"BALMER'S FORMULA" FOR THE SOLAR SYSTEM
Aleksandr Timofeev
paper in the Original Usenet format.
For understanding value of this paper for fundamental physics
I shall bring some examples of fundamental discoveries from
a history of physics:
Example 1 Kepler's laws of planetary motion
Example 2 Bode's law
Example 3 Balmer's formula
Example 4 Planck's constant
(Example 5 Timofeev's Rule for the Planetary Masses or
. Quantization of a gravitational charge)
If you can make the common conclusion what principles integrate
all indicated fundamental physical discoveries then it will become
clear to you that the same principles are puted in a basis of the
given paper.
You can easily find the descriptions of these discoveries on a site:
http://www.eb.com Encyclopædia Britannica, Inc.
"BALMER'S FORMULA" FOR THE SOLAR SYSTEM
1.1. Magic ratios of linear combinations of planetary masses.
Here are the most reliable values of the Solar System [1]
planetary masses that can be experimentally obtained by celestial
mechanics:
Planet Symbol Mass | Ratio Exact Rounded
used for value | considered value ratio
each planet Earth=1 | of the ratio
. |
Jupiter MJU or 1 317.735 |(MJU+MSA)/(MUR+MNE) = 12.9959 ~ 13
Saturn MSA or 2 95.147 | MJU/(MUR+MNE) = 10.0010 ~ 10
Neptune MNE or 3 17.23 | MSA/(MUR+MNE) = 2.9948 ~ 3
Uranus MUR or 4 14.54 | (MJU+MSA)/MNE = 23.9630 ~ 24
Earth MTE or 5 1.000 | MUR/(MTE+MVE) = 8.0110 ~ 8
Venus MVE or 6 0.815 | (MNE+MUR)/MVE = 38.9816 ~ 39
Mars MMA or 7 0.108 | (MTE+MVE)/MME = 33.0000 ~ 33
Mercury MME or 8 0.055 | MVE/(MMA+MME) = 5.0000 ~ 5
The difference between computed values of ratios and the closest
integer can possibly be explained by an effect similar (Francis Aston
1920) to mass modification caused by dense packing in atom nucleii.
When organised graphically, the ratios [2] of linear combinations
of the planetary masses considered, reveal a chain of gravitational
correlations between triples of planets possessing chiral symmetry:
. 10
. I<----------->|
. I 13 |
. I<==============>I
. I | I
. ? 39 I | I
. |<----------------->I 33 |<---------------->I 24 | I
. | |<------------------>I |<----------------->I
. | | I ? | | I 5 | | I 8 | | I 3 | | I
. | | I<====>| | I<====>| | I<====>| | I<====>| | I
. | | I | | I | | I | | I | | I
. 10 9 I 8 7 I 6 5 I 4 3 I 2 1 I
. I | | I | | I | | I | | I
. I Mercury MarsI Venus EarthI Uran NepI Saturn JupiterI
. I I I I I
. 10+9 8+7 6+5 4+3 2+1
. ln(mass)
- - -------------------------------------------------------------->
The following symbols here are used in this graphic:
MSA + MJU <-> 2 + 1; MUR + MNE <-> 4 + 3;
MVE + MTE <-> 6 + 5; MME + MMA <-> 8 + 7;
MJU <-> 1; MSA <-> 2; MNE <-> 3; MUR <-> 4;
MTE <-> 5; MVE <-> 6; MMA <-> 7; MME <-> 8;
5
Direct gravitational correlation - <====>;
33
Reverse gravitational correlation - <---------->
1.2. Formula for pairs of conjugate gravitational correlations.
We shall name "pairs of conjugate gravitational correlations" the
following pairs of values that can be identified on the previous graph:
33,5 39,8 24,3 10,13
We shall now consider relating of sums of those pairs of conjugate
gravitational correlations with squares of natural numbers:
33+5=6^2+2 39+8=7^2-2 24+3=5^2+2 10+13=5^2-2
+2 -2 +2 -2
From these relations, a common formula for the sums of the pairs
of conjugate direct and reverse gravitational correlations can be
established:
(value of reverse correlation)+(value of direct correlation)=n^2 +/- 2
To some extent, this formula is analog to Balmer's formula for
spectral series of the Hydrogen atom. The analysis of the chained series
of conjugate gravitational correlations clearly reveals here a periodic
alternance of the sign before number 2.
1.3. Gravitational correlations for groups of four planets.
For a long time astronomers have been aware of dynamic relations
in celestial bodies in groups of four, in the stable gravitational
system which the Solar System presents us with. On this specific
criterion and on some other dynamic criterions stemming from celestial
mechanics, we can select two groups of four planets in the Solar System.
