Chapter 10

 

Masses and ray of gravitation

 

French version

 

In the preceding chapter, we saw that the range of the ray of gravitation of the masses, postulated by the temporalist model, is given by the formula r = m½. The ray of gravitation is the limit of the links between the gravitational masses, weak or important (such as stars, galaxies, clusters, and so on…). That means that the range of the gravitational influence of a mass can be equal or less than r, in other words, than the acceleration G’ (6,582 10^-8 cm/sec^2) of the gravitational field. In Newtonian mechanics, the acceleration due to the masses is also mG/L2. So, if we apply this formula to the Milky Way (about 2-3 10^45 g, radius 50.000 L.Y., we get (in the cgs system) : 2,5 10^45 g x 6,67 10^-8 /  5.10^22 cm x 5.10^22 cm = 6,67 10^-8 cm/sec^2. The acceleration, at the outer limit of our galaxy is equal to the acceleration of the external gravitational field. It is, thus, neutralized and, depending of the temporalist model, its ray of gravitation is determined by the formula r = m½. (Chapter 9), is 2,5 10^45 ½ = 5.10^22 cm.

We will calculate, for the well-known concentrations of matter, from the earth planet to the greatest structures of the universe, the theoretical ray of gravitation, with finished range, and to confront it with dimensions observed of these various masses (in the cgs system). When the masses are not known with precision, we considered the total mass of a structure equal to approximately 10 times the visible mass (in accordance with the estimates of the total mass  of  a structure equal to about 10 times the visible mass (according to estimate by 4 % visible mass and 24 % the dark mass : 28 / 4 = 7, is approximately  10 times).

We must, at first, remember that the masses and the distances of the different structures, especially if they are distant, are relatively accurate. Thus, ZWICKY (1933), indicates that the relationship between dynamic mass and visible mass of a structure is about 400. In addition, it is recognized that the constant of proportionality between redshift and distance is determined by a factor 2.

Considering all these uncertainties, we will confront the theoretical gravitational ray of the different cosmic masses and their real gravitational ray, indicated either by the dimensions of these masses or by the limit of their gravitational influence on other masses. We consider that if we have, rarely, a difference of an order of magnitude, this difference is acceptable, considering the cosmic parameters approximations.

1) The earth : mass 6 10^27 g - ray of gravitation 7,7 10^13 cm - distance from the lunar satellite 3,5 10^10 cm - magnetosphere about 8.10^9 cm ( Philippe Escoubet 2001)

2) The sun : mass 2.10^33 g - ray of gravitation 4,5 10^16 cm - limit of the solar system and interstellar space 1,4 to 1,8 10^15 cm (NASA 1993), heliopause 4,5 10^15 cm, Ort Cloud influenced by stars of the Milky Way 3 10^18 cm (Rosanna L Hamilton 1999)

3) The globular clusters :

Average mass of 10.000 stars is 2.10^33 g x 10.000 = 2.10^37 g - estimated total mass 2.10^38 g - ray of gravitation 1,4 10^19 cm - average ray several tens of L.Y. or 2 to 3 10^19 cm (Hartmut Frommert - Christine Kronberg - 2001)

Average mass 1 million stars or 2.10^33 g x 10^6 = 2.10^39 g - estimated total mass 2.10^40 g - ray of gravitation 1,4 10^20 cm - average ray 200 L.Y. or 2.10^20 cm (Hartmut Frommert - Christine Kronberg - 2001)

M92 - estimated mass about 330.000 suns or 2.10^33 g x 330.000 = 6,6 10^38 g - ray of gravitation 2,6 10^19 cm - radius from 30 to 42 L.Y. is 3 to 4 10^19 cm (Hartmut Frommert - Christine Kronberg - 2001)

4) The Milky Way : 200 billion stars is 2.10^11 x 2.10^33 g = 4.10^44 g, estimated mass 4.10^44 g x 10 =   4.10^45 g - ray of gravitation 6,3 10^22 cm - radius 50.000 L.Y. or 5 10^22 cm - satellite dwarf galaxy SagDEG located to 5 10^22 cm (Hartmut Frommert - Christine Kronberg - 1999) ; the satellites of the Milky Way, the Little and the Great Magellan Clouds are located at 60 Kpsc of our galaxy , is 2.10^23 cm.

5) Galaxies clusters : Typical cluster 10^15 masses of the sun is 2 10^33 g x 10^15 = 2 10^48 g - ray of gravitation 1,4 10^24 cm - typical Abell radius 1,5 Mpsc is 5 10^24 cm - (Coma cluster) (Cambridge Cosmology)

According to the agreement of experts, we have selected the following numbers:

Group of 10 galaxies: average mass 10^13 sun mass, is 2.10^46 g (average mass of a galaxy : 2.10^45 g)

Standard cluster : 500 galaxies, average mass 3.10^14 sun mass, is 6.10^47 g (average mass of a galaxy :1,2.10^45 g)

Rich cluster : 3.000 galaxies, average mass 5.10^15 sun mass, is 1.10^49 g (average mass of a galaxy : 3.10^45 g)

We, therefore, selected the mass of 2.10^45 g as average mass of a galaxy.

6) Cluster of the Virgin (Virgo)  : estimated mass 8.10^48 g – ray of gravitation 3.10^24 cm – maximum distance of the galaxies from the center of the cluster : 7 million L.Y. is 7.10^24 cm.

