First gravitational model

25 Apr

I have been working on the three elements theory at first. After that, I have been creating successively 2 gravitational models, which are similar but different in precision and complexity.  

The first one is described on this page. It was the most complicated one, because its applying scale was not restricted. It is not completed, but shows the fundamentals of my model, through the window of gravitation. 

The second one is the best one and can be seen here. 

The first gravitational model of the three elements theory was an alternative theory to dark matter. It uses a modification of Newton's law in order to possibly explain gravitational mysteries.

The results of this model are possible explanations for the dark matter mysteries. The disparity of the gravitational constant measurements might also be explained. Concerning the Earth flyby anomalies, the theoretical order of magnitude is the same as the experimental one. A very small change of the perihelion advance of the planet orbits is calculated by this model.

Meanwhile, this gravitational model is perfectly compatible with Restricted Relativity and General Relativity.

The shape of galaxy speed profiles is quite explained. Indeed, it is the presence of the stars themselves in the galaxies, which, with their masses, reveals this correction which is noticed only inside galaxies. On the contrary classical Newton's law is retrieved for other cases like for example planetary systems.

An expression of G, the universal constant of gravitation, is also given. It would need a summed limited ray, for avoiding divergence. This equation is using the surrounding matter density along a given orientation. This equation gives a much greater value for G outside the galaxies than inside. Hence it suggests a very simple explanation for other dark matter mysteries : speed of the galaxies inside their groups, deviation of a light beam passing nearby a galaxy.

The old mystery of the disparities of the measurements of G might be explained. This work is in progress and is encouraging. Two theoretical ways are existing, but each of them using the important role of the surrounding distribution of matter (buildings, hills, montains, sea ...). That's because the model prediction is the following. The effect of surrounding matter during a measurement of G is not a linear effect as it is predicted by classical physics. The classical addition, or "superposition", of gravitationnal forces is slightly modified. Hence a slight violation of linearity is predicted. The result is that measurements of G done in different contexts regarding surrounding matter distribution, may yield completely different results. From this rises the idea of designing specific dedicated experiments.

In this old model an assumption was asserted which was proved to be false later. It's about the attenuation law of the "contributions" which was supposed to be of 1 above the square of the distance. Because of that the explanation about the Pioneer anomaly is no longer valid. But hopefully this does not change the other results of the model.

Publication in International Journal of Modern Physics E. This is a 10 pages document describing the basis of the model, and some comparisons with experimental data. Published may 2012 in I.J.M.P. (International Journal of Modern Physics E).

The basis of this model in a 2 pages document For a quick overview: mystmassextract.pdf
The basis of this model, detailed and complete version For full details : mystmass.pdf
Second publication in Journal of Modern Physics. This is a 10 pages document describing the mathematical basis of the gravitational model. Published in july 2013 with Scientific Research.
Detailed calculations for this second publication: MathDetailedCalc.pdf

Validation of this model with galaxy speed profiles: results with NGC3310, NGC1068, NGC157, NGC7541, and NGC7331 galaxies: Calcul_NGC3310.pdf 
Comparison with experimental data coming from the Pioneer anomaly, Sideral Gravity, disparities of the measurements of G, etc ... : pioneerexpl.pdf
Recapitulative array of some model's results: 


Distance range

Newton s law



Next steps

Dark matter, velocities of the galaxies

>100 kpc

Groups of galaxies.



Finding the exact ratio Gprime/G from experimental data.

Dark matter, galaxies speed profiles

1-100 kpc

A galaxy.


Very encouraging.

Construction of the exact occulting equation, solving the sign issue and with better results than today.

Tully-Ficher relation

1-100 kpc

A galaxy



Stars/dust ratio profile in a galaxy. Experimental data on the galaxies used in [11].

Sideral gravity

1 kpc.


Very encouraging

More precise calculations.

Finding and using the exact ratio.

Saturn flyby

9.6-10.5 AU



Experimental data is needed.


1-70 AU

Solar system.


Bad result for the four inner planets.

Obtaining exact accuracy of ephemerides for the four inner planets. Execute precise calculations. Estimation of the compensating effect. Correction of the following geodesic principle in the Riemannian metric context.

Ephemerides: missing asteroid mystery

1-5 AU

Main belt of solar system.



Experimental data. Calculation of an estimation of the total mass of the missing asteroids.

Disparities of Gmeasurements

10000 km.


Very encouraging

More precise experimental data. Specific Gmeasurements.

PPN formalism

All ranges




Sagnac effect




Sagnac effect is a direct consequence of postulate 1.

A specific measurement of G. Designing specific and dedicated experiments in order to eventually validate or invalidate the model.

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