77807E-13
9.40861E-10
4.21671E-07
4.26448E-07
2.04597E-05
2.04801E-05
2.0562E-05
2.06643E-05
2.08688E-05
2.14826E-05
2.25056E-05
2.45516E-05
3.06895E-05
4.09193E-05
6.1379E-05
8.18386E-05
0.000102298
0.000204597
0.001022982
0.002008619
0.002455154
0.003068939
0.003478127
0.004017222
0.005114869
0.006137819
0.007160757
0.008034315
0.009615741
0.010085849
0.011252335
0.012888869
0.014525333
0.016067592
0.016570804
0.017184418
0.01779802
0.018411609
0.019025183
0.019127444
0.019229705
0.019331965
0.019434225
0.019536485
0.01953853
0.019540575
0.01954296
0.01954296
0.019638743
0.01984326
0.020047775
0.020252289
0.020456801
0.021422023
0.021888334
0.022501821
0.022910804
0.023524263
0.023933617
0.025160065
0.025275812
0.025977916
0.027633957
0.02802239
0.030066629
0.03027104
0.030475448
0.030679853
0.030884256
0.031088656
0.031293053
0.031497448
0.031701841
0.03190623
0.032126893
0.032126893
0.032126893
0.032126893
0.032126893[ aτsinθ ] ωτsinθexp(+ρ)cosδ=wτsin 2θ exp(wτcosθ)cos(wτsinθ)00.002605377
72949.93001
14652860038
14986694167
3.44961E+13
3.45652E+13
3.4842E+13
3.51895E+13
3.58898E+13
3.8032E+13
4.17403E+13
4.96744E+13
7.76163E+13
1.37984E+14
3.10464E+14
5.51934E+14
8.62393E+14
3.44944E+15
8.61326E+16
3.30882E+17
4.93171E+17
7.67445E+17
9.82563E+17
1.30437E+18
2.08896E+18
2.96593E+18
3.96948E+18
4.91464E+18
6.79362E+18
7.38493E+18
8.89561E+18
1.10622E+19
1.31862E+19
1.50446E+19
1.56032E+19
1.6244E+19
1.68338E+19
1.7366E+19
1.78336E+19
1.79047E+19
1.79739E+19
1.8041E+19
1.8106E+19
1.81689E+19
1.81701E+19
1.81714E+19
1.81728E+19
1.81728E+19
1.82296E+19
1.83446E+19
1.84505E+19
1.85472E+19
1.86345E+19
1.89103E+19
1.89578E+19
1.89285E+19
1.88479E+19
1.86305E+19
1.84182E+19
1.74381E+19
1.73177E+19
1.64792E+19
1.37225E+19
1.29085E+19
7.49753E+18
6.84804E+18
6.17818E+18
5.48778E+18
4.77669E+18
4.04477E+18
3.29186E+18
2.51783E+18
1.72255E+18
9.05871E+17
14986696969
14660395047
470908384
175219.2549
24101.06402[v]

ω2exp(+ρ)cosδ/(σ 2+ω2)=
sin2θexp(wτcosθ)cos(wτsinθ)05.33051E-05
1492.530397
299792458
306622589.1
7.05779E+11
7.07191E+117.12855E+11
7.19965E+11
7.34293E+11
7.78122E+11
8.53993E+11
1.01632E+12
1.588E+122.82311E+12
6.35199E+121.12924E+13
1.76443E+13
7.05744E+13
1.76224E+15
6.76972E+15
1.00901E+16
1.57016E+16
2.01028E+16
2.66868E+16
4.27388E+16
6.06809E+16
8.12121E+16
1.00549E+17
1.38989E+17
1.51085E+17
1.8199E+17
2.2631E+17
2.69756E+17
3.07767E+17
3.19193E+17
3.32297E+17
3.4436E+17
3.55242E+17
3.64803E+17
3.66258E+17
3.67672E+17
3.69043E+17
3.70372E+17
3.71658E+17
3.71683E+17
3.71709E+17
3.71738E+17
3.71738E+17
3.729E+17
3.7525E+17
3.77415E+17
3.79392E+17
3.81175E+17
3.86809E+17
3.87777E+17
3.87172E+17
3.8552E+17
3.81068E+17
3.76721E+17
3.56665E+17
3.54201E+17
3.37044E+17
2.80651E+17
2.63999E+17
1.53328E+17
1.40044E+17
1.26345E+17
1.12225E+17
9.76828E+16
8.27145E+16
6.73173E+16
5.14884E+16
3.5225E+16
1.85244E+16306464419
299791839.4
9629651.17
3583.075521
492.8449932[ ]ω2exp(-ρ)cosδ/(σ 2+ω2)=

