Sprouts of New Gravitation Without Mathematical Chimeras of XX Century

Aleksandr Timofeev

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Apr 17, 2001, 8:26:48 AM4/17/01

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. THE SYMMETRY INSIDE THE SOLAR SYSTEM

GRAVITATION. THE EXPERIMENTAL FACTS AND PREDICTIONS

Abstract. The empirical law connecting values of planetary masses in the
Solar system is demonstrated and is analyzed. A characteristic property
of this law is the existence of groups consisting from four planets. The
law allows to predict existence and properties of three unknown planets
inside the Solar system. This law can serve the useful tool for a research
of extra-solar planetary systems.

1. Empirical gravitational regularities of a symmetry in 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:

Table I
Planetary masses and Ratios of linear combinations of masses

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. The planetary
masses are measured with some errors also.

1.2. Chiral symmetry ratios of linear combinations of the planetary masses

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:

Table II
Chiral symmetry ratios of linear combinations of the planetary masses

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 - <---------->

Note: Here it is necessary to understand exclusive importance of
the numbers Fibonacci for gravitational regularities inside
the Solar system in common case:

If you look at direct gravitational connections than you will see the
following numbers: 3, 5, 8, 13.
For the third hypothetical quad there should be now following numbers
accordingly: 21 and 34.

1.3. 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.

1.4. 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:

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

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

1.5. Principles of ratio selection

As we examine Table I, we might wonder why these specific ratios were
selected, among the many combinations that are mathematically possible.
Here are the principles that guided the choice of ratios. All these
principles should be fulfilled simultaneously.
From a mathematical point of view, the problem gravitational
interaction between planets of the Solar System is the nonlinear
n-body problem. Principles 1,2,3,4 and 5 are the physical restrictions
superimposed on the mathematical formalism of ratioes of linear
combinations of planetary masses. The given method has analogs in
radiophysical, atomic and molecular spectral researches. The considered
method is not statistical, it leans on properties nonlinear stationary
systems.
Principle 1. The ratios having the least difference in value from
integers are chosen.
Principle 2. The ratios containing only three bodies are chosen
(there is one elemination stipulated by a Principle 4).
Principle 2 leans on existence of the closed solution of the three-body
problem. The three-body problem was solved by Karl Fritiof Sundman [3].
This solution has a very complicated structure and that one does not give
direct tie between coordinates and time, i.e. there is a full analogy to
the solution for the two-body problem.
Principle 3. The ratios containing the planets, closest on masses are
chosen.
These ratios are the most essential and reliable from the physical point
of view. The Principle 3 integrates in a ratio those planets which have
the greatest potential energies of gravitational interaction. The
Principle 3 take into account also that the absolute errors in masses of
large planets can exceed masses of small planets.
Principle 4. The ratios ensuring existence of a symmetry of a high
level are chosen.
For the first time in the world the French mathematician and physicist
Henry Poincare has paid attention to a symmetry of the physical laws [4].
The fundamental physical laws have properties tightly connected with a
symmetry [5]. In the given work the properties of a symmetry of the
Solar System are studied.
Principle 5. Only main terms of the ratios are chosen.
When the significant ratioes satisfying to Principles 1,2,3 and 4 are
sorted in ascending order, the following sequence of natural numbers are
obtained:

3,5,7(*),8,10,13,24,33,39...

Only these terms (except for number 7) are main in gravitational
interaction between planets of the Solar System. These terms represent
the main nonlinear process of the Solar System. The remaining ratioes are
the causal corollary of the main terms, therefore they are excluded from
the analysis in the given paper.

2. Revision of classical statement of a many bodies problem

2.1. Analogies between kinds of chemical and gravitational connections
or gravitational chemistry

Let's consider analogies between steady chemical substances and fixed
gravitational systems.
The varieties of symmetries of crystals of various minerals is a
corollary of a varieties of chemical elements and various versions of
their spatial packing, which generate a delightful symmetry of an exterior
form and symmetry of physical properties of crystals.
The varieties of chemical substances is a corollary of a varieties of
chemical elements and various combinations of their spatial packing. The
stationarity of a structure of steady chemical substances is provided with
various kinds of chemical connections. By analogy, the stationarity of
structures to gravitational systems should be provided with various kinds
of gravitational connections. Here authors shall specify on the following
kinds of gravitational connections:
1 - connection in groups of bodies, each of which has not a satellite or
satellites;
2 - connection in groups of bodies, each of which has of a satellite or
satellites;
3 - mixed connections in groups of bodies, the part of which bodies has
of a satellite or satellites and other part of bodies has not a satellite
or satellites;
4 - other possible or probable unknown kinds of connections in groups of
bodies, for which detection there are no necessary experimental data or
which are not identified in the given moment.

