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The Scales of the Cosmos

  This statement introduces first of all the various fundamental interactions of the nature into their relative importances following the considered scale.

Then are treated the various methods allowing to elaborate a scale of the distances of the Cosmos.

The notion of time scale is also exposed with their precise definitions, and for some the necessary ascent to their historic roots.

This allows us finally to illustrate the impact of the movements of the Earth on the various scales of time.


1 The creation, the fruit of scales and fundamental interactions *

2 Distances and time of the cosmos *

2.1 Reminder of the distances *

2.2 The measure of the distances *

2.3 The measure of time*

2.3.1 The year *

2.3.2 The day *

2.3.3 Definition an hour. *

2.3.4 Definition of second *

2.3.5 The origin of the week *

2.3.6 The measure of the lunar month *

2.3.7 Earth oscillations : impact on the durations*

1 The creation, the fruit of scales and fundamental interactions

Every shape in the universe tends naturally to look for the stability.

This solution of organization, structure depends on the report of the intensities of the fundamental interactions in the considered scale

Every scale thus gives place to a shape of organization of the matter the variety of which reflects an attempt of unpredictable search for a stable state but the reactions of feedback, the impossibility to maintain continuously a stable environment are going to engender an evolutionary dynamics aiming at finding another balance. The evolution of the alive reflects perfectly this opportunist method of the nature to exploit in an unexpected direction a resource constituted initially in another purpose.

This evolution of the conditions will make an optimal solution collapse, one moment, what will tend to privilege the variety of the solutions in front of a variety of conditions.

So, of the life on a planet surface.

So of the situation of an atom and its procession of electronic wave in an environment propitious to the collisions.

So, apparently durable balances within stars what leads to their chemical evolution.

So, crossed evolutions of the couples of stars.

So, of the stellar organization in the interactive pool which constitutes a galaxy.

So, of the galactic organization in the densest star cluster.

Other "less adaptive" phenomena are the fruit of complex chains which require the intervention of all the interactions at time reduced as the explosion of a heart of supernovae, which will allow, in final, the enrichment of the galaxy thanks to apparently marginal quantum effects.

Conversely he can involve a single type of interaction but which acts on a big duration leading to a big complexity of forms removing the conditions of their genesis as the alterations of the galaxies by their collision and the change of shape of irregular in spiral then in elliptic in case of collision in heap galactic.

The organization of the matter depends only on the superimposing of the fields of interaction and the intensity of these fields depends only on 3 factors:

  • The fundamental constants of coupling
  • The value of charge for 2 objects in interaction

  • - Their distance

    The angular effects can be cancelled by the choice of repository appropriate one because the space is isotropic, safe in the rare cases where an intermediate body can intervene by phenomenon of absorption (electric conduction by Faraday cage, masking gravitation by a black hole interfacing).

    Because of the inertia of objects, the effects can be movements in 3 dimensions and not only attraction or repulsion (example precession by gravitation).

    The fundamental interactions are transmitted by vector particles. These particles are as a rule virtual that is that they are not stable and that their life expectancy is conversely proportional in their mass. These particles are extracted from the potential of energy of the space between the particles which undergo the interaction and their energy after annihilation  increases back the potential of the space.

    4 natural forces are:

    - The strong force

    Its characteristic is that the vector particles of the interaction interact between them; the more the receiver is far from the source, the more the vector particles are numerous and the more the force strengthens. The effect is the seclusion of particles undergoing the effect in a very reduced zone (the nucleus of the atom).

    The vector particles being massive, they quickly annul and the force is in short reach.

    - The weak force

    Its intensity is weaker and she acts only more slowly (seen by the macroscopic observer). It allows two or three particles to interact. Particles lose their localization changing into waves. The sum of their energy is reconverted to another set particles.

    The weak force is also charged with but because it is about a changing force, it does not confine the matter.

    The vector particles being less massive than the strong force, they annul more late but the weak force is still in short reach.

    - The electromagnetic force.

    Its vector ( the photon) is not charged with its intensity decreases with the distance but its reach is infinite because the mass of the particle is equal to zero: its detection supposes its absorption and its proper time is equal to zero because it moves in the maximal rate. It possesses the property to be transformed into real particle when its energy is sufficient ( very high frequency).

    It is a force self- maintained  because the wave propagates with her the electric field and leads a magnetic field. The distribution of the magnetic field leads in his turn the electric field.

    The intensity of the force depends on the stream of photons and decreases with the surface of emission.

    It is a directed force (by the orientation of the electric and magnetic fields). Fields can counterbalance by the accumulation of unpredictable directions.

    - The gravitation.

    Its vector is hypothetical and its properties are not quite compatible with the theories of unification of the interactions

    The gravitation depending only on the distance, it has a centripetal effect and thus bends all the trajectories (effect of tides). The effect of local curvature propagates through the space and decreases with the surface of emission.

    The curvature is also modified by the rotation of the broadcasting source.

    The curvature in a zone of the space produces a distortion of time (the time seems to slow down there seen from the outside less bent).

