The solar system

The Solar System constitutes naturally the first chapter of an astronomical presentation. The discovery of the constituents of this system was the object of the debuts of the astronomy and allows to redraw the historic process of this discipline.

The second part is dedicated to the Solar System detailed description.

A particular accent was put on the constitution of atmospheres because, by the comparison to the others planetary models, the evolutions of our own atmosphere can be better understood and  the risks of intensification of the greenhouse effect better estimated.

Finally the chaos in the Solar System, because it constitutes a new chapter for the astronomy, deserved a separate development.
 

1 Geocentrism, Heliocentrism and new revolutions *

1.1 The first questions*

1.2 The Greek vision *

1.3 The Renaissance *

1.4 The Lights *

1.5 XIXème=achievement, XXth =révolution *

2 A modern description of the solar system*

2.1 The nomenclature of 2000 billion celestial bodies. *

2.2 Physical characteristics of the Solar system *

2.3 The origin of the solar system *

2.4 Physical structure of planets *

3.1 The origin of the chaos *

3.2 The drift of the solar system *

3.3 The chaos and the life *

3.4 The chaos in asteroids*

3.5 The chaotic running of satellites *

3.6 The global orbits *
 
 

1 Geocentrism, Heliocentrism and new revolutions
1.1 The first questions

Where are we?

In this central question, the Man initially gave the evident answer of a fixed place, in the point of balance of a universe organized around this centre.

This fixedness had to come along with absolute parameters: speeds, movements, time.

The human eye being the absolved reference the visible fixedness of the stars became fixedness of the relative positions of stars pricked on a heavenly sphere turning in a single block.

The periodic wandering of the Sun, the Moon and the planets made them move by divine forces to move closer to them to the human sphere of influence. But the regularity of the sky defined an eternal and pure space, the phenomena of the Earth undergoing the corruption of time.

Aristarque of Samos was historically the first one to express a model replacing the Sun in the center of the universe by considering its size superior to that of the Earth and raising for the first time the notion of relativity of the movements, no mechanical effect of our rotation around the Sun seeming perceptible.

By knocking down the problem of our distance with regard to the Sun, he urged Archimède to raise the problem of the volume of the Universe by trying his new system of arithmetical numbering.

Archimède supposed that the report of the beams of the universe and the beam of the ground orbit around the Sun was equal to the report of the size of the universe on the size of the Earth.

By imagining this universe filled with grains of sand, he ends strangely in the same figure as Eddington 23 centuries later for a universe immensely bigger but immensely emptier (10 power 63 grains or 10 power 80 atoms) expressed.

1.2 The Greek vision

The Greeks discovered the abstract and rigorous representation of the World. They expressed main rules deductible from first principles: axioms inventing by there even the geometry and the arithmetic.

Thalès would have by the observation of the first pyramids put the principle of the equivalence of angles. This method strictly coupled with the statement of an ideal world led the Greek philosophers to put the principle of the sphericity of the Earth.

By the slope of the shadow of the Sun at the same moment in two points of the Earth, Erathostène calculated the ground circumference; the first cosmic standard was put.

By measuring the shadow thrown by the Earth on the Moon, the distance in the Moon was estimated. By measure of the space of the trio Earth-moon - sun when this trio forms a right angle, the distance in the Sun was also approached and thus its real dimension.

The sun of a simple shield glittering over mountains had become a sphere in the almost unacceptable dimensions.
 
 

1.3 The Renaissance

The only considerable progress in the Middle Age was the actual recognition of round Earth the rotation of which explained the alternation of days but the Earth stayed in the center of world balance of power and our preservation on the surface of a sphere in fast rotation was not explained.

Copernic in the middle of the XVth century restored the principles of the Greek precursors. The simplistic vision of Earth in the center of the World had remained in spite of its questionings and the system said about  Ptolémée of Alexandria had gradually  complicated during 14 centuries to report distances in the orbits of planets.

Copernic simplified the problem by supposing spherical orbits around the Sun breaking a theological dogma.

But it was Kepler who, expressing the elliptic orbits, made them again corresponding to the observations.

Galilee by the first use of the optics discovered the variety of the World, the satellites turning around Jupiter quite as the Moon around the Earth, the moreover mountainous Moon just like our landscapes. The vague cloud of the Milky Way became a sea of stars.

The observation of 2 supernovae in XVth and XVIth century contributed to break the artificial barrier between the Ground world and the Cosmos.

By wondering following the martyr Giordano Bruno if stars were not so many suns, the centre of the universe had got lost.

1.4 The Lights

The classic age restored of the order in the revolutionary turnover of the revival by the first mathematical statement of a natural Law.

Newton discovered the principle of the gravitation and verified that the Moon turned around the Earth by the balance between its fall and its inertia. The attraction on the surface of the Earth deducts from the calculation corresponded to the observations. From a local description, the observation of the attraction of bodies, Newton had proceeded to a generalization to the whole universe. The calculation allowed to predict and the model could be confronted  with the observation; the modern physics had been born.

The classic age pushed away quite the distances: the epic expeditions around the world allowing to measure the moment of passage of Venus in front of the Sun allowed to estimate exactly our distance at the Sun and this standard allowed Bessel in 1838, thanks to a telescope equipped by the optician Fraunhoffer, the first reliable measure of the estrangement of a star: about 100 000 billion kilometres...

The most remarkable observer of this period was William Herrschel of German origin who, settled in England at the end of the XVIIIth century, dedicated his life (and those of his close relations) in the discovery: that of Uranus, that of the global nebulas, signal of the end of life of an average star. He baptized Orion " a foyer of young stars ", trying to draw our position in the Milky Way. He understood that Andromède was a fishpond of stars similar to our galaxy...

The classic age was also that of the appearance of the chemistry which resulted in the XIXth century in the study of the stellar spectres manifestly looking like the solar spectrum. The physical conditions of temperature, pressure, density could be directly studied
 
 

1.5 XIXème=achievement, XXth =revolution

Neptune was discovered from the theory of the gravitation which was the archetype of a determinist theory.

Although observed previously by Galilee and  Lalance, Neptune was effectively discovered by the Prussian astronomer Gall in 1846 on the basis of the calculations of Le Leverrier. The calculation was made in a similar way by Adam in England. The discovery of Neptune often presented as the triumph of the mathematics applied to the flight mechanics finds its foundations in the chance and the stubbornness of the researchers because the various hypotheses of mass and distance taken by The Glassworker and Adam were false but their errors counterbalanced.

Pluto was discovered in 1930 by the young astronomer Clyde Tombaugh to the term of twenty five years of campaigns by several look-out posts. There also Pluto was mathematically looked for as a factor perturbing Neptune but the real position of the planet remote from the prediction demonstrates that the discovery is connection to the doggedness to find what had to exist. In fact the orbit of Neptune is much more regular than that estimated at the beginning of the century, even there this  discovery was based on an error.

