The idea is to explain the mystery of the disparity of the measurements of G, the gravitational constant. Indeed, this mystery is explained by an application of the equation of G obtained by this model. This equation is predicting that G depends of the surrounding distribution of matter during the measurement, along the "attracting lines". An attracting line is a straight line in space which connects 2 space points. Each of them must be part of, respectively, each of the 2 attracted masses. The equation of G is showing that the G value is depending of those attracting lines and the presence or absence of matter along those lines. For example, in the non-realistic but limit case of pin pointed masses, it exists only one attracting line. If those objects are located exactly at the same altitude on earth, then this line is an horizontal line. Moreover, if those objects are located in the bottom of a valley, then this line is encountering an important quantity of matter. This matter is the matter of the surrounding mountains. On the contrary, if those objects are located on the top of a hill, then it is possible that this attracting line will not encounter any matter at all on earth. Faraway, of course, this line will probably encounter asteroids, planets, or celestial objects such as stars or gas.
The model (first gravitational model) is predicting a difference in the G value between the two extreme cases above. The value of this relative difference is around 0.001. This value is in accordance with available experimental data. Indeed, the greatest difference between the measured G values is around 0.0065.
1) First experiment.
Realisation of an apparatus, such as the attracting lines between the attracting objects are horizontal, as much as possible. An apparatus such as the one used by Cavendish in 1798 should be enough. It seems to be mandatory to use a laser beam in order to measure the angular deviation. This laser beam will reflect on a little mirror attached to the pendulus beam. One measurement consist of two distinct angular measurements, one with, and another without the presence of the attracting objects nearby.
2) Second experiment.
Execution of two measurements, on distinct locations. For example, one measurement can be done in the bottom of a valley, and the other one at the top of a hill, or at the top of a mountain pass. In the case of a pass, it will be unsured that the attracting lines are encountering as less as possible the nearby mountains (attracting lines perpendicular to the top line of the pass).
For those 2 experiments, only the relative difference of the two measured values matters. This implies that the apparatus is not required to be very precise for an absolute measurement of G. Therefore, a first experimentation might consist of only detecting this difference between the two measurements. If a difference is ever noticed, systematically, then it will be possible on a second step, to get an experimental estimation of the apparatus precision. Concretely, a precision on G of around 0.002 should be enough. Hence, this should allow to detect a relative difference of 0.004 between the two measurements, which is less than the extreme value of 0.0065 above.
To be continuated.