In the given article are considered only 2 and 3 types of connections
accordingly for the Jove group of planets and for the Earth group of
planets.

2.2. Reduction of a symmetry in a gravitational many bodies problem

Methods of the solution of a many bodies problem in its conventional
statement and various versions finally come into dock. The researches in
this direction have not fundamentally new outcomes already very long time.
The authors adhere points of view about necessity of revision of classical
statement of a many bodies problem.
1. In a classical problem the collisions between bodies are considered.
The authors offer to limit by consideration of stationary problems, in which
there are no collisions. This limitation contains a broad class of systems
widespread observed (observable) in a nature.
2. In a classical problem all bodies have identical dynamic properties,
i.e. they are considered equivalent apriorly. The empirical observations of
stationary systems contradict this supposition. In the Solar system, for
example, we have obvious properties of "multiplicity" - join of bodies in
groups in four bodies in each group. Inside such group of four bodies the
division on two groups in two bodies in each is brightly expressed. Each
body in group of two bodies has distinguished from other dynamic property.
Whether want to recognize this fact whether or not orthodox experts in the
theory of a gravitation, there should be at least one (unknown now)
fundamental gravitational law adequate (answering) for a property of
"multiplicity". The group property of "multiplicity" removes degeneration
for values of bodies masses of inherings to different groups of bodies.

The account of a property of "multiplicity" - join of bodies from a system
in groups expresss in reduction of a symmetry of a problem for a system as
a whole. For each group of bodies in a stationary system (presumably) there
should be, at the present unknowns, integrals of motion.

2.3. PHYLLOTAXIS AND THE EXPONENTIAL SOLAR SYSTEM REGULARITIES
BASE UPON IRRATIONAL PHY

An interesting fact is that, for ALL series that are formed from adding
the latest two numbers to get the next, and, starting from any two values
(bigger than zero), the ratio of successive terms will always tend to Phi!
Phi is a more universal constant than the Fibonacci series itself. [13]
The golden ratio and the Fibonacci series, the Fibonacci Spiral and
sea shell shapes, seeds and flower petal, branching plants, leaves and
petal arrangements, leaf and pine cones arrangements: all involve the
Fibonacci numbers - why? Just what causes plants to grow in tendency accord
with the dictates of the irrational Phi remains a mystery after more than
100 years of study.
In his research "Spira Solaris" [12] real genius John N. Harris wrote:
"It has long been recognized that the Phi and the Fibonacci Series are
intimately related to the subject of natural growth. The Phi, the Fibonacci,
Lucas and related series, far from being confined to plant and animal
natural growth alone, occur in numerous diverse contexts over an enormous
range that extends from the structure of quasi-crystals out to the very
structure of spiral galaxies. And this being so, should there really be any
great surprise if Phi should also prove to be an underlying element in the
structure of planetary systems?".
In research "Spira Solaris", J. N. Harris has opened the exponential law
connecting mean periods circulation and mean distances for planets of the
Solar system, which leans on the irrational Phi series. The research,
considered in the given article, confirms existence of correlation with
the Fibonacci series for direct gravitational correlation (see 1.2).
Just what causes plants to grow and planets to coordinate their motions and
their values of masses in tendency accord with the dictates of the
irrational Phi remains a mystery till now.
See into [14] " The Keplerian Harmony of the Planets and Their moons "
by Lothar Komp.

3. Predictions on trans-pluto planets

" The Voyagers 1 and 2 trajectories give negative evidence about
possible planets beyond Pluto. " [8]
" The mystery of the tiny unexplained acceleration towards the sun
in the motion of the Pioneer 10, Pioneer 11 and Ulysses spacecraft remains
unexplained. " [7]
" The positional measurements do not bode too well for the existence
of Planet X. They do not entirely rule out the existence of a Planet X,
but they do indicate that it will not be a large body. " [6]

Here will be used the new analytical method, considered in chapter 1,
for the prediction of the unknown new planets. This method is not based on
classical positional measurements. This method concerns to qualitative
methods of a classical celestial mechanics. It can predict common dynamic
properties of unknown planets, but it can not predict exact coordinates
(like QM) of these unknown planets.
Prediction 1. The total number of planets in the solar system should
be equal 12. There are three groups and in each group there are 4 planets.
If to lean on empirical theory described above in chapter 1 item 1.5,
in each group of planets there should be four planets. Now group of Pluto
consists of one known planet, which has the title Pluto. For this reason
there should be three unknown planets which together with Pluto will make
full group of four planets. These planets are not members of the Kuiper
Belt, they are far behind Pluto. These planets have distinguishing masses
close on value to the mass of Pluto.