The XIXth century appeared to his contemporaries as a century when the physical theories were going to be completed and where the essential truths were about to be formulated.

This century was marked by the discovery of the electromagnetic waves (Augustin Fresnel's undulatory theory, James Clerck Maxwell's electromagnetic theory, revealing by Heinrich Hertz) and with principles of the thermodynamics (SadiCarnot , James Joule, Rüdolf Clausius, William Thomson Kelvin, Ludwig Bolztmann).

These theories were conceptually prolonged and found their astronomical applications only in the XXth century.

The XXth century appears as revolutionary century as well in the physical concepts as in the techniques of observation. Their frame of application modified partially our vision of the solar system but radically transformed our abstract approach of the World. The particular aspects in the solar system can be evoked only as a particular case.

4 abstract revolutions date the beginning of the century:

• The determinist chaos of Henri Poincaré (study of the macroscopic phenomena integrating the limitations of the knowledge of a system) At the level of the solar system this theory applies to the processes of evolution of orbits, climates and atmospheres.

• Albert Einstein's special relativity (theory of the measure of objects without acceleration with regard to the referential). This theory concerns the description of any object, the microphysics in stars in fast movement. In the solar system it is applied in itself only to the explanation of the source of the energy of the Sun, to the variations of radiation wavelengths  and to the fine determination of the trajectories of space probes.

• - The quantum physics (Max Planck, Albert Einstein, Niels Bohr, Edwin Schrödinger, Louis de Broglie,  Werner Heisenberg, Wolfgang Pauli, Paul Dirac, Enrico Fermi) which by its description  by events and centred on the possibilities of the act of observation determine by its partial coupling with the special relativity the current understanding:
• Of the structure microphysics of the matter (at the only level of the solar system, the explanation of the magnetic fields of the Sun and of planets, proportion and origin of the chemical elements, of the radiation and the streams of particles received from internal origin (solar wind, sun neutrinos) and external(day pupils) (space rays, stream of neutrinos of supernovae),
• Chemical processes (on the surface of planets),
• Extreme forms of matter and the generation of energy in the hearts of massive celestial bodies (structure and balance of the Sun and the planets).
• All these capacities become widespread in the understanding of the physical phenomena whatever is its distance by the principle of the extension of the same laws in all the scales. She also allows by her application the cosmology to redraw the sequences of the  theory of Big-Bang.

• - The relativity generalized by Albert Einstein in association with Marc Grossman (extension of the special relativity in any object in acceleration and by the principle of equivalence in the laws of the movement of a body subjected to a field of gravity. This theory allows a description of the macroscopic objects (of the forming(training) of the black holes the models of global evolution of the Universe). At the level of the solar system, she allows the explanation of the drift long-term  orbits and allows to describe the fine movements of  balances  of the Moon (libration).

The  in - situ study by the sending of probes allowed since the sixties to deepen our knowledge of the global atmospheres and the internal structure planets (geology, magnetism, hydrodynamism).

The techniques of spectroscopy and the fantastic development in the precision of the measures allowed a knowledge as well external atmospheres and magnetic fields of the objects of the solar system and the stars of our Galaxy, the knowledge of the structure and the composition of nebulas and galactic environments, the determination of the structures of the galaxies and their magnetic field, the variations of their main stars.

The modelling of the stellar functionings and an often  thankless task of classification resulted in the constitution of methods of determination of stellar distances, an essential pillar of the determination  of the cosmological distances. The evolution of the astronomical measure through the use of satellite allowed to refine strongly the measures of distances. The use of the shift of spectres was of use to Edwin Hubble in the construction of a grading of the galactic distances.

The ground radio astronomy on the basis of big instruments possibly established in network (of premises in intercontinental) allows the study of close objects (Jupiter, Sun) or distant (galactic magnetic field, diffuse environment of the galactic or extragalactic domain).

Satellites allowed to free us from reduced windows of observation of the wavelengths imposed by the ground atmosphere and to discover new classes of objects and phenomenas (pulsars , holes blacks, active core of galaxies, brown dwarfs, cosmic microwave background  radiation), by opening on the astronomy in infrared cold objects (stars in the beginning of primal global life, disc, nebulas, dwarfish stars, spectre of the galactic heart masked by dusts, distant galaxies because of the cosmological shift), of X-rays for the extreme events (synchrotron   emission around stars with neutrons, fall of matter on novæ, disc of accretion in fast rotation, explosion of supernovae), of gamma rays (supernovae, space rays)

The first planets outside the solar system  are discovered by 3 methods today the domains of application of which confirm each other only partially: the measures of speeds radial roads of stars by Doppler effect, enfeeblement of luminosity (notably stars with eclipses), of timing of eclipses. Tomorrow is possible a direct observation of these celestial bodies, notably in the field of the infrared and more certainly by the use of the  interferometry (recorrelation of a signal arrived on spaced out detectors equivalent in detector of the same diameter).

The use of the Doppler effects also allowed to discover the internal structure of the Sun (helioseismology ) with the hope to spread this technique to close celestial bodies.

The techniques of timing also allowed to confirm the effect of the gravitational waves on tight couples of massive stars.

The techniques of neutralization of the effect of stellar aberration or interferometry of telescopes give a new run-up to the ground look-out posts. But the  interferometry on very wide base in the space should end in earnings in resolution of several orders of height allowing to study possible Earths  outside the solar system.

The computer techniques used in the treatment of the signal intervene in all the domains previously quoted and in the entry in new methods some the interferometry,

These computer techniques also allow the modelling: understanding of the functioning of the sun, the global atmospheres, the origin and the evolution of magnetic fields, problem of the long-term stability of orbits within the solar system.

New additional techniques in phase of display will allow the study:

- Of the distribution of the masses without emission electromagnetic but in gravitational effect (gravitational lenses allowing to reveal the hidden masses extra galactic)

• Neutrinos or rare events connected to space rays, this to base of matrix of detectors in liquid masses of big volume (studies of the structure of the Sun and the supernovae, even the cosmological diffuse radiations)
• Gravitational waves by detectors of modification of optical road of  laser emission(studies of binary tight, of the forming of black holes, the coalescence of stars, the process of essential inflation of the Universe).

And even more profoundly still, our abstract approach of the reality was revolutionized, breaking the absolute separation of time and of the space, by localizing totally the perspective of the flowing of time and of the measure. And quite conversely the concepts of the stretchable fundamental physics in any scale envisage the world as the product of an infinity of local observations and not an independent reality. The same approach allows to consider every aspect of the reality as a facet of  merging laws and demonstrates that the separation of objects,  the granularity, of the objects of the physics is a concept not corpuscular but concerning the considered system and concerning its coupling when it was generated.