    The effect of the gravitation is to reduce the distortions of time between the massive bodies by reducing their distance.

    It is the reflection of a tendency of the nature to level the local variations of time to move closer to all the local drainages of an average drainage of time says cosmic time of the universe (defines as time since Big-Bang).

    The gravitation is a not directed field . The curvature cannot be thus compensated (at least for the matter, the doubt remaining for the antimatter) and increases theoretically. But the movements are determined by the relative curvatures between the attracted  and the attracting objects. The two bodies can create a point of balance between 2 attractions, that is a zone of not privileged direction where a body of test would be almost immovable with regard to them (but pulled by their rotations).

    The attraction can be also compensated with a divergent movement (centrifugal force or of inertia) so as nearness of a black hole where the effect of inertia becomes centripetal.

    This inertia which is the pursuit of a movement is only the continuous reflection of the variation of the curvature of the space; in every point the curved space is tangent in a flat space where the initial movement remains. The inertial movement  requires an orbital speed (thus high) to compensate for the attraction.

    Because of the reports of intensity between the forces:

    - The strong force acts only in the nucleus atomic  (dimension of Fermi = 10-15 m) Because it has a reach of 2 Fermi slightly lower than the size of the nucleus indicating that it acts directly between 2 nucleus in close relations (neutron or proton).

    - The weak force acts in all the exchanges of identity of particles and its reach is limited to 0,01 Fermi (10-17 m)

    - The electric force acts of 10-15  to 10-8 m (some hundreds of Angström). Beyond the orientations of fields nullify. The exception constitute the phenomena of large-scale plasma (lightning, ionosphere, stars, stellar and intergalactic plasma). Nevertheless the global environment is constituted by neutral matter and the electrons of the electric atoms exercise their effect of aversion and thus pressure on all the surfaces in contact of the solid bodies (or between molecules for the liquid and gas bodies).

    Beyond 100 000 km, bodies are so massive that the heat loosened by their contraction ionizes them again; the electric force acts directly

    - The force of gravitation is cumulative. Bodies from 0,1 m feel the global effect of the gravitation and this effect believes with the mass as the effect of pressure by contact connected to the electric interactions becomes unimportant.

    We thus distinguish 7 in 8 zones

    Below 10-17 m, the weak force is dominating

    Between 10-16 and 2*10-15 m, the strong force is dominating

    Between 10-14 and 10-8 m, the electromagnetic interaction acts in a direct way but

    Between 10-14 and 10-9 m, the electromagnetic field allows the constitution of still waves (the electrons of the atom); the attraction of the nucleus is so neutralized.

    Bodies between 10-8 m and 105 km is statistically neutral and the electromagnetic interaction acts step by step by the effects of pressure and superficial tension there.

    The effect of pressure increases in opposition with the influence of the gravitation but becomes sensitive for bodies in surface of the planets only beyond 0,1 m.

    Another zone is between the border of fast waste of the structures by electromagnetic disturbance (less than 10-7 m) and the border beyond which the pressures compensating for the weight are too high for volum structures (some dozens metres). That  is the zone of the alive .

    Between 105 km and 109 km, the electromagnetic interaction acts in plasmas and engenders the pressure of radiation by the engendered collisions.

    Even there the electromagnetic effects oppose to the gravitation but in that case the opposition is between a centripetal interaction and an effect of stochastic distribution.

    An exception is the zone between 104 and 105 km for the massive bodies of the order of the sun mass. It is a zone of balance between the gravitation and the aversion between electrons owed to a phenomenon of destructive interferences of the electronic waves: electrons occupy limp with minimal dimension. It is the zone of the brown and white dwarfs whose matter is degenerate.

    Between 109 km and at least 1024 km (size of the observable Universe), only the gravitational interaction acts.

    2 Distances and time of the cosmos
    2.1 Reminder of the distances
    Time of crossing of an atomic nucleus by the light = 3*10-21s

    Gap of time between 2 individuals distant of 1m = 3 ns

    Gap of time between 2 individuals connected by telephone satellite = 0,25s

    Gap of time with the Sun 8mn 20s

    Gap of time with Proxima Centauri 4,29 years

    Gap of time with the pole star = 400 years

    Gap of time with the galactic centre = 30 000 years

    Gap of time with the galaxy Andromeda = 2,7 million years

    Gap of time with the most distant quasar 13 billion years

    Gap of time with Big-Bang 14 billion years
    2.2 The measure of the distances
    What are the methods used to estimate the distances?

    The estimation of the distances is a pyramid every floor of which bases on the precedent. Every floor corresponds to a method of estimation calibrated on the distances of more close objects measured by the previous method. The calibration corresponds to the connecting between both methods for objects which can be measured according to at least 2 methods.

    The first stage to measure outstrips them in stars consists in using a very wide base. For example the diameter formed in 6 months by the rotation of the Earth around the Sun.

    But what is the distance Earth Sun?