Closely consider the symmetry of the mass distribution of planets
inside group of the Jove. In the pair the Jove - Saturn the heavier planet
the Jove is closer to the Sun. On the contrary in the pair Uranus - Neptune
the heavier planet Neptune is further from the Sun.
Closely consider the symmetry of the mass distribution of planets
inside group of the Earth. In the pair the Earth - Venus the heavier
planet the Earth is further from the Sun. In a pair the Mars - Mercury
the heavier planet the Mars also is further from the Sun. Here has the
difference of group of the Earth from group of the Jove.
For compensating the mass distribution in group the Earth, by analogy
to group of the Jove is necessary that in pairs of planets of Pluto group
the heavier planets in pairs were closer to the Sun!:

Table 3

The symmetry of the mass distribution in pairs of planets

planet mass
------------------------------------------------------------------------>
__
Mercury
_________
Venus
___________
Earth
____
Mars

...
Asteroid Belt

____________________________________________________________________
Jupiter
_____________________________
Saturn

the line of the symmetry inside the Solar planetary system
=========================================================
Mirror
___________________
Uran +the mirror reflection of Saturn;
_____________________
Neptun +the mirror reflection of Jupiter;

.......
Kuiper Belt +the mirror reflection of Asteroid Belt;

__
Pluto(?) +the mirror reflection of Mars;
________
Planet X (pseudo Earth) +the mirror reflection of Earth;

_______
Planet X1 (pseudo Venus) +the mirror reflection of Venus;
_
Planet X2 (pseudo Mercury) +the mirror reflection of Mercury;

Prediction 2. The mass of unknown planet pseudo Earth (the mirror
reflection of Earth) is more than the mass of Pluto. The planet pseudo
Earth has a satellite or more. The planet pseudo Earth rotates about the
axis faster than planet Pluto. It is very weak object, it has very small
sizes.
Prediction 3,4. There are two unknown planets pseudo Venus and pseudo
Mercury. The mass of unknown planet pseudo Venus is more than the mass of
Pluto but its mass is less than the mass of pseudo Earth. The mass of
unknown planet pseudo Mercury is less than the mass of Pluto. Similarly
to the Mercury and the Venus these planets have not satellites, i.e. these
two unknown planets are "bald". These unknown planets have rather slow
axial rotation.
Prediction 5. Similarly to the Mercury, Venus and Earth these three
planets have resonances.

Note. The additional foundation for these Predictions is served with
the following prerequisites:
1. There is the law which links periods of axial rotation of planets.
2. There is the law which links potential energies of planets.
These laws make essentially reduce number of theoretically possible
solutions for dynamic parameters of hypothetical planets.

These unknown planets can be detected in an infra-red telescope.

If to consider the mass distribution of planets of the Solar System with
acceptance in attention of the predicted masses of unknown planets then
the mass distribution of planets becomes surprising symmetrical concerning
pairs of planets.

4. Conclusions

The General Theory of Relativity was created by transactionses Henri
Poincare, D. Hilbert and A. Einstein, when the base of
experimental data for the Solar system was very poor, therefore this
theory has many hypothetical suppositions in the base concepts and
the GTR creators were in main mathematics. It is paradoxical, but this
theory does not give useful outcomes for practical needs of research of
circum-solar space. The precisiouly gravitational measurements are
accessible extremely within the limits of a Solar system. Now base of
experimental data for Solar system is vast, but we have not the good
theory of gravitation till now.

The Nobel Laureate, Irving Langmuir, coined the term "pathological
science" for "the science of things that aren't so".

Einstein warned: "Most mistakes in philosophy and logic occur because
the human mind is apt to take the symbol for reality".