The planets of the Terrestrial group are: Earth, Venus, Mars and
Mercury. The planets of the Jovian group are: Jupiter, Saturn, Neptune
and Uranus. The empirical facts discovered here indirectly confirm the
existence of further relations.
For the group of planets Earth, Venus, Mars and Mercury
((n^2 + 2);(n ^ 2 - 2)) the relationship is established in the
following manner:
( 33 + 5) + (39 + 8) = 6 ^ 2 + 7 ^ 2 = 9 ^ 2 + 2 ^ 2 = 85
For the group of planets Jupiter, Saturn, Neptune and Uranus
((n ^ 2 + 2); (n ^ 2 - 2)) the relationship is established in the
following manner:
( 10 + 13) + (24 + 3) = 5 ^ 2 + 5 ^ 2 = 7 ^ 2 + 1 ^ 2 = 50
In each of the groups considered, there is a higher pair
(n ^ 2-2) and lower pair of planets (m ^ 2 + 2). Therefore, a
possibility seems to exist to derivate various combinations of these
pairs to obtain mixed combinations from these two groups of four
planets. In our particular case, only the combination of the two lower
pairs ((n ^ 2 + 2); (m ^ 2 + 2)) Neptune, Uranus, Mars and Mercury,
forming a mixed group, allows a correlation to be determined:
( 33 + 5) + (24 + 3) = 7 ^ 2 + 4 ^ 2 = 8 ^ 2 + 1 ^ 2 = 65
Some conclusions:
ž The considered relations can be expressed as the following formula:
(sum values of all correlations of the given group) = k^2+l^2=m^2+n^2
ž What is remarkable in these correlations by groups of four planets, is
that the sum of the pairs of conjugate gravitationnal correlations are
equal in each case to natural numbers (50, 65, 85) which are the first
terms of a sequence of natural numbers, which are the sum of two pairs
of squares of natural numbers. Please look Diophantus's theorem of a
number theory (III, 19). Here is the beginning of this series:
! ! !
number 1 25 50 65 85 100 125 130 145 169 170 185 200 205 221 225 250 260
1 1 5 7 8 9 10 11 11 12 13 13 13 14 14 14 15 15 16
pair 0 0 1 1 2 0 2 3 1 0 1 4 2 3 5 0 5 2
2 0 4 5 7 7 8 10 9 9 12 11 11 10 13 11 12 13 14
pair 1 3 5 4 6 6 5 7 8 5 7 8 10 6 10 9 9 8
1.4. Conclusions
It can be infered from the observed regularities that such
regularities should also occur for stable gravitational systems:
ž In extra-solar planetary systems, by analogy with the Kepler's Laws
(from simple inductive assumption);
ž In multiple star systems, which each can have planetary systems;
ž In hierarchies of galaxies, gas and dust clouds and so on.
From the authors' point of view, the physical properties
considered in this paper, represent a totally empirical development,
which is incomplete at best at the present time, but which strongly
suggests that quantization mechanisms may be at play in gravitational
systems. The authors readily recognize that this interpretation of the
phenomenon can be disputed, but they nevertheless consider it a valid
working hypothesis.
The empirical regularities described in this paper clearly
emphasise the incomplete state of the modern set of fundamental physical
laws in the field of gravitation, and therefore the incomplete state of
the modern theories of gravitation. The historical analysis of the role
played by Kepler's Laws, which were also empirically developped, in the
subsequent development of celestial mechanics and laws of gravitation
demonstrate the fundamental value of empirical laws for the fruitful
analytical development of physical theories.
1.5. References
1. William B. Hubbard - PLANETARY INTERIORS, (Professor of Planetary
Sciences University of Arisona), Van Nostrand Reinhold Company 198?;
2. A.N. Timofeev, V.A. Timofeev, L.G. Timofeeva - Gravitational mass -
some properties, Russia, Podolsk, 1996
3. Henri Poincaré:
1. La Science et l'hypothèse (1903; Science and Hypothesis),
2. La Valeur de la science (1905; The Value of Science),
3. Science et méthode (1908; Science and Method), Paris,
Flammarion, 13 mille 1914, 14 mille 1918
These three writings can be found in:
The Foundations of Science,
containing Science and Hypothesis, The Value of Science,
and Science and Method, trans. by George Bruce Halsted,
Lancaster(Pa), Science press, cop. 1946
4. Dernières pensées (1913);
This writing can be found in:
Mathematics and Science: Last Essays,
trans. by John W. Bolduc, New York, Dover, cop. 1963
Traslation this article from Russian reviewed by André Michaud
http://www.microtec.net/~srp/
---
Aleksandr Timofeev
http://solar.cini.utk.edu/~russeds/unknown/astrochem/
==============
FAQ
==============
> Aleksandr,
>
> Can you summarize what the implications of these ratios are in a
> short
> paragraph - perhaps geared for laymen like me? I'm not sure I
> understand what is implied here.