    The first measure in the XVIIIth century based on the parallax of the Mars planet  sight of 2 distant points on the Earth. Knowing the distance between these 2 points on the globe and the distance from position of March on the heavenly sphere at the same moment because of the different perspectives, we deduct the distance from it of the Earth to Mars.

    Then it is necessary to use the laws of the mechanics and the gravitation formalized by Newton.

    F = M d (dr / dt) / dt (the force applied to an inertial  mass M induces the acceleration d (dr / dt) / dt with r distance of the object with regard to a centre of referential and by report at which the parameters engendering the force are estimated.

    If F is the force of gravitation between the Sun and the planet

    F= G Msun M planet / (distance Sun to planet)².

    In the classic mechanics of Newton the masses are independent from referential and the distance Earth to Sun does not depend on the movement of the referential. In the relativist calculation, these parameters depend on the state of the movement of the observer referential with regard to the mesurate object but the notion of force acting without intermediary  disappears.

    So G M sun M planet / r² = M planet d (Dr / dt) / dt with r distance of the planet with regard to the centre of mass of the couple Sun / Planet.

    We deduct the relation from it of Kepler (deducted empirically from movements of Mars) The square of the period of rotation of the planet around the Sun is proportional in the cube of the length of the main axis of the crossed ellipse.

    This proportion expresses himself by P²= 4 pi² G G/(M sun +M planet) x A3 With p period and A half main axis.

    In fact the sun is not fixed but its own barycenter is pulled by the planet and forms a small ellipse around the barycenter of 2 masses sun planet.

    By neglecting the mass of the planet, we find the relation of Kepler.

    So the determination of the distance between the Earth to Mars and the knowledge of their 2 periods of rotation around the Sun has to allow to obtain the distance Earth sun.

    Afterward we shall use the passage of Come in front of the Sun ( partial eclipse) seen by 2 different points what is much more practical because Come can be seen in the axis Earth Sun and its orbit is much closer to the circle than that of Mars. The error of precision on the length of the main line is minimized.

    We so end in the determination of the astronomical unity (a.-u.).

    The distance averages Earth - Sun is 149,5 million km.

    For the close stars (first stonemark of the grading), the estimation bases on the direct measure of the trigonometric parallax.

    The position of the close star is tracked down with regard to the bottom of the sky of almost fixed distant stars. The ground orbit allows over 6 months a movement of the Earth with regard to these stars of 2 astronomical units.

    But if these stars have the same amplitude of proper movement this one is not visible over a short period because of their distance. Nevertheless the movement being secular it eventually moves strongly stars and deform the constellations.

    The proper movement of stars was measured for the first time by Halley in 1718.

    But the first reliable measure of the distance of stars was made only in 1838 by Bessel.

    The movement of the star on the bottom studed during half a ground year is essentially a visible movement which depends:

    - Of the precession of the Earth on its axis (movement of top of the axis of rotation with regard to the perpendicular in the plan Earth sun or ecliptic)

    - Of the report between the diameter of our orbit and the distance of the star.

    Bitter to have removed the effect of the precession, the angle finds shape the annual parallax.

    The amplitude of the annual parallax of the closest star is of 0,76 seconds of bow (1 degree represents the 1 hour of bow or 3600 seconds).

    We reach today a precision of the order of 3 millisecond of angle .

    With the distance and the proper movement, we deduct the tangential speed from it of the star (the speed of movement which is parallel to the movement of the solar system). The speed radial road (speed of approaching or recession) requires to use the Doppler  Fizeau effect. The French optician Fizeau has adapt to the light what Austrian Doppler, an Austrian physicist, had determine for objects; the frequency of the waves received from an observed object depends on its speed with regard to us. So a gap of the lines towards the red indicates a speed of precise recession and a gap towards the blue supplies a speed of approaching).

    The visual magnitude of a star represents the luminosity in the visual spectre.

    M is the absolute magnitude, that is, the luminosity of the star if it was situated in 10 parsecs.
    1 parsec is the distance to which the space Earth-Sun would seem equal to 1 second of angle.

    We so arrange a base of fair comparison between stars, the effect of  distance dissapears.

    With the distance d of the star we can so convert some visible magnitude m to the absolute magnitude Mr.

    M = M +5 - 5 log d

    By historic convention(in accordance with the first catalog classified in 6 magnitude of the visible stars by Hipparchus), the magnitude increases when the luminosity decreases.

    Stars shine according to their temperature. The star is in thermic balance inside. It absorbs so much that it emits. If we neglect the effect of the lines absorption connected to the cooling of the stellar atmosphere by the broadcasting towards the space, the star is a body perfectly absorbing and its luminosity shone from the absorbed energy depends only on its temperature.

    The colour ( the wavelength) corresponding in their maximum of radiation is connected to the temperature by the relation

    Maximal lambda = 2,9 107 /T.

    The temperature can be deducted from the maximal lambda.

    The stream emitted by square meter is given by:

    Flow =  x  T with   xof the material (or some gas under pressure) and being able to be measured in laboratory.

    Where from Luminosity = total flow = Surfaces x unitarian stream = 4 p x R T 4

    The absolute magnitude can be thus deducted from the temperature.