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
http://www.friends-partners.org/~russeds/unknown/astrochem/
3. Sundman, Karl Fritiof Nouvelles recherches surle probleme des trois
corps, Acta Societatis scientiarum fennicae, T 35, N 9, Helsingfors, 1909
and other papers 1910-1912
4. Henri Poincari:
1. La Science et l'hypothhse (1903; Science and Hypothesis),
2. La Valeur de la science (1905; The Value of Science),
3. Science et mithode (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. Dernihres pensies (1913); This writing can be found in:
Mathematics and Science: Last Essays, trans. by John W. Bolduc,
New York, Dover, cop. 1963
5. Richard Feynman "THE CHARACTER OF PHISICAL LAW";
A series of lectures recorded by the BBC at Cornell University USA;
Cox and Wynman LTD, London, 1965
6. [sci.astro] Solar System (Astronomy Frequently Asked Questions)
http://www.deja.com/threadmsg_ct.xp?AN=606966502
Subject: E.11.1 What about a planet (Planet X) outside Pluto's orbit?
7. http://spaceprojects.arc.nasa.gov/Space_Projects/pioneer/PNStat.html
8. http://www.seds.org/billa/tnp/spacecraft.html#pioneer10
9. Theoretical Motivation for Gravitation Experiments on Ultra-Low Energy
Antiprotons and Antihydrogen
Michael Martin Nieto, T. Goldman, John D. Anderson, Eunice L. Lau,
J. Perez-Mercader
http://xxx.lanl.gov/cits/hep-ph/9412234 Citations for hep-ph/9412234
10. The Apparent Anomalous, Weak, Long-Range Acceleration of
Pioneer 10 and 11
Slava G. Turyshev, John D. Anderson, Philip A. Laing, Eunice L. Lau,
Anthony S. Liu, Michael Martin Nieto
http://xxx.lanl.gov/cits/gr-qc/9808081 Citations for gr-qc/9808081
11. The Apparent Anomalous, Weak, Long-Range Acceleration
of Pioneer 10 and 11
Slava G. Turyshev, John D. Anderson, Philip A. Laing, Eunice L. Lau,
Anthony S. Liu, Michael Martin Nieto
http://arxiv.org/abs/gr-qc/9903024 Citations for gr-qc/9903024

12. Harris, J. "Projectiles, Parabolas, and Velocity Expansions of the
Laws of Planetary Motion," Journal of the Royal Astronomical Society of
Canada, Vol. 83, No.3 (June 1989):207-218.
http://www3.telus.net/JNHDA/index.htm
http://www3.telus.net/JNHDA/sbb4c.htm

13. Ron Knott, "Fibonacci Numbers and Golden sections in Nature";
http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat.html#pinecones
http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat2.html

14. Komp, Lothar, " The Keplerian Harmony of the Planets and Their moons ",
21st Century, Spring 1997:28-41, translated by Rick Sanders and
David Cherry from the original article first published in FUSION,
April-May-June 1996.
15. Aleksandr N. Timofeev, Vladimir A. Timofeev, Lubov G. Timofeeva
"GRAVITATION. THE EXPERIMENTAL FACTS AND PREDICTIONS", proceeding of
congress-2000
"FUNDAMENTAL PROBLEMS OF NATURAL SCIENCES AND ENGINIRING", St.Petersburg
University, Russia, 2000 http://www.physical-congress.spb.ru

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Uncle Al

unread,

Apr 17, 2001, 11:14:44 AM4/17/01

to

Aleksandr Timofeev wrote:
>
> . THE SYMMETRY INSIDE THE SOLAR SYSTEM
>
> GRAVITATION. THE EXPERIMENTAL FACTS AND PREDICTIONS
>
> Abstract. The empirical law connecting values of planetary masses in the
> Solar system is demonstrated and is analyzed. A characteristic property
> of this law is the existence of groups consisting from four planets.

[snip]

Thesis empirically disproven by more than 60 extra-solar systems
detected by telescope examination.

--
Uncle Al
http://www.mazepath.com/uncleal/
http://www.ultra.net.au/~wisby/uncleal/
(Toxic URLs! Unsafe for children and most mammals)
"Quis custodiet ipsos custodes?" The Net!

Aleksandr Timofeev

unread,

Apr 17, 2001, 12:53:38 PM4/17/01

to

>===== Original Message From Uncle Al <Uncl...@hate.spam.net> =====

>Aleksandr Timofeev wrote:
>>
>> . THE SYMMETRY INSIDE THE SOLAR SYSTEM
>>
>> GRAVITATION. THE EXPERIMENTAL FACTS AND PREDICTIONS
>>
>> Abstract. The empirical law connecting values of planetary masses in the
>> Solar system is demonstrated and is analyzed. A characteristic property
>> of this law is the existence of groups consisting from four planets.
>[snip]
>
>Thesis empirically disproven by more than 60 extra-solar systems
>detected by telescope examination.
>

From a physical point of view your statement is groundless, but your
statement has really very deep physical sense and your statement is a key
to understanding and explanation of the given problem as a whole.

Please, closely consider structures of satellite systems in the Solar
system. To what conclusion you come?

I shall ask you two problems on:

1. To what historical period of an astronomy of the Solar system
you can relate the modern level of accuracy of measurements of values
of masses and other parameters of motion reached for extra-solar
planetary systems?

2. What type of gravitational connections is supposed in the implicit
form in mathematical models for the interpretation of measurements for
extra-solar planetary systems?
What reliability and completeness of these models?
The history of physicis abounds examples of error initial mathematical
models of physical phenomena.

You are the expert in physical chemistry. Look at the following text:

Best Regards
Aleksandr