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The Sun system’s model of discrete natural
periods
Steady discrete oscillations with periods of up to
at least until 2Ma, including earth orbital alterations that change
fluxes of energy to the earth surface, have formed inside the solar
system. Orbital movements of planets stabilize rhythms of sun activity
and moon-sun tidal waves create in the shells of the Earth the system of
geophysical processes.
Long evolution of the Sun system lead to the
resonance and commensurabilities in
periods of planet and satellite revolutions with accuracy of
about 10-3 (ratio the mass of planets to the mass of the Sun). That
determines the precision of following calculation. The periods of
resonance system can be approximately expressed by the geometrical
progression (Berry, 1991), which is similar to the geometrical
progression for accounting frequencies (periods) of discrete musical
instruments, for example, the piano (FP ):
(1) FP = F0
2P/n = 440 2P/12Hz;
where F0 = 440Hz - the frequency of the
note A4; P - sequence of whole numbers, the number of a note
FP; n = 12 - the amount of notes into octave (Oct).
There are only exact data about revolution and
rotation periods of celestial bodies, but we should determine all main
free frequencies (periods) the solar system. Let’s imagine ourselves
an old musical instrument having not more than one string in separate
octaves. The solution of the inverse problem is to know how many notes
into an octave this instrument had. We gave the answer by the method of
consecutive comparison of terms of different geometrical progressions
with the revolution periods of planets and the satellites of heliotidal
planets the Earth and Jupiter (20 periods) and assessment dispersions of
deviation to meet Fisher criterion. Analyzing periods are changing from
0.5d to 167y and composing the range in 18 octaves. The piano row has
only 7 octaves.
As a result we have taken the geometrical
progression (TK) that best describes the discrete spectrum of
the natural oscillation periods of the solar system:
TK = T0
2K/n = 0.075 2 K/n
y
(2)
where TK - periods of oscillation of
the Sun system; T0 = 27.32d = 0.075y - the sidereal period of
the moon revolution; K - sequence of whole numbers, the number of a
period TK; n = 16 - the amount of harmonics into an octave
(Table 1).
Table 1. Comparison revolving period TPS
of planets (years, underlined) and satellites (days) and terms TK
of geometrical progression (2)
|
Planets
|
Revolving
|
Calculated
|
|
|
|
DT
=
|
|
and
|
period
|
period
|
K
|
Octave
|
N*
|
100(TK
-TPS)/TK
|
|
satellites
|
TPS(y,
d)
|
TK(y,
d)
|
|
|
|
( % )
|
|
|
|
|
|
|
|
|
|
Mercury
|
0.241
|
0.2414
|
27
|
1
|
12
|
0.166
|
|
Venus
|
0.615
|
0.625
|
49
|
3
|
2
|
1.6
|
|
Earth
|
1
|
1.006
|
60
|
3
|
13
|
0.596
|
|
Jupiter
|
11.86
|
11.89
|
117
|
7
|
6
|
0.252
|
|
Saturn
|
29.46
|
29.55
|
138
|
8
|
11
|
0.305
|
|
Uranus
|
84.01
|
83.53
|
162
|
10
|
3
|
-0.575
|
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Neptune
|
164.8
|
167.1
|
178
|
11
|
3
|
1.376
|
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Moon
|
27.32
|
27.32
|
0
|
0
|
1
|
0
|
|
Jupiter’s
|
|
|
|
|
|
|
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satellites
|
|
|
|
|
|
|
|
V Amalthea
|
0.489
|
0.486
|
-93
|
-6
|
4
|
-0.617
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I
Io
|
1.769
|
1.786
|
-63
|
-4
|
2
|
0.952
|
|
II Europa
|
3.551
|
3.561
|
-47
|
-3
|
2
|
0.281
|
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III Ganymede
|
7.155
|
7.13
|
-31
|
-2
|
2
|
-0.351
|
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IV Callisto
|
16.689
|
16.96
|
-11
|
-1
|
6
|
1.598
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XIII
|
240
|
238.4
|
50
|
3
|
3
|
-0.671
|
|
VI
|
250.6
|
248.9
|
51
|
3
|
4
|
-0.683
|
|
X
|
260
|
260
|
52
|
3
|
5
|
0
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VII
|
260.1
|
260
|
52
|
3
|
5
|
-0.038
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XII
|
617
|
618
|
72
|
4
|
9
|
0.162
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XI
|
692
|
703.8
|
75
|
4
|
12
|
1.677
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VIII
|
735
|
735
|
76
|
4
|
13
|
0
|
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IX
|
758
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767.5
|
77
|
4
|
14
|
1.238
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sn-1
= 0.779
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s = 1.25
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F
= (s /sn-1)2
= 2.57
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* N - the number of a harmonic in the octave.
The discovered regularity (2) exists with
probability 99% and 95% when Fisher parameter F more than limit amounts
of Fisher criterion F01 and F05 accordingly:
F = (s /sn-1)2
= 2.57
> F01 = 2.49 >F05 = 1.88
(3)
where
sn-1
= 0.779 is standard deviation of data, F01 and F05
are tabular values given for the different degrees of freedom, s = 1.25
is a standard deviation of the geometrical progression (2) for the
homogeneous distribution of periods (nil-series):
s = [ò-aa(x2/2a)dx]1/2
= a/(3)1/2 =1.25
(4)
where the interval +a, -a is a distance in
percentages between TK and TK+1.
Berry, B.L. 1992. Basic systems of geosphere -
biospheric cycles and the prediction of natural conditions. Biophysics,
Vol.37, N3, 414-428, (in Russian), Pergamon Press Ltd. Printed in Great
Britain, 1993, 328-341 (in English).
Berry, B.L., 1998. Regularities of natural cycles,
prediction of climate and surface conditions. Hydrol. Process. 12,
2267-2278.
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