    Then, for the estimation of the distance of the stars of our galaxy, the comparison of the intrinsic luminosity of a star to its moderate luminosity allows to determine its distance.

    Now a diagram establishes by Hertzsprung and Russel supplies diagrammatically the curve of evolution of stars and indicates the luminosity according to the temperature. This temperature is a function of the degree of evolution of the star. The study of the spreading of the lines in the spectres of light of a star and the knowledge of its mass is going to allow to affect a star in a category (red dwarf, young star, red red, super huge main, huge sequence, white dwarf) and to deduct the expected luminosity from it.

    The knowledge of the mass becomes established for the binary stars by the measure of their period of rotation according to the laws of Kepler.

    An important difficulty appears to build completely the diagram. Indeed, if numerous dwarfish stars are close to the Sun any great giants and few huge stars have a parallax being enough for being measurable of the Earth, because of the rarity of this type of stars and the short duration of the associated stellar phases.

    The astronomers took advantage of an essential property of stars: their forming in star cluster and their weak dispersal during ages because of their reduced relative speed and of the weak life expectancy of the massive stars, the objects of the study,

    So the heap of Hyades is so close to us as we cannot only measure the movement of the stars which compose it but also to track down their flight point where they seem to converge ( the Vertex).

    This point informs us about the real movement of the heap in the space; the angle of aim formed by the Vertex, the Earth and the heap is also the angle between the orientation of the movement of the heap and its movement towards us.

    From the measure of the speed radial road of the heap (by Doppler effect), we can so deduct the tangential constituent from it of its speed.

    The comparison of the tangential speed calculated in the proper movement measured by parallax allows to deduct the distance of the star cluster.

    We so end in the diagram H-R of the star cluster.

    Regrettably there are no super huge or huge stars in Hyades. But in Pleiads, there are brilliant dwarfish stars of type B..

    We build the diagram H-R of Pleiads by putting back the visible magnitude and we make it slide on the diagram H-R of Hyades until have the best possible correspondence. We so deduct the difference from it between the visible magnitude of Pleiads and the magnitude absolved from Hyades and thus report of the distances between both heap.

    Distant from 150 parsecs, Pleiads have measurable parallaxs. The combination of both methods supplies an excellent reference base. The following stage is to find heap with stars of type O and great giants. Step by step, we so manage to build a complete reference diagram H-R.

    The reminder of this diagram and the couples Temperature magnitude absolved from the stars the appropriate movement of which we were able to determine has constituted the first fundamental diagram.

    This diagram allows to calibrate any new measures: the knowledge of the temperature and the class of the star allows to associate it an absolute magnitude and thus a distance by the knowledge of the visible magnitude.

    The fundamental diagram benefited recently from a jump forward thanks to all the astrometric measures  by the European satellite Hipparcos (systematic measures until 1000 Y.-L) completed by measures in about twenty years of a new satellite which should allow to reach the clouds of Magellan (100 000 Y.-L.) by direct measure of parallax.

    The distances in the galactic centre and in heap spherical of the galactic halo are deducted from the observation of stars said RR-Lyrae among which the intrinsic average luminosity these stars oscillate) is determined well where from their distance

    For the intergalactic distances are used cepheids stars the relation of which period of variation / intrinsic luminosity was calibrated in our galaxy.

    Beyond, the average luminosity of the galaxies is calibrated by type (elliptic, lenticular, barred spiral or not) corresponding to variable report of brilliant young stars and interstellar gas with regard to the remaining mass of less brilliant stars.

    All these methods based on the luminosity must be corrected by the enfeeblement of the light by dusts in the axis of aim and corrected by the way connected at the origin of the object (example the initial rate of metals during the forming of a star which impact its intrinsic luminosity).

    To go beyond the measure of the spectral gaps is used.

    One of the methods is the measure of the longitudinal gap connected at the speed of galactic rotation. Now there are empirical relations connecting this speed with the age of the galaxy thus at the distance in the hypothesis of the expansion which connects the age of objects with their observed distance whatever is the point of observation.

    Finally the grading of the distances by the spectral gap radial nerve says gap Doppler connect the distance of the object with this gap which is due to a visible speed of estrangement.

    The laws of relativist expansion connects at first this gap at the speed of visible recession and the use of the constant of Hubble allows to deduct a distance from it. This constant  is moreover constant only in first estimate .

    But the age strictly speaking of the universe is connected with a distance following a law of expansion dependent on the total energy of the universe (practically of the energy contained in its mass because of its energy of unimportant brilliance).

    Now if today the deducted mass measure of the abundance of the light elements and the mass deducted from the laws of gravitation applied to the galaxies are in agreement this mass, there is a distance from 1 to 10 unexplained between the visible mass and the mass estimated by the relations of gravitation between galaxies (enigma of the hidden mass).

    And there is a report of at least 5 between the mass deducted from the gravitation and a said mass criticizes where the universe would would be neither opened and infinite nor closed, value criticizes resulting inevitably from a phase of fast expansion in the whole (1033 !) first moments of the universe.