Finally the unpredictible   evolution, exceeding the scale of the uncertainty of the microphysics,  reach at the end all the scales of the universe by the notion of determinist chaos.

And it is indeed the unified and total vision not of the Universe but its processes and its variations that became the ultimate stake of physics.

The new revolution started here is a century propagated up to foundations and widens its brilliant perspective towards our future.
 
 
 
 

2 A modern description of the solar system
 
 

2.1 The nomenclature of 2000 billion celestial bodies.

The solar system must be described by category.

First of all the Sun, the star of size average situated in the middle of its life of 10 billion years. It represents 99 % of the mass of the solar system. With a diameter of 1,3 millions kilometres. Because of the report of diameters, the solar system could contain 3000 billion billion Suns.

The Sun possesses a structure in onion as all the stars with a core surrounded with a layer where the thermic energy produced in the core diffuses by radiation without major movement of the matter because of the pressure. Over this radiative layer the external layer is a convective zone ; in this zone the evacuation of the energy produces big  convectives movements where from the forming in surface of million granules, each of the size of Texas or France.

Around the sun, we distinguish 4 zones: the telluric planets; the jovian planets, the belt of Kuiper ; the sphere of Oort.

Except the sphere of Oort , the orbits of all the bodies are close to the plan of the ecliptic.

This plan contains the virtual circle formed by the visible course of the Sun seen by the Earth.

The telluric planets possess a  ferric heart surrounded with a rocky coat with a slender atmospheric film produced after their forming or even limited to the contribution of the solar wind in the case of Mercury.

The Earth is situated in this group and possesses the remarkable characteristic to be for a distance of the compatible Sun of 3 states of the water in particular its liquid shape, its important mass having allowed it to preserve its atmosphere and its oceans.

The belt of asteroids separates the zone of the telluric planets of the jovian planets.

It is a zone where the respective influence of Mars and  Jupiter prevented the forming of a planet.

The jovian planets are essentially constituted by gas and by liquid.

Their rocky hearts are bigger than the Earth although of weak dimensions with regard to these planets. They roughly preserved their primitive atmospheres and possess quite rings because of the phenomena of tide on their most close satellites.

Then the zone of Kuiper of comets in short period and small rocky bodies. The most important constituent (Pluto, Charon its satellite, Triton the main satellite of Neptune and Kuiper belt's asteroid Varuna) would form to them four the last group of little planets and satellites outsides of a sufficient size to have a spherical shape.

Then we leave the ecliptic for the cloud of Oort.

The cloud of Oort was constituted by the huge planets which ejected comets in short period towards the outside of the solar system. The mass of this cloud still connected  by gravity in the Sun is of several times the Earth but the mass ejected towards the interstellar space is several hundreds of time the Earth (or some Jupiter). We consider that the hyperbolic or almost parabolic orbits of comets provoke a crossing with the trajectory of one of the Telluric planets in a case on a million.

In the case of the absorption of a comet by a planet, we speak of diverse about accretion (posterior than the homogeneous accretion of  planetoids of close compositions because situated on the same orbit around the Sun).

We consider that the layer deposited on the Earth is 60 kilometres of common chondrites , 6 km of carbon chondrite (which brought 75 % of the ground water) and 2 kilometres of comets (which brought the 25 % remaining).

The solar system possesses two limits:

- The limit of the solar wind

- The limit of the gravitational influence of the sun.

The one determines the border area where the solar wind shocked by the stream of stellar particles eventually stopped not to extend any more. This bubble possesses a shelf from 10 to 20 billion kilometres.

Other one, much more vast, stops there where the gravitational influence of stars begins to play a sensitive role on the gravitational behavior of bodies, on the suburb of the solar system.

By determining the slope and the period of comets,  Oort determined that a spherical bubble centred on the sun and of a shelf about 10 000 billion kilometres of beam constitutes a reservoir of comets in long period different from comets in short period situated in the belt of Kuiper, globally aligned according to the plan of the ecliptic.

This comet mass representing several times the ground mass.

Considering its centring on the Sun, the  tangential  disturbances of the close stars, although very weak (Alpha of the Centaur has an influence only of 4 % and  Sirius of 3 % with regard to the Sun in 1 year light of distance), these stars eventually drop out the comets which go away definitively or fall towards the Sun. The zone of Oort thus dissolves in 1 light year.
 
 

2.2 Physical characteristics of the Solar system
 
 

	Average Distance to the Sun	Mass ( Terre:1)	Diameter Equatorial (km)	Density g / cm3 H20=1	Average duration of planet day *	Duration of the year	Satellites Number	Surface Temperature  ** ( Celsius)	Calculated equilibrium temperature	Atmosphere
Sun	----	332 952	1 392 000	1,20	27,3 days	----	2000 billions	5800 °	5800 °
Mercury	0, 36	0,055	4 878	5,48	58,65 days	87,97 days	0	-180 °/460 °	+232 °	Ne, H (residual)
Venus	0,72	0,816	12 101	5,24	243,01 days	224,70 days	0	+480 °	+ 42 °	CO2 (95 %), N2
Earth	1,00	1,000	12 756	5,52	23,93 hours = 1 day	365,25 days	1	+80 °/-76 °	-23 °	N2 (78 %), O2 (21 %)
Mars	1,52	0,107	6 794	3,94	24,61 hours	686,98 days	2	+30 °/-120 °	-57 °	CO2 (90 %), Ar, N2
Cérès	2,76	0,0003	1 000	3,43	522 days	4,6 years	0	-200 °	-200 °	----
Jupiter	5,20	317,9	142 984	1,34	9,83 hours	11,86 years	30 + rings	-145 °	-163 °	NH3, CH4,H2 , He
Saturn	9,54	95,2	120 536	0,7	10,23 hours	29,45 years	36 + rings	-170 °	-193 °	NH3, CH4,H2 , He
Uranus	19,22	14,6	51 118	1,47	16 hours	84,01 years	21 + rings	-220 °	-213 °	NH3 CH4 H2,  He
Neptune	30,11	17,2	49 528	1,73	18,2 hours	164,79 years	8 + discontinuous rings	-200 °	-222 °	NH3 CH4 H2,  He
Pluto	39,80	0,002	2 275	2,1	6,39 days	248,54 years	1	-230 °	-230 °	N2
Varuna: Kuiper belt	43	~10-4	900	?	?	285 years	?	?	-230 °	?

* We speak about average rotation for the Sun and the jovian planets which are fluid celestial bodies; the period in the equator being shorter in that case than in the poles.

** The temperature of Surface corresponds to the surface of brilliant emission for the Sun (photosphere) and to the height where the pressure is 1 ground atmosphere for the jovian planets.

2.3 The origin of the solar system

There is four and a half billion years a cloud of gas and dusts underwent a contraction probably under the push of an explosion of supernovae. In the center of the cloud the thermonuclear reactions engage when the barrier of 6 million degrees is reached. The pressure of radiation balances then the attraction due to the gravitation.