7) Superclusters of galaxies : average 10 to 32 clusters per super cluster - Our super cluster (which contains our Local Group), centred on Virgo, mass 10^16 masses of the sun is 2 10^33 g x 10^16 = 2 10^49 g - the ratio mass/luminosity being of 570 indicates the presence of a significant dark mass - probable ray of gravitation 4,5 10^24 cm / 1.10^25 cm ( about 1,5 to 3 Mpsc ) - radius 2 10^25 cm (Cambridge Cosmology)

8) The Great Attractor : super-supercluster whose center is the supercluster ACO 3627 (or Norma cluster) mass 5 10^16 masses of the sun is 2.10^33 g x 5 10^16 = 1.10^50 g  ( its mass is probably more important; one suspects the existence of other indeterminate superclusters - ray of gravitation 1.10^25 cm - distance from the earth 60 Mpsc or 1,8 10^26 cm. The data are dubious, because owing to the fact that the Great Attractor is largely hidden by dust of the disc of the Milky Way (Kraan-Korteweg 1998 - 2000)

9) Great Structures of universe : the galaxies made of stars, gas and dark matter are grouped into clusters of galaxies, and then super clusters of galaxies clustered in gigantic formations, big walls, filaments and huge voids. According to the authors, the universe is structured  in foam, sponge, sheets, pancake or three-dimensional spider web. In fact, it may be considered that the universe is structured in filaments formed of gas, stars, clusters and superclusters of galaxies and dark matter. The filaments represent approximately 10 % of the space and contain 15 % of the galaxies. Their typical length is between 50 and 80 Mpsc (1,5 and 2,4 10^26 cm). They delimit the border of huge voids. These voids have, typically, diameters from 25 Mpsc (8.10^25 cm) to 125 Mpsc ((4.10^26 cm). Located between 6 and 10 billion L.Y. of the earth, the greatest void discovered, in the direction of the Eridan constellation, by Lawrence RUDNICK (August 2007), would have a diameter of about 1 billion L.Y. (1.10^27 cm). This gigantic void whose the probability of existence is 5.10-^10 and the various existing inhomogeneous structures seriously call into question the standard model of cosmology  based on a principle attributing to the cosmological universe an isotropic and homogeneous structure. The model of Big Bang, with the expansion of the universe, note the repetitive and irregular structure of large masses of the universe and especially of those huge voids from 1.10^26 cm to 1.10^27 cm. The standard model is unable to explain the causes of the existence of these vast voids whose the probability is very small (5.10-^10).

The temporalist model, by contrast, provides a simple explanation of the structure of the universe and the reason for the existence of filaments and large voids. In the temporalist model, the gravitation has a finished range as embodied in the concept of ray of gravitation r = m½ ( r = ray, m = mass). In filaments, the influence of the gravitation of the galaxies and the clusters of galaxies is longitudinal because the masses are relatively close and, therefore, below the threshold of the rays of gravitation. If we take the example of a rich cluster of galaxies (3.000 galaxies), whose the average mass is 1.10^49 g, its ray of gravitation is 1.10^49½ = 3.10^24 cm. It can, like this, exert a gravitational influence on galaxies and clusters of galaxies whose average distance is 1 Mpsc  ( 3.10^24 cm – see below, article 10), this all along the filaments.

As for the voids, the galaxies,  clusters and superclusters of galaxies can have a gravitational influence only if their gravitational ray is equal or greater than the radius of the voids that they border. For example, for a void of  1.10^25 cm, the necessary gravitational mass  is 1.10^50 g, is the mass of 40.000 galaxies; for a void of 1.10^26 cm, the necessary gravitational mass  is 1.10^52 g, is the mass of 4 million  galaxies; for a void of 1.10^27 cm (void of RUDNICK), the necessary gravitational mass  is 1.10^54 g, is the mass of 400 million galaxies. The importance of the masses needed for a gravitational influence of galaxies and clusters of galaxies on large voids and the rarity of such concentrations of galaxies explain the existence of these voids, which is a serious contradiction for the model  of Big Bang.

Let us recall that the concept of expansion of the universe and the Big Bang are refuted by the temporalist model. In this model, there is no temporal origin of the universe, nor singularity.

10) Average rays of gravitation and average distances :

Stars in the galaxies: ray of gravitation 4 10^16 cm - average distance 1 Psc is 3 10^18 cm

Galaxies in the groups and clusters: ray of gravitation 4 10^22 cm - average distance 1 Mpsc is 3 10^24 cm

Galaxies clusters in the superclusters: ray of gravitation 1,4 10^24 cm - average distance from 1 to 10 Mpsc is 3 10^24 cm to 3 10^25 cm

Superclusters of galaxies: ray of gravitation 5 10^24 cm to 10^25 cm - average distance 100 Mpsc is 3 10^26 cm

The voids have average dimensions equal to 1.10^26 cm or higher (1.10^27 cm).

Conclusions : If the preceding results are summarized, one notes that, in accordance with the requirements of the temporalist model, the sizes of the concentrations of matter, from the earth to the greatest structures, are, in order of magnitude, equal or lower than the rays of gravitation. Only the Great Attractor makes exception, with an order of magnitude near. It is probable that its mass or its distance, or both, are to be revised. This is all the more probable since the Great Attractor is hidden by dust of the disc of the Milky Way, which deteriorates the precision of measurements. The dimension of the voids, about 10^26 cm and more, is also explained by the lower ray of gravitation of the superclusters of galaxies of about 10^25 cm.

The classical theories of the gravitation at which the range of the forces is unlimited, just as the Big Bang, can give no account either of the preceding results or of their precision. The universe is structured at intervals of distribution in three dimensions, separated by average voids of 120 Mpsc (4 10^26 cm), as in a chess-board. These structures, not to be understood in the preceding models, rise naturally from the finished range of the rays of gravitation specific to the temporalist model of gravitation.

Besides the formation of these broad voids, poses a serious problem with the model of Big Bang. To cross a void of about 4 10^26 cm, at the average speed for a galaxy of 600 Km/sec, it would be necessary approximately 200 billion years for it, which means that the current situation of the galaxies and the voids reflects their situation at the time of Big Bang !

 

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