    This phase is a solid hypothesis explaining the large-scale homogeneity of the universe as well as the dilution of extremely massive zones of the universe deducted from the laws of a big symmetry in physical appearance of particles. This necessity of a strong dilution appears in the visible absence of such zones in the observed universe.

    Besides the age of the universe depends on the mass of the universe. This mass modifies its curvature and thus its rate of expansion. To calculate the mass of the universe allows to determine its age. The mass of the universe is estimated by the gravitation and by the abundance of elements produced by the nucleosynthesis, Now this age is too weak (13 billion years) with regard to the age considered of the oldest stars according to the apparently reliable stellar models (between 14 and 17 billion years). The reduction of this discord requires the introduction of a cosmological constant the value of which was supposed for a long time nobody not to particularize our universe. The value of this constant deducted from the quantum vision of the space should reach in theory gigantic proportions, contradicted by the observation.

    The contraction is not still raised but this distance between these estimated ages already results from a recent reduction (see Hipparcos and successors) because the distance of stars was measured with higher accuracy and the estimation of distance was increase; stars being more brilliant intrinsically. To compensate for it, their life expectancies were decreased and their age also. In the current state of the models implying a flat universe, a cosmological constant is integrated implying that the density of the space constitutes 70 % of the energy of the universe.

    2.3 The measure of time

    2.3.1 The year

               The year can take several values following its definition.
    The equinox is defines as the moment when the sun day is of 12 hours everywhere on Earth.

    It is in fact the moment when sunbeams in the plan of the orbit of the Earth (the ecliptic) reach the equator at noon (the Sun is for the top at noon).

    Because of the Moon, the ground axis undergoes a movement of precession, that is that this axis which passes practically by the ground poles, while maintaining an almost constant angle of 23 degrees with regard to the perpendicular in the plan of our orbit is going to describe a cone of constant opening of 23 degrees with regard to this axis. This phenomenon of precession of the equinoxes discovered by Hipparchus  is going to modify the point of the sky pointed by the ground axis; the ground axis crossing by the poles the star which indicates in the North will not still be the Polar.

    The equator is perpendicular in the axis of rotation of the Earth and forms a plan in 23 degrees of the ecliptic, but the movement of the ground axis is going to make that a point places on the equator be also going to turn with regard to the ecliptic. The moment when the sunbeam will be for the top of this point is going to be to modify every year with regard to a fixed mark in the sun orbit.

    Because of the precession of the equinoxes the tropic year  (time put between 2 passages in the spring equinox) is thus slightly shorter than the sidereal year (time put by the Earth to buckle its sun orbit).

    Year tropic = 365,242 1935 j

    The Gregorian calendar tends to get closer of the year tropic.

    1 day added every 4 years: 1an = 365,25 days

    1 leap year removed every end of century (25 x 4 years) = 365,24 days

    Except 1 leap year maintained every 4 centuries: 1 year 364,2425.

    It results from it another 3 days too on the calendar every 10 000 years with regard to year tropic actual.

    Sidereal year = 365,256 3605 j

    The sidereal year is defines as the interval of time between 2 passages of the centre of the Earth in the same point of the orbit, this point can be defines with regard to 3 axes leaving the sun towards 3 fixed distant, supposed stars.

    Finally the anomalistic year (from one perihelion to another ) = 365, 259 6440 j

    The anomalistic year is the interval of time separating 2 identical positions of a body on its orbit.

    It is different from the sidereal year (the same position with regard to stars). Indeed the perihelion of the orbit moves, due to the global movement of planets turning anticlockwise with regard to the axis the North - the South of the sun (that indicated by the orientation of its magnetic field for example).

    A weak correction must be also added because of a relativist phenomenon (the pulling of the space in the sense of rotation of the Sun because the Earth which turns around the Sun has to see the same abnormality of the sunlight as Earth which would not turn around the Sun).

    2.3.2 The day

    The astronomical coordinates are the equivalent of the ground geographic coordinates.

    The heavenly equator is the line that the sun in the sky in autumn and spring equinoxes that is draws when the duration of day night and are equal.

    The equivalent of the latitude is the declension.

    The declension of the Sun is the angle of the Sun at noon with regard to its position on the heavenly equator.

    The declension of a celestial body is its height on the horary circle ( the meridian) with regard to the heavenly equator.

    The equivalent of the longitude is the right ascension.

    That is the angle on the heavenly equator of the celestial body with a reference point (the point gamma is the passage of the Sun at noon on the heavenly equator in the spring equinox).

    The angle which makes the heavenly equator with the top (the vertical line of the place) is the Latitude (49 degrees in Paris). His(her,its) complement (41 degrees) is the height of the heavenly equator on the horizon.

    The Sun in its culmination forms with regard to the heavenly equator a maximal angle of 23 during the summer solstice and 23 during the winter solstice.