The rest of the nebula moved gradually in a flattened disc.

In the internal part under the influence of the magnetic forces and the electrostatics dusts gather together altogether of the order of a metre. At this stage the gravitational force acts and of the shock of  accretions is born  the first planetoids .

Under the sun wind pressure of the Sun in active phase (said T-Tauri), gases of the internal part are blown. The planetoids which possess elliptic orbits merges to give bodies big as the Moon on circular orbit which  stricked then to form the telluric planets..

In the term of hundred of million years,  planets is almost formed. Nevertheless at least two titanic events  are again going to occur:

• The likely lifting of a wide fraction of the crust of Mercury by a body which strikes it  ,  Mercury being essentially today a dense and ferrous body constituted by a sticky heavy coat of materials with a very reduced crust.
• The percussion of the Earth according to a shaving incidence by a body of 10 % of its mass which is going to tear away a fraction of the ground crust, forming in 24 hours a ring of light material which will quickly condense in a satellite: the Moon. The event would go back up(raise) 120 in 130millions of years after the beginning of the forming(training) of the Earth.

Beyond, the rings of gas of the nebula broke loose by gravitational instability and condense to form Jupiter and Saturn.

Uranus and Neptune probably joined as the Telluric planets but their composition is more based on the ice than on the cliffs.

Outside of the system in forming, small celestial bodies were able to form by aggregation of cliffs and ices but only Pluto, its satellite Charon and Triton probably arrested by Neptune remained relatively close, the other bodies (thousands of diameters close to 1000 kilometres) were ejected towards the outside of the system or formed with comets in the belt of  Kuiper.

The disturbance of comets by planets modifies gradually their orbits, pulling them towards the internal regions. This process engenders the periodic comets.

On the contrary during the forming(training) of Uranus and Neptune, comets disrupted by planets also fed an external reservoir: the cloud of Oort. The first disturbances took away comets, a distance averages of 1500 billion km forming the internal region of the reservoir. Gradually the continual turnovers of the galactic matter push away comets even farther, until distances from 7 to 20 000 billion km forming an immense sphere. Comets would be from 600 to 2000 billions and the distribution between the internal and external regions would vary in a report 5/1 in 1/1.

We can also explain the origin of the rotation of planets; a global embryo is struck by faster planetoids if they have an orbit external in the planet ( planets close to their perihelion ) and by slower  planetoids if they have an orbit interns ( planetoids close to their aphelion ). In the first case  planets will come relatively with regard to the back and front planet in the second case. Their combined effects engender a couple of rotation in the direct sense (the corkscrew sinks); the essential rotation is of the order of 10 hours. We notice that this value was kept for Jupiter and Saturn, the most massive bodies of the system.

The axis and the speed of rotation can be appreciably modified by collisions.

On top of the secular effects such as tides can considerably slow down the global rotations.

2.4 Physical structure of planets
 
 

2.4.1 Telluric planets
 
 

	Venus	Earth	Mars
Density averages in g / cm 3	5,24	5,52	3,94
Magnetic sphere	Magnetic moment ~ 3 1014 T/m3 Field in surface: 25 105 Gauss ( Variation in opposite of the radius in the cube)	Magnetic moment ~ 7,8 1015 T/m3 Field in surface = 0,45 gausses Variation factor 2 in 20 000 years Inversion frequents  polarity in the scale several dozens thousand years  Almost adipole field, axis of the oblique field of 11° with regard to the axis of rotation modified by remanent magnetism of old cliffs and disturbances ( magnetic thunderstorms) due to currents of ionized particles crossing  the ionosphere (80 km) and the  magnetic sphere. Shelf magnetic sphere ~  100 000 km (direction of the Sun)	Magnetic moment ~ 2 1011 T/m3 ~ 9 105 Gauss No global field: magnetism  remanent of oldferromagnetic cliffs: magnetic abnormalities 10 times as important as Earth abnormalities. Disappeared magnetic field there is 3,9 billion years
Atmosphere	93000 millibars 150 km of CO2 + Clouds of sulphuric acid (sulfur + oxygenate evaporated oceans)	1015 millibars ( N2 By degassing miscellany iron / nickel and O2 By photosynthesis)	6 millibars ( CO2 Residual after sublimation oceans)
Oceans / Ice Pack	Disappearance in 100 million years	H2O: 3000 m Ice Pack H2O: 2000 to 3000m	Ice pack boreal H2 O and southern CO2
Crust	Probably identical to Earth (30 in 70 km)  No ridges or subduction zone: no tectonics. Likely volcanism Strong correlation reliefs and abnormalities of gravity where from Very stiff inside or reliefs supported by updraughts of the coat	30 in 70 km Tectonics of patches Expansion of the oceanic capital by magmatic ascent and flotation of lithospheric patches on the slow currents of convection  of the coat	~ 50km  No tectonics since 3,9 billion years Volcanism puts out of trouble spots Stiff internal layer (lithosphere): 200 km
Coat	likely convective layer  evaluation ~ 2200 km	Convectivelayer: 2900 km (< 3000 K)	Likely Convective layer evaluation ~1400 km (< 3000 K)
Core	Silicates and Iron core Evaluation ~ 1200 km	Silicates and Iron core External  liquidates layer (2200 km) Granulate Iron + Metals heavy 1250 km	Likely silicates and Iron core Evaluation ~1700 km

 
 
 

2.4.2 Jovian planets
 
 

	Jupiter	Saturn	Uranus	Neptune
Density averages in g / cm 3	1,34	0,7	1,47	1,73
Magnétosphère	Magnetic moment ~ 1,0 1020 T/m 3 Field in "surface" ~ 4 gausses  Almost dipole field axis of the oblique field of 11° with regard to the axis of rotation Out of center source of 0,1 Jupiter radius Reservoir electric particle fed by satellite IO and rotation fast planet pulls the particles of the internal  magnetic sphere towards an equatorial disc where circulates a current influencing the magnetic field Radius of magnetic sphere ~ 3 million km (direction of the Sun)	Magnetic moment  1,5 1019 T/m 3 Field in "surface" ~ 1 gauss  Magnetic axis tilted to only 1° with regard to axis of rotation Magnetic abnormalities in longitude near surface: magnetic thunderstorms Big variabilitymagnetic sphere radius  on some days ~ 1,2 million km (direction of the Sun)	Magnetic moment 3 10 18 T/m3 Field in "surface" 2,9 gausses  Magnetic axis tilted to 60° with regard to axis of rotation Radius of magnetic sphere : ~ 500 000 km (direction of the Sun)  Magnetic field engendered by effect dynamo of the ocean  containing ionized atoms	Magnetic moment ~ 10 18 T/m3  Field in "surface" ~  1 gauss  Magnetic axis tilted to 47°  with regard to axis of rotation: source halfway between core and surface
Internal source of energy	Emitted energy = 1,7 * absorbed solar energy  Waste of the heat of the solid core compressed since the initial global accretion.	Emitted energy 1,76 * absorbed solar energy Thermic source of energy: fall  gravitational drop of not miscible helium in H metal	No internal source of energy	Emitted energy = 2,7 * absorbed solar energy:  Thermic source of energy: fall  gravitational of drops of pure carbon (diamonds) produced by destruction by pressure of the methane CH4

 

The direct knowledge of the jovian planets concerning only 1000 in 2000 km of the high atmosphere, it is about models.
 