ratio/v=3.51767E-43

G#DIV/0!
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43

1/(aτsinθ)#DIV/0!
383.8216632
1.3708E-05
6.82461E-11
6.67259E-11
2.89887E-14
2.89309E-14
2.8701E-14
2.84176E-14
2.78631E-14
2.62937E-14
2.39576E-14
2.01311E-14
1.28839E-14
7.2472E-15
3.22098E-15
1.81181E-15
1.15956E-15
2.89902E-16
1.161E-17
3.02222E-18
2.02769E-18
1.30303E-18
1.01775E-18
7.66653E-19
4.78708E-19
3.37162E-19
2.51922E-19
2.03474E-19
1.47197E-19
1.35411E-19
1.12415E-19
9.03979E-20
7.58371E-20
6.64692E-20
6.40893E-20
6.15613E-20
5.94042E-20
5.75838E-20
5.6074E-20
5.58511E-20
5.56363E-20
5.54294E-20
5.52304E-20
5.50392E-20
5.50354E-20
5.50317E-20
5.50273E-20
5.50273E-20
5.48557E-20
5.4512E-20
5.4199E-20
5.39164E-20
5.3664E-20
5.28812E-20
5.27487E-20
5.28305E-20
5.30564E-20
5.36754E-20
5.42943E-20
5.73457E-20
5.77443E-20
6.06827E-20
7.2873E-20
7.74685E-20
1.33377E-19
1.46027E-19
1.6186E-19
1.82223E-19
2.0935E-19
2.47233E-19
3.0378E-19
3.97167E-19
5.80536E-19
1.10391E-18
6.67258E-11
6.8211E-11
2.12356E-09
5.70714E-06
4.14919E-05

sin2θexp(-wτcosθ)cos(wτsinθ)01.8751E-47
5.25023E-40
1.05457E-34
1.0786E-34
2.4827E-31
2.48767E-31
2.50759E-31
2.5326E-31
2.583E-31
2.73717E-31
3.00406E-31
3.57508E-31
5.58607E-31
9.93078E-31
2.23442E-30
3.97229E-30
6.20667E-30
2.48258E-29
6.19898E-28
2.38136E-27
3.54935E-27
5.52329E-27
7.07148E-27
9.38751E-27
1.50341E-26
2.13455E-26
2.85677E-26
3.53697E-26
4.88916E-26
5.31469E-26
6.40179E-26
7.96085E-26
9.48911E-26
1.08262E-25
1.12282E-25
1.16891E-25
1.21135E-25
1.24963E-25
1.28326E-25
1.28838E-25
1.29335E-25
1.29817E-25
1.30285E-25
1.30737E-25
1.30746E-25
1.30755E-25
1.30765E-25
1.30765E-25
1.31174E-25
1.32E-25
1.32762E-25
1.33458E-25
1.34085E-25
1.36067E-25
1.36407E-25
1.36194E-25
1.35613E-25
1.34047E-25
1.32518E-25
1.25463E-25
1.24596E-25
1.18561E-25
9.87236E-26
9.28662E-26
5.39355E-26
4.9263E-26
4.44439E-26
3.94772E-26
3.43616E-26
2.90963E-26
2.368E-26
1.81119E-26
1.2391E-26
6.51627E-27
1.07804E-34
1.05457E-34
3.38739E-36
1.26041E-39
1.73366E-40