    By increasing the latitude of the place of observation the trajectory of the Sun approaches the horizon; on the polar circle (66 degrees), the height of the Sun is under the horizon in winter solstices; the Sun arises very shortly  at noon in the South on the horizon.

    And in the summer solstice the Sun is higher than the horizon which it touchs the North at midnight.

    Conversely on the Tropic of Cancer (for instance Abou Simbel), the Sun is so high as it reaches the top at noon the summer solstice.

    In the equator, the Sun is for the top during the equinoxes. In the summer solstice it peaks in 180+23 degrees in the direction the North and in 180-23 degrees in the direction the South in the winter solstice.

    At the time of the equinoxes, the day length is the same everywhere on the meridian because the day gets up simultaneously on all the points of the meridian.

    In the summer solstice, if the Sun gets up for example in Paris, it gets up simultaneously on everything the points of an oblique axis of 23 degrees with regard to the meridian of Paris.

    The axis is tilted northward the West because the dawn comes earlier to the North than to the South.

    Conversely during the winter solstice the axis is tilted northward the East because the night persists much longer in the North where in the South.

    2.3.3 Definition of an hour

    The usage of hours bases on the idea that the rotation visible connected to the diurnal movement move the 15 degree celestial bodies per hour. In fact the Earth turns on itself in 23 h56 mn 4s where from a delay which accumulates within official hour with regard to the sun hour.

    The time of our watch is based on the average sun day, that is the duration of 24 hours which separates 2 consecutive passages of the Sun in the direction of the South.

    The average sun day of 12 pm is different from the sidereal day.

    The difference of 3mn 56 is the time necessary for the ground rotation to mean placing the observer in the same position with regard to the Sun because of the movement of 360/365 degrees of the Earth in its sun orbit.

    We thus have the sidereal Hour = the average hour x 1,002 737 9.

    In summary the sidereal day defines the rotation of Earth on itself with regard to a distant star: 24 hours x (1-360/365) = 23 h 56 mn 4s

    The sun day is the difference of time between 2 culminations.

    The average sun day is of 24 hours but the true sun day oscillates around 24 hours (noon in the sun is not noon in the watch).

    The line which follows the Sun on the field of stars is the ecliptic. It crosses the constellations said about the Zodiac. In fact as it is the Earth which turns around the Sun the ecliptic corresponds to the course of the Earth on its orbit.

    The point of departure of the ecliptic is the crossing by rising of the equator; it is the vernal point or gamma. It stands out the first day with the spring.

    The sidereal time starts when the point gamma crosses the local meridian.

    In first estimate the point gamma is fixed with regard to stars.

    The hourly angle of a celestial body is the time which passed by since its passage in the meridian of the observer.

    Because of the distance from longitude between the meridian of Greenwich and that of Paris, are needed 9 mn 21 so that the Sun in the highest of its journey passes from Greenwich to Paris. The legal hour is thus delayed this interval with regard to the average hour.

    The average hour is the time of the clocks which separates 2 passages of the Sun in the meridian forming twenty the fourth part of the average day.

    The movement of the Earth around the Sun (in fact the angle of the ground axis with regard to the perpendicular in the ecliptic) makes that the Sun has to describe a pendular movement.

    The Sun oscillates around a duration of 24 hours to come back upright from the meridian of a place.

    The average hour of constant 24 hours thus deviates from a sun hour (the distance between noon of the watch and in noon in the Sun can be 15 mn in more or less).

    The point of reference is the moment when the Sun passes in its highlight: noon in the Sun. From day to day, the distance between two culminations can achieve 30 seconds. The variation depends collectively on the promotion in the year tropic (days vary faster in the equinoxes) and of the position of the Earth in the anomalistic year because it describes its ellipse in a variable speed.

    But for the observation of the time of day, a much more regular measure is constituted by the sidereal day, time which passes by between two passages of a star on a given mark.

    The difference of time between the sun day and the sidereal day accumulates

    And fall 24 hours at the end of an orbit; the sidereal hour (with regard to a star) and the sun hour coincide again (for the observer the angle between distant star and the Sun is again the same; it returned to the same position with regard to the Sun).

    To illustrate it  let us consider a star in the top when the Sun peaks.

    6 months later, the sidereal and sun hour will be moved of 12 hours.

    This indicates that the star is in the nadir (of the other side of the Earth); it will be midnight at the sidereal hour.

    2.3.4 Definition of a second

    Originally the inhabitants of Sumer created a numeration on base 60.

    Ptolemy, Alexandrian astronomer of the IIth century, generalized this notation for the units of hours and angles.

    During the invention of clock in the VIIIth century, dials were absent because the populations were illiterates. The precision being weak, clocks were provided that of a single minute hand.

    The marking of minute, the division by 60 an hour just like the unity of angle and the Italian dial in two needles, date the environment of the XIVth century.

    The minute " small part" was followed by the second minute, second small part " too resultant of a division by 60.

    The classic definition of second based for a long time on the unchangingness of the duration of ground rotation. The international second ( Universal Time ot U.T.) was established in 1961. Its precision was of 1ms but it was strongly variable. The second basing on the period of rotation of the Moon around the Earth was more uniform but known about only 10 ms of accuracy.