 

	Jupiter	Saturn	Uranus	Neptune
Atmosphere	Clouds of ammonia / methane: 140 km with regard to the level ( 0°C, 5 bars)  Variation (140 km, 150K, 0,01 bar), (90 km, 120K, 0,1 bar), (20 km, 310K, 10 bars) Wind 1200 kph  H2 ( 90 %)He (10 %) gas: 3000 km  Continuum of gas phase with fluid phase	Clouds of ammonia, methane  Variation (85K, 0,1 bar) in ( 210K, 10 bars) Wind 1500 kph (2/3 speed of sound)             H2 ( 93 %)He (7 %) gas 18 000 km Continuum of gas phase with fluid phase	Clouds methane T high atmosphere: 50 K                         H2He (15 %), CH4 Gas: 7500 km	Clouds methane T high atmosphere: 60K  Blue colour by red absorption by methane Wind 2200 kph Methane in crystals towards 1,3 bars and cloud H2 towards 3 bars H2He (25 %), CH4 ( > 1 %) gas: 7500 km T < 2500 K, 200 000 bar
Oceans	H2 ( 90 %) He (10 %)  12 000 km of  H and liquid He Bottom: density 1,1  11 000K and  2 million bars	H2 ( 93 %) He (7 %)  12 000 km of  H and liquid He Bottom: density 1,1 8000K and  2 million bars	Ionic ocean of 12000 km  H20+ NH4+OH- Bottom 7 000K and  6 million bars	Ionic ocean of 12000 km H 20+NH4+ OH- Bottom: 7 000K and  6 million bars During the clearing threshold T = 3000K and P = 500 000 bars cracking methane, forming and fall pure carbon
Crust	Layer of 36000 km of helium and especially of H metal below 2 106 Bars: crystal semi-liquidates of protons and conductive cloud of electrons High temperature: miscible  He in H metal settle(liquidate) Density 4 Bottom 30000 K and 45 million bars	First layer of 4000 km of H metal; rather low temperature for not miscible  He, forms drop of helium in H metal solid (coherent with 3 % He atmosphere with regard to Jupiter) Main layer of 12 000 km H metal liquid and not miscible  He Bottom 14000 K and 10 million bars	Not applicable	Not applicable
Coat	Non-existent: no  convective movement or strata of pressure	Non-existent: no  convective movement or strata of pressure	Non-existent: no convective movement or strata of pressure	Non-existent: no  convective movement or strata of pressure
Core	Seed of 14000 km Fe/Si +  freeze H20+ NH3 CH4 Up to 100 million bars Density = 15 20 in 30 Earth masses	Seed of 15000 km  Fe / Si + freeze  Density = 5 10 in 20 Earth masses	Seed of 7500 km  Fe / Si 7000 K Up to 20 million bars	Seed of 7500 km  Fe / Si 7000" K

 

2.5 History compared by the Telluric planets
 
 

2.5.1 The origin of atmospheres

The internal planets formed in a homogeneous way by collision of a multitude of global bodies. Under the influence of the heat which they had stored during their forming and during the heater due to the radioactive destructions, these planets differed: this differentiation corresponds to a redistribution of the chemical elements inside the planet.

The core is established by individualization of a nickel and iron phase which collected in the center of the planet by gravitation.

In surface we find the lightest elements such continental granites lighter than basalts of the oceanic ridges which by subduction provoke the continual expansion of the oceanic capital.

The big differences in the concentrations  of neutral gas between Venus the Earth and in Mars eliminate the hypotheses  of the acquisition of atmospheres by arrest of gases of the primitive nebula  or by bombardment of meteors. The hypothesis  of the accretion stays: the volatile compounds were present in dusts which formed planetoids .

The isotopes of rare gases present in laves inform us about the composition of the ground coat. The primitive atmosphere comes from the degassing of this superior coat through  hydrothermal panaches resulting from the volcanism of ridges.

The big size of Venus and Earth  led an important internal heating and a degassing of cliffs within 1 billion  years. But the small size of Mars led only a partial degassing.

The distance in the sun was the main factor of evolution.

On 3 planets, seas and ica floes formed, CO₂ The hydrogen settled in calcareous rocks and escaped.

On Earth, the history of the conquest of the oxygen was able to be reconstituted by the discovery of the composition of cliffs not oxidized in old detrital sediments of more than 2 billion years, followed by the appearance of red iron bedstead by the oxidation there is 1,8 billion years. This time corresponds to the appearance of the blue-green algae practising the photosynthesis from the CO₂ Extract of the bicarbonate of calcium. It was followed has 420 million years by the explosion of the biomass during the colonization of lands protected of UV by the ozone, the by-product of a high content in oxygen there.

At the same time as the oxygen (21 % of the atmosphere except steam), N₂ ( 78 %) and CO₂ ( 2 for one thousand) formed by the degassing of the nitrogen and the carbon contained in iron miscellanies - nickel and chemical reaction with the oxygen of the olivine and the  pyroxene.

Now the nearness of Venus, Earth  and in Mars leads the same initial composition in Nitrogen and Dioxide of carbon. If in the case of Venus CO₂ Stayed in the atmosphere, on Earth it was fixed in the water and the carbonate of calcium of the cliffs which to them only contain the equivalent of 20 atmospheres of dioxide of carbon. Venus and Earth possess thus well the same quantity of nitrogen and carbon dioxide if we take into account the CO₂ Fixed in the ground cliffs.

The nitrogen being neutral  geochemically gradually stored in the atmosphere unlike the oxygen which turns in the cycle oceans, biosphere, atmosphere and sedimentary rocks.

The quantity of oxygen depends on the quickness of reaction between the atmospheric reservoir of oxygen and the reservoir of the carbon in sedimentary rocks.

The photosynthesis produces some oxygen and consumes some carbon dioxide, the breath of the human beings absorbs the oxygen and the product of the carbon dioxide.

Bacteria provoke a cycle of the nitrogen which transforms into nitrate which consumes by the other bacteria reject the nitrogen. We estimate at 15 % of the atmosphere the part in transit.