G
1/(wτv)#DIV/0!
383.8216632
1.3708E-05
6.82461E-11
6.67259E-11
2.89887E-14
2.89309E-14
2.8701E-14
2.84176E-14
2.78631E-14
2.62937E-14
2.39576E-14
2.01311E-14
1.28839E-14
7.2472E-15
3.22098E-15
1.81181E-15
1.15956E-15
2.89902E-16
1.161E-17
3.02222E-18
2.02769E-18
1.30303E-18
1.01775E-18
7.66653E-19
4.78708E-19
3.37162E-19
2.51922E-19
2.03474E-19
1.47197E-19
1.35411E-19
1.12415E-19
9.03979E-20
7.58371E-20
6.64692E-20
6.40893E-20
6.15613E-20
5.94042E-20
5.75838E-20
5.6074E-20
5.58511E-20
5.56363E-20
5.54294E-20
5.52304E-20
5.50392E-20
5.50354E-20
5.50317E-20
5.50273E-20
5.50273E-20
5.48557E-20
5.4512E-20
5.4199E-20
5.39164E-20
5.3664E-20
5.28812E-20
5.27487E-20
5.28305E-20
5.30564E-20
5.36754E-20
5.42943E-20
5.73457E-20
5.77443E-20
6.06827E-20
7.2873E-20
7.74685E-20
1.33377E-19
1.46027E-19
1.6186E-19
1.82223E-19
2.0935E-19
2.47233E-19
3.0378E-19
3.97167E-19
5.80536E-19
1.10391E-18
6.67258E-11
6.8211E-11
2.12356E-09
5.70714E-06
4.14919E-05

j#DIV/0!
7.19704E-45 7.19704E-45 7.19703E-45 1
7.19703E-45 2
7.19703E-45 3
7.19703E-45 ・
7.19703E-45 ・
7.19703E-45 ・
7.19703E-45
7.19703E-45
7.19703E-45
7.19703E-45
7.19703E-45
7.19703E-45
7.19703E-45
7.19703E-45
7.19703E-45
7.19703E-45
7.19702E-45
7.19701E-45
7.197E-45
7.19699E-45
7.19698E-45
7.19697E-45
7.19694E-45
7.19689E-45
7.19685E-45
7.19679E-45
7.1967E-45
7.19667E-45
7.19657E-45
7.19644E-45
7.19627E-45
7.1961E-45
7.19605E-45
7.19596E-45
7.1959E-45
7.19582E-45
7.19573E-45
7.19572E-45
7.19571E-45
7.19569E-45
7.19568E-45
7.19567E-45
7.19566E-45
7.19566E-45
7.19566E-45
7.19566E-45
7.19564E-45
7.19561E-45
7.19558E-45
7.19555E-45
7.19552E-45
7.19538E-45
7.1953E-45
7.1952E-45
7.19515E-45
7.19504E-45
7.19497E-45
7.19474E-45
7.19473E-45
7.1946E-45
7.19428E-45
7.1942E-45
7.19377E-45
7.19374E-45
7.1937E-45
7.19365E-45
7.19361E-45
7.19356E-45
7.19351E-45 ・
7.19347E-45 ・
7.19342E-45 ・
7.19337E-45 n-2
7.19331E-45 n-1
7.19331E-45 n
7.19331E-45 7.19331E-45 7.19331E-45 -The self correction by the gravitational field
ι(≒-sinw jτ)
∞

Π(

1-

n=1

n
(wjτ) n

ο
∞

)

Π(

1-

n=1

n

wτ
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
ι

48.87668
0.979540345
0.999162805
0.999974307
0.999999299
0.999999982
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0.978694429

48.901915
0.979550903
0.999163669
0.999974347
0.999999301
0.999999982
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0.978705864

n2(wjτ) n

)
n

wτ
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
ο

48.87668
0.979540345
0.99832561
0.999922921
0.999997196
0.99999991
0.999999997
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0.977822005

48.901915
0.979550903
0.998327338
0.99992304
0.999997202
0.999999911
0.999999997
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0.977834359