    But since 1967, the atomic time A.T.  is use and results from the average of 150 atomic clocks restarted in the world today. The reference is constituted by the said time of hypertight transition of the fundamental level of the atom of cesium 133.

    Since 1972, the U.T.C. the universal time coordinate was adopts; it possesses the same unity as Atomic Time but is straighten periodically to stay unless 0,9 seconds of Universal Time.

    The variability of the ground rotation requires that this time is straighten of 2 seconds all 3 years. June 30th or December 31st, reference clocks are stopped 1 second; it is thirteenth knock of midnight.

    2.3.5 The origin of the week

    The days of the week correspond to 7 visible celestial bodies.

    But the order of days is less known; it bases on the tradition of the Hebrew which imported of their exile in Babylon the superstitions of the Chaldeans such calculates it 7 consider as fatal (and quite its multiple). The 7th day becomes a forced day of rest (to the Hebrew the day of rest is Saturday because Saturn is the 7th bus considered as "malefic"). We inherited from it but the Christians moved this day of rest the next day. The Hebraic week starts with the Sun whereas the Christian tradition makes it start with the Moon (Monday). The Moslems start with Saturn and base in the daytime of Come on Fridays).

    We note that the order of days does not correspond to the logical order which would be that of the speed of the wandering celestial bodies in the sky.

    Of the fastest in the least fast: Saturn, Jupiter, in March, the Sun, Come, Mercury and the Moon.

    In fact, the Hebrew have import another principle during their second exile, that of Egypt. The Egyptians applied the principle of the Lord an hour; every hour corresponds to a planet; Saturn from the very beginning, Jupiter assists it...

    Dion Cassuus, historian of the 1st century, gives us the explanation of the Hebrew organization.

    By registering planets as so many branches of a heptagon and by jumping 2 branches between 2 planets we find the current order. An order in the cabalistic appearance.


    2.3.6 The measure of the lunar month

    The Moon turns around the Earth in 27,32 days. The bulge of tide produced by its attraction should follow the Moon in the same speed. Now the Earth turns on itself in a different speed and the Earth is not smooth; the bulge of tide is thus late with regard to the Moon. The bulge the closest to the Moon exercises an attraction stronger than the bulge in contrast; the resultant of these two forces accelerates the Moon.

    The Earth system - the Moon being isolated (its influence on the other celestial bodies being unimportant) the energy of rotation of the couple Earth - The Moon is a constant.

    If the Moon is accelerated, the Earth is slowed down. A part of the effect of friction is absorbed by the viscosity of the earth's crust and dissipates in heat but the balance becomes a reality by a kinetic slowing down of the Earth; the day lengthens.

    The effect is 20 times as important for the Moon which for the Earth and the Moon has so well slows down since its forming that its day is synchronize with its period of rotation: 27 days.

    By extrapolating in the distant and hypothetical future, the ground day will lengthen until the ground day coincides with the period of lunar rotation (near 1200 hours or 50 current "days"). In fact the Sun will have exploded and will have well before gone out.

    The Moon accelerating, it goes away from us and the tide become weaker.

    Today the Moon goes away on average from 2 to 3 centimeters a year

    We measure the recession of the Moon by examining streak them with nautilus!

    Nautilus are small maritime animals of the Pacific of the alive fossil type which live in the last compartment of their shell and which rise and come down daily by using the compartment as of a roadbed.

    Every streak in a compartment corresponds in the day and every compartment possesses a number of streak lunar one-month-old correspondent.

    By going back up to only 25 million years, it turns out that the Moon turned in 25 days (25 streaks by compartment). Here is 420 million years there was only 9 streak. The Moon was 40 % of the current distance and tides 7 times as strong.

    But where from comes the Moon and which was its initial influence?

    The beginning of the accretion of the Earth dates 4,55 billion years and spreads out on 10 in 20 million years. In its premium youth that is hanging 700 million years it was subjected to an intense bombardment initially by meteors, then essentially by comets.

    130 million years after the forming of the Earth, the Moon was created. It would result from the lifting of the earth's crust by a celestial body of the Size of March. The original Moon was very close to the Earth and the had a good laugh had a disastrous aspect on the oceans and the first continental crusts

    During its creation, the Moon was probably less than 100 000 km of the Earth and tides were dozens times stronger than today.

    2.3.7 Earth oscillations : impact on the durations

    The Earth undergoes 3 main disruptive movements which affect its rotation around the Sun:

    - The precession of the equinoxes, that is the change of date of its passage at least of the distance in the Sun (perihelion): conjugation of two periods moved in phase of 19 000 and 23 000 years, what ends in a pseudo-period of 26000 years.

    - The change of slope of the ground axis which fluctuates of +/-1,5 degrees around 23 27: period 42 000 years

    - The eccentricity of the orbit on a cycle close to 100 000 years.

    Seen by a ground observer situated in one of its poles, stars seem to describe concentric circles the centre of which defines the celestial pole around the ground axis of rotation.