The helium comes from the radioactive destruction and the neon of the sun cloud. Finally the ozone is constituted by the destruction of  O_2. By the  UV and the recombination of the atoms of oxygen. The ozone protects  UV but its proportion is limit notably by its ability to react in the fluorine.

Venus originally had to possess oceans close to ground oceans because the conditions of  accretion were the same. The temperature of surface was of 80°C and an atmosphere of 2 bars, rich from 20 to 30 % of steam, essentially consisted of N₂ With 1 for 3000 of CO₂.

The degassing of the CO₂ provoked its rise in 100 bars but the oxygen produced by the evaporation of the oceans disappeared in 4 billion years by the appearance of new cliffs and the burying of cliffs oxidized with a rhythm comparable to the ground rhythm. Only remains the heavy hydrogen in the Venus atmosphere  produced late but not reagent of the evaporation.

The vapor of water escapee increased the greenhouse effect and to accelerate the evaporation: it is a greenhouse effect diverging unlike the ground stabilized greenhouse effect.

If the ground greenhouse effect is the product combined by some steam of the CO₂ And new sulphurated pollutants, the atmosphere increasing of 33°C the temperature on the ground, the greenhouse effect of Venus due to the CO ₂ Increased the temperature of 500°C.

Over Mars, the degassing of only 20 % would have only allowed to form that a layer of 100 metres of water and from 2 to 5 bars of CO_2. But the absorption of the CO _2. By cliffs and especially the absence of their renewal by the tectonics of patches eased the greenhouse effect: the temperature is crossed under 0°C and the liquid water disappeared, settling icy according to an effect of divergent glaciation.

Models indicate that Earth 5 % closer of the Sun would have been transformed into Venus and 1 % farther in Mars...
 
 

2.5.2 Climatology and Planetology

Planetoidshaving formed Venus and Earth saw their volatile elements (in particular the water) evaporating and only the diverse accretion explains the presence of water. The content raised in heavy water in the atmosphere of Venus explains by the presence of a primitive ocean Venus similar to  Téthys of the beginning of the Earth.

The content in CO₂ Between Venus and the Earth is similar: in the case of the Earth the gas was absorbed by cliffs to form carbonates. In the case of Venus, the water of the atmosphere was not blocked as on Earth by a cold  stratospheric trapdoor.

The nearness in the sun, by the effects of engendered tides, also provoked a considerable slowing down of the daily speed of rotation and reduces the magnetic field and there was not trapping of particles by ionized high layers coupled with the magnetic field. The mass of Venus was insufficient to maintain a fluid core and an active volcanism but a disappearance of the differential movement stopped the dynamo.

The contribution of the negative factors thus allowed the water is to rise in the high atmosphere to be separated by the UV, due to its weakest mass the hydrogen escaped in the space. There is not any more today than a weak proportion of dioxide of sulfur and steam (less of one ten thousandth). But their combination engendered the clouds of sulphuric acid of the high atmosphere. With a dry atmosphere the temperature rose and began to dissipate all the carbonates accumulated in cliffs, what provoked the racing of the greenhouse effect until the current situation: a pressure on the ground of 93 bars with a rate of carbon dioxide in 97 % for a temperature of 450°C.

Reminder: the greenhouse effect is connected to the fact that the sun radiation absorbed by the couple ground + atmosphere and  emitted back in the infrared is strongly absorbed by the CO₂ And by quite other absorbent (on Earth there is so a lot of steam and the methane CH₄ Or the nitrous oxide NO_{2, b}oth in strong increase).

On Earth, the forming of the Moon by the percussion of a planet of the size of Mars eliminated the first atmosphere: the current atmosphere is the double product of the degassing of cliffs and the Life.

The carbon cycle stabilizes the ground climate.

Indeed the evaporation of the  water under the heat increases the rains which increase in return the dissolution  of the CO₂ Of the atmosphere. This one is going to fix of the carbonate by attacking cliffs. The rate of carbon in the decreasing atmosphere, the temperature will fall. The phenomenon plays in the other sense during a decrease of the temperature and thus some evaporation.

Carbonates formed in cliffs are eventually pushed under the oceanic pedestals and provoke the push of mountains and other volcanoes. The carbonate dissolved in the lave is  injected back in the atmosphere.

The marine shells by fixing a part of the carbon by the constitution of calcium carbonate  have slows down the carbon cycle, the shells being sooner or later reconverts in maritime sediments.

The ground plants at the origin of the petroleum and the coal accumulated since the environment of the Secondary here is approximately 300 million years, approximately 25 % of the carbon dioxide of the atmosphere. Plants thus allowed our climate to be moderated by burying in the ground an important part of the carbon of the CO₂ The rejected oxygen being essentially of use to the breath of the mobile parasites (the animals a modest branch of which we are but in strong impact).

But the rate of carbon dioxide is supposed to be by 1 for 4000 at the beginning of the century in 1 for 3000 today.

If the restoration of the carbon dioxide by the decomposition of the fossil fuels (and more certainly still the waste in the atmosphere of compounds sulphurated in the very effective greenhouse effect) raised the temperature up to the point of racing where the absorption of the carbon dioxide by the ocean would become insufficient, the heat would release the carbonates of cliffs still increasing the greenhouse effect until the final result: an atmosphere of 60 bars and the evaporated oceans...

Over Mars, the pressure of the  atmosphere consisted in 95 % of carbon dioxide was initially 10 bars. The  liquid water poured between 3,8 billions and 2 billion there years. But the mass of Mars represents only the tenth of that of the Earth and the eighth of Venus. In Mars thus contained from the very beginning much fewer radioactive elements allowing to maintain on a geologic duration the preservation of the fusion of the core where from the slowing down of the volcanic activity  and the disappearance of the magnetic field leads by the fluid movement of the core. The volcanic activity which allowed the initial degassing is breathless and was not able to counterbalance the leak of the atmosphere due to the weak gravity of Mars. This leak accelerated when the high ionized  layers which acted as trap did not undergo any more the Martian influence  of the magnetic field. With the waste of the atmosphere, the greenhouse effect disappeared, the water froze and sublimated in gas under the decline of pressure. In Mars became an immense desert with two poles where the dry ice settles alternately during the southern and boreal winters.

So of a situation initially the  same  3,8 billion years ago, 3 planets endowed of atmospheric one  nitrogenous and carbonic of several bars, we notice 3 totally different situations today: an oven, an Eden, a desert .
 
 

Let us summarize the table of the temperatures
 
 

	Venus	Earth	Mars
Yesterday, the beginning of the life (-3,8 billion years)	+80°C	+55°C	+30°C
Today, the bend	+450°C	+15°C	-20°C
Tomorrow ( 10 000 years) *	+450°C	+200°C	-20°C

* If the sudden decomposition of the fossil matter and the eviction of the sulphurated matter exceeds the absorption capacities of the carbon dioxide by the ocean which transforms it into carbonates and engenders a racing .
 