>
Look " Principles of a selection of the ratioes " below in this paper.
> The empirical regularities described in this paper clearly
> emphasise the incomplete state of the modern set of fundamental
> physical laws in the field of gravitation, and therefore the incomplete
> state of the modern theories of gravitation (GR also ...).
Moreover. As a corollary of this statement, I consider, that to us
the speed of propagation of gravitational interaction of substance is
unknown.
From my point of view, the person were in healthy mind cannot
consider, that the gravitational and electromagnetic interactions of
substance are subject to the completely identical fundamental laws of a
Nature (Why so c?).
>
> Well, this seems a little off-topic, but...
>
> Why did you not consider:
>
> (MJU+MSA)/MUR = 28.3963 or
> (MNE+MUR)/(MMA+MME) = 194.9080 or
> (MNE+MUR)/(MTE+MVE) = 17.504
>
> ...(among others) in your ratios?
>
We must to select the ratioes have the least difference of values
from integers (Principle 1 below).
> What was your reasoning behind the ratios that you DID select?
>
Principles of a selection of the ratioes.
1. We select the ratioes have the least difference of values from
integers.
2. The masses of planets have errors of measurements of different sorts
(till now we have not reliable methods of measurement of masses of
celestial bodies! The large physical mysticism is hidden here). The
absolute errors in masses of large planets exceed masses of small
planets. This fact requires to discard a majority of the ratioes
satisfying to a principle 1, as the ratioes not have of a physical
sense.
Under pressure of measuring errors, values of the ratioes
containing the planets, closest on masses, are most reliable from a
physical point of view.
3. If we shall sort out the ratioes satisfying to principles 1 and 2 in
ascending order of values of the ratioes, we receive the following
sequence of natural numbers:
3,5,7(*),8,10,13,24,33,39...
We shall see further, that only these terms (ratios) are main in
gravitational interaction between planets of the Solar system. (From a
mathematical point of view, the task circumscribing gravitational
interaction between planets of the Solar system is the nonlinear task of
many bodies. The remaining ratioes are a causal corollary of the main
ratioes (the main (nonlinear) process).
The first terms of this sequence of natural numbers (excepting
number 7) correspond to the ratioes, selected by me:
Planet Symbol Mass | Ratio Exact Rounded
used for value | considered value ratio
each planet Earth=1 | of the ratio
. |
Jupiter MJU or 1 317.735 |(MJU+MSA)/(MUR+MNE) = 12.9959 ~ 13
Saturn MSA or 2 95.147 | MJU/(MUR+MNE) = 10.0010 ~ 10
Neptune MNE or 3 17.23 | MSA/(MUR+MNE) = 2.9948 ~ 3
Uranus MUR or 4 14.54 | (MJU+MSA)/MNE = 23.9630 ~ 24
Earth MTE or 5 1.000 | MUR/(MTE+MVE) = 8.0110 ~ 8
Venus MVE or 6 0.815 | (MNE+MUR)/MVE = 38.9816 ~ 39
Mars MMA or 7 0.108 | (MTE+MVE)/MME = 33.0000 ~ 33
Mercury MME or 8 0.055 | MVE/(MMA+MME) = 5.0000 ~ 5
Here is shown the graphics representation for the ratioes,
selected by me, from this sequence:
. 10
. I<----------->|
. I 13 |
. I<==============>I
. I | I
. ? 39 I | I
. |<----------------->I 33 |<---------------->I 24 | I
. | |<------------------>I |<----------------->I
. | | I ? | | I 5 | | I 8 | | I 3 | | I
. | | I<====>| | I<====>| | I<====>| | I<====>| | I
. | | I | | I | | I | | I | | I
. 10 9 I 8 7 I 6 5 I 4 3 I 2 1 I
. I | | I | | I | | I | | I
. I Mercury MarsI Venus EarthI Uran NepI Saturn JupiterI
. I I I I I
. 10+9 8+7 6+5 4+3 2+1
. ln(mass)
- - -------------------------------------------------------------->
The following symbols here are used in this graphic:
MSA + MJU <-> 2 + 1; MUR + MNE <-> 4 + 3;
MVE + MTE <-> 6 + 5; MME + MMA <-> 8 + 7;
MJU <-> 1; MSA <-> 2; MNE <-> 3; MUR <-> 4;
MTE <-> 5; MVE <-> 6; MMA <-> 7; MME <-> 8;
. 5
Direct gravitational correlation - <====>;
33
Reverse gravitational correlation - <---------->
=======================================================================
= When organised graphically, the ratios of linear combinations =
= of the planetary masses considered, reveal a chain of gravitational =
= correlations between triples of planets possessing chiral symmetry. =
=======================================================================
---
Aleksandr Timofeev
http://solar.cini.utk.edu/~russeds/unknown/astrochem/