    The position of this celestial pole today close to the pole star moves because the ground axis of rotation describes in 26000 years a cone of opening 23 degrees 27 minutes around the pole of the ecliptic pointed by a perpendicular in the plan of the ground orbit.

    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 precession 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 Hipparchus here is 23 centuries, is the precision of the equinoxes.

    Because of the flattening of the Earth in the poles, the centre of pressure due to the attraction of the Sun does not pass by the centre of mass and the engendered couple tends to return the ground axis on the perpendicular axis to the orbit.

    But the centrifugal forces connected to the ground rotation oppose to this couple. As in a top tilted the perpendicular force to the axis engenders the precession of the axis of rotation.

    Let us remind that the rotation of a made place change constantly the orientation of its vector speed and engenders a pseudo acceleration what leads a pseudo force ( a force due to a change of referential).

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

    The absence of the Moon, which counts for 2/3 in the effect of precession of the equinoxes, would lead a precession 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 adaptation of superior forms of life.

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

    The lunar precession must be added to the solar precession .

    The eccentricity of the ellipse formed by the ground orbit create a periodic variation of the couple Earth / Sun, also for the couple Earth / Moon. All the irregularities of the movement of the Earth around the Sun and around the movement of the Moon around the Earth create periodic oscillations of the ground axis. They are the forced nutations among which the main term in a period of 18,6 years equal to the period of variation of the lunar orbit on the ecliptic (it is the revolution of knots or cycle of Samos).

    Besides the movement of the axis of rotation around the axis of Earth inertia makes describe a circle in the pole of a circumference of some metres with 2 constituents, one of the period of 14 months (said of "Chandler") and other one of 12 months.

    The first one is an oscillation free of the ground axis which seems to be a phenomenon which amortizes connected to the seismic activity and engenders a movement of the pole in a  20 metres diameter.

    Other one is a forced oscillation connected to the seasonal distribution of the atmospheric masses.

    The influence of earthquakes on the holding of the oscillation free of 14 months is always for the study.

    An earthquake indeed moves the axis of inertia of the Earth with regard to its axis of rotation. But the correlation enters the movement of the axis (and thus of the pole) with the big earthquakes remain to prove.

    A variation of the axis of rotation of 3 milliseconds of bow (1 millionth of degrees in the direction of 70 degrees West) would also be due to the differences in the sea levels on the globe and thus to the no-homogeneous distribution of the masses inside the globe.

    The duration of ground rotation is measured thanks to very precise clocks by the passage of stars in the meridian. Variations of the order of millisecond are observed. These irregularities in impressive number appeal to the Earth sciences: movement of the atmosphere and the oceans, the ground deformations connected to tides, movement of lithospheric plates, movement of the core propagating by the coupling which allows the magnetic field.

    The set ground -sea -atmosphere being isolated in the space, any movement of a constituent engenders a modification of the rotation to keep the total moment.

    Also the sum of the movement of ground rotation and the orbital movement of the Moon that must keep(preserve), the phenomenon of tide slows down the ground rotation and takes away successively 2 celestial bodies. The ground day so has slows down of more than 2 hours since the devonian era , there is 400 million years (the initial day according to the models of global forming seems to be of a dozen hour). The friction would be amplify in the little deep seas (such the Mediterranean Sea, the Bering Strait, the Irish Sea).

    As a consequence the Moon tends to go away from us from 2 to 3 centimeters a year (but the complexity and the interweaving of the phenomena aims so sometimes at its approaching).

    The passage in the perihelion then in the highlight of the Moon engenders periodic effects of 14 and 28 days connected in solids tides on the Earth.

    The important variations of the speed of rotation on the scale of decade would be due to a disturbance of the magnetic field in association with the movements of the core.

    Indeed the ground, sticky and relatively elasticated coat, is couple by the magnetic field in the hard and compact core.

    The Earth being either perfectly spherical or perfectly homogeneous, the convective movements of the core propagate in the coat and lead variations of the ground rotation.

    When the superior core becomes less thick because of the convective boiling , the coat follows the internal core, On the other hand, it accelerates when the superior core slows down as a result of an effect of inertia with regard to the core, an effect connected to the differences of viscosity.

    We are for a period of acceleration what requires that the official time is amputate of one second to follow Earth which turns punctually faster.

    In return any internal movement pulls with him the magnetic field.

    The reversal of the magnetic field could be of for these variations of the duration of day, for these couplings which, modifying the electric effects in the border coat - core, perturb the magnetic field.

    Seasonal swings even of only some days have an atmospheric origin.

    The asymmetrical distribution of continents modifies the  radiation properties of the low atmosphere and thus the zonal winds. So the annual cycle of the rotation is a measure of the imperfect balance enter the atmospheric traffic of 2 hemispheres. In April the day is longer of one millisecond than in August!

    All these phenomena require that step by step second 1 round dance is removed from the Universal Time Coordinated (or civil time) to fit the Universal Time connected to the ground rotation.