 
 
 
 
 
 
 

3 The chaos in the solar system
 
 

3.1 The origin of the chaos

F =  GM / R²

The trajectory of a body orbiting around a central celestial body is an ellipse around 2 foyers. If the main body is more massive than the secondary body, one of the foyers will be very close or same inside the main celestial body .

But the presence of the third body, however little massive it is, leads a disturbance of this ellipse which gradually becomes a major disturbance and, by definition, there is no algebraic formula describing their respective trajectories: these are described by an infinite suite. If this series is convergent in the case of 3 bodies, the problem arises if it remains convergent for systems more complex.

Should the opposite occur, the body will go away eventually towards the infinity and the orbit is not stable.

The second problem is to determine if this instability will occur before the destruction of the system, notably by the expansion of the central star.

Now it seems that the calculations are of a redoubtable complexity and that numerous solutions leaving different physical parameters (distance and masses) can lead to the same results. For example, the parallel study by Gall and The Glassworker of the disturbances of Uranus gave place to a completely fortuitous discovery, the couple mass / distance used as hypothesis to determine the position of Neptune being false in both cases but equivalent in their effects to the couple mass / distance reality.

It was the same for Pluto there whose reduced mass does not explain the disturbances of Neptune.

The hypothesis of a massive body  endowed with a very oblique trajectory on the ecliptic remain possible (but little credible within the framework of the plans of planetary forming).

Rather than to examine analytically if the trajectory of a body plunged into a superimposing of fields deviates from it eventually infinitely,  Poincaré used a geometrical representation to determine the conditions of stability.

In a space coordinates of which are the impulses and the positions, the closed buckles indicate that the body will find periodically the same physical configuration.

By examining the intersection  of these orbits with a section (a little the equivalent of a spectroscopic image to display an abstract image), Poincaré realized that the trajectories of two infinitely close points diverge and that the engendered points eventually fill whole regions of the section. The representation is so complex as it requires powerful computers to represent them.

The increase of the images of this virtual space, where regions seem completely occupied by the trajectory and the others remain empty, reveals a hierarchical structure with again occupied zones and zones empty of solutions.

It is difficult to distinguish, with these points which roam for a long time, the divergent trajectory of that in long period. The interweaving of spaces makes the graphic separation impossible.

In fact a variation, however reduced it is, initial conditions can in limit situations make fall over convergent towards the divergent. In many situations, the initial uncertainty is transformed into major or total forward uncertainty.

These minimal uncertainties are cumulative during the echos where the massive bodies get closer periodically some of the others and increase gradually their disturbances .
 
 

3.2 The drift of the solar system

Keplerhas defines the orbits of the bodies of the system solar as elliptic and thus periodicals

But all the planets incurring  between them, set ordered by Kepler breaks  in short term.

The problem of the stability of the solar system was one of the major problems of the XVIIIth century and resisted to the assault of eminent mathematicians such as Clairaut, Euler or d'Alembert.

Indeed because of the disturbances exercised by the presence of the other planets, the orbits of the wandering celestial bodies are not fixed.

Over a short period, ellipses deform and turn slowly in the space. In particular the second foyer of the ellipse describes a complicated curve.

Laplace , fine XVIIIth century, made an estimate of the curve as a superimposing of circular movements the periods of which stage of 40 000 years in several million years

The second foyer so describes  epicycles without report of those imagined in the Middle Age to report the ellipse of Kepler.

In the case of Jupiter the variation  of the second foyer follows buckles on a main trajectory over 200 000 years, with a variation of the order of 1 %, the major disturbance coming from Saturn but every planet bringing a disturbance growing in time by adding supplementary buckles.

Laplaceand  Lagrange is going to show, by using a linear estimate of the equation of the movements, which the mean values of the main trunk roads of the global orbits do not change and which the eccentricity and the slope of orbits undergo only of small oscillations guaranteeing the stability of the system.

Poincaréis going to underline that successive estimates and ceaselessly more precise consist in adding terms in series which do not converge!

We cannot rule on trajectories at the infinite time and thus on their stability.

Much better, trajectories can become extremely complex. We call them the chaotic solutions.

The current method consists in  programming directly the equations of Newton on computer with a relativist correction  including the shift of the perihelion  instead of the method Lagrangienne of the disturbances.

The most recent calculations on computers indicate that the prediction of the position of a planet depends on the precision of its initial position but that any precision is imaginary medium-term for the telluric planets, the huge planets remaining stable.

The error on the position of 4 telluric planets derives with an  exponential law. So a distance in the position of the 15 micron Earth leads to an error of only 150 metres at the end of 10 million years but 150 million km at the end of 100 million years. It is the distance Earth-sun and it forbid any prediction.

In the estimate of  Laplace, ellipses undergo slow, regular and limited deformations. Planets do not meet there.

In a more complete model, the chaotic movement becomes perceptible and prevents on the scale of some million years any prediction of their movement.

A long simulation on 5 billion  years was begun by the team of J.Lasker ( Paris-Meudon).

We so notice that the variation of the eccentricity of Mercury can make it cross the orbit of Venus and them return in collision or allow the ejection of Mercury of the solar system.

Mars can also get closer strongly to the Earth.

In this simulation, this type of phenomenon require approximately 3,5 billion years from the current situation.

The fact that such events are possible does not mean that they are likely. The simple fact that the ground temperature is not strongly changed on 5 billion years proves it.

3.3 The chaos and the life

The ground equator is tilted by 23 degrees with regard to the plan of its orbit.

Now the combined effect of the Moon and the Sun on the ground equatorial led swelling a movement of pretransfer on the axis of rotation of ground which makes it describe a rotation of a period of 26000 years around a fictitious axis.

This movement of the type undergoes by a top in rotation when it undergoes a lateral push and discovered by  Hipparque here is 23 centuries is the precision of the equinoxes.

But the long-term influence of the other planets make undergo in the ground axis of the variations of the order of 1,3 degrees responsible for the periods of glaciations and for reheating.

But the absence of the Moon which counts for 2/3 in the effect of pretransfer of the equinoxes would lead a pretransfer of a period of 75000 years and either of 26000 years, entering phase and thus cumulative echo with the disturbances of the other planets.

The result would be typical variations of the orientation of the ground axis of 50 degrees in 2 million years what is incompatible of the rhythm of possible superior adaptation of forms of life.

In fact for durations of ground rotation from 12 to 48 hours the slope of the axis, without the Moon, could varyin a chaotic way from 0 to 85 degrees.

The angle mattering between the axis of rotation and the plan of rotation of Venus (177 °) or of Uranus (97 °) could be due to rocking of these planets, in the absence of satellites enough massive with regard to their mass to limit theirs oscillations.

The Moon would thus be a necessary presence for the blooming of the life, but such circumstances would be rare...

It is not thus enough any more to find a planet at good distance of its Sun so that  an evolved life is possible.

The discovery of close planetary systems lets understand that our system is a stable particular exception with massive planets at distance and thus stable orbits for the telluric planets.

There where the knowledge of the chaos joins that of the life in the universe.

3.4 The chaos in asteroids

The term chaos means being the object of sudden variations due to a so small cause as it seems unpredictable.

In the case of the belt of asteroids,  it was determined by Jacques Wisdom whom the disturbances of Jupiter on the asteroids of third period with regard to orbital period  of Jupiter modify gradually their trajectories to the point that the eccentricity  of their pseudo ellipse increases and to the point that they eventually collide the Earth or in Mars, where from their progressive rarefaction.

On the contrary the echos 3/2 of the echo 3/1 do not correspond to a chaotic zone because asteroids tend to be grouped together there: it is about a well of stability.

In the case of the echo 2/1, it is about a zone where the density is gradually reduced but the hypothesis  of the chaos is insufficient to explain this deficit because these asteroids  far from the Earth and of Mars have a very weak probability to collide them and to disappear. On top of asteroids on chaotic orbits can be confined in precise regions. We speak about stable chaos due to a periodicity which prevents them from touching Jupiter ( remember Schoemaker-Levy comet). If the reports of periodicity are not whole, the influence of the massive body is not periodic and does not allow the trajectories to diverge.

Concerning 130  known celestial bodies trajectories of which cut the ground orbit, nobody should strike the Earth during the next two centuries.
 
 
 

3.5 The chaotic running of satellites

In the general case, the forces of tide engendered by the difference of the gravitational forces enter the hemisphere turned to the satellite and the opposite hemisphere, deform the planet so that the various regions accelerate together in reaction to the variable gravitational action the object of which they are. The swelling along the right-hand side connecting the centre of 2 celestial bodies possesses a speed of equal revolution at the speed of revolution of the satellite around the planet .

But a part of the energy involvement in the movement of the materials of the planet is dissipated in friction; the planet reacts with delay to the action of the satellite and the equatorial swelling is late with regard to the satellite. It is the gravitational interaction between this swelling and the satellite which slows down the rotation of the planet and increases the distance with regard to the satellite. But the effect being symmetric; the movement of the satellite is slows down and this one eventually turns on itself it a time equal to the period of revolution around the planet.

But there are exceptions. So the case of Hyperion, satellite of Saturn the period of rotation of which is of 13 days against 21 for its revolution around Saturn.

The orbit of  Hyperion, this irregular little potato about 200 km in diameter surrounds Titan's orbit, perfectly spherical satellite of 4000 km.

The report of the periods of revolution Titan / Hypérion is 3/4. Titan's presence allowed Hyperion to find a stable orbit in spite of the fact that it did not synchronize its rotation with its global revolution.

But if the orbit is predictable, the orientation of its axis of rotation seems chaotic. The irregular shape of Hyperion makes its movement look like to that of a bottle which would only be half full; the axis of rotation can pass in a chaotic way of the main line in the small axis. The slightest distance from the axis of rotation with regard to the perpendicular of the  orbital plan can increase very quickly.

Prisoner of its echo with Titan,  Hyperion is exactly in this chaotic region which deforms its ellipse of rotation and engenders gears of rotation.

By using the representation of  Poincaré of the space of the phases where the angle of the axis of rotation is represented according to the speed of rotation, we notice that points do not fall to the same place, but scatter in a whole domain of the phases, what shows a chaotic behavior.

The behavior of  Hyperion illustrates the general case according to which any not regular satellite passes by a chaotic episode consecutive to its slowing down by the forces of tides before locking its movement of rotation and presenting eternally the same face towards its planet. But  Hyperion would be the only satellite to have gone out never of its chaotic phase without stable axis of rotation due to its locking of  orbital phase with Titan.
 
 

3.6 The global orbits

At the turn of the XVIIth century, Kepler looked for the order in a solar system by trying to make correspond the global trajectories with 5 regular polyhedrons discovered by the Greek geometry based on the search for the aestheticism in the Nature. It was a failure and the geometrical analysis left place with the analytical analysis which allowed it to discover its famous laws.

But an elementary approach allowed collectively Titius in 1766 to notice that the global orbits of the solar system follow a simple arithmetical suite. It is the law said about  Titius-Bode.

This law allowed to determine  that there was a missing planet between Mars and Jupiter. This planet was well discovered in 1801: it was about Cérès  who started the works of Gauss on the flight mechanics which allowed to progress in the forecast of trajectories from limited information. Time after time the main bodies of the belt of asteroids were discovered confirming the aptness of the law. But it was about a happy but amazing statistical fate or was a sign of a hidden order.

During more than two centuries the explanation in this phenomenon in been lacking. It was advanced that in the disc protosolar an instability saw itself naturally automobile answered according to an arithmetical law but the explanation was a little bit short and put ad hoc.

The discovery from 1993 of planets  outside solar system   at a very reduced distance of their Sun (as  Pegasi 51 ) seemed not to suit to a law Titius-Bode. The discovery of planets re-formed later around pulsar (star with neutrons, broadcasting of pulses by effect of acceleration of electrons swept by a magnetic field with fast rotation) still led to the other global conformations. How to put hand of the order in these divergent observations?

It seems today that a deep and original approach said about the relativity of scale leads to the solution.

As regards this particular problem, this theory leads to use an equation comparable to the equation of  Schrödinger to determine the geodesic of the global trajectories. An appropriate value of speed appears naturally. From this appropriate value, the global speeds of the solar system were able to be reconstituted (and leaving their distance in the Sun) because geodesic the most likely correspond to an elementary suite. Only 2 planets in the call are missing. If one, too close to the sun could not correspond, in a stable orbit and in a compatible temperature of a rocky body, the other , closer to the Sun than Mercure, is actively looked for.

But the appropriate value of the speed which has allowed this reconstruction   from an observation was able to be determined only by an approach: it exists  privileged relative speeds in a cluster of galaxies and these lead to harmonious  peaks in  the relative  redshift of  bodies measured by couple. The noticed appropriate value was empirically  considered as universal and, injected back  in the equations, led to the law Titius-Bode.

But the essential fact is that  planets outside solar system very close  to their sun were exactly discovered, and their estrangements stick perfectly  on the forecast, the configuration being statistically quasi-impossible if planets were distributed at random (1/10 000). As for planets around pulsars (measured indirectly by the Doppler shift of pulsars), they correspond even better to the forecast (1/100 000).

The global orbits follow laws connected to the structure auto replicated to the various scales of 4 equivalent dimensions of space and of time. But this continuum in 4 dimensions takes a fractal dimension in the smallest scales. The structure of the reference space is directly connected to the resolution where we observe it and the phenomena with small scales have a direct effect on the macroscopic organization of the solar system .