The close relation between mass and speed of electro­magnetic waves (9)

Observe how many expresses the things the known formula for the gravitational force: 

Fgrav = G M1 M2 / r²

We say that the force is equal with the product of two spherical masses M and reversely proportionally to the square of their distance r² (from their centers). If however, we do not insert the gravitational constant G, then the result is not correct in units of force (Newton). The masses from alone them and the distance that separates be taken like static sizes. Is not expressed the phenomenon of attraction except the presence of two masses in some distance from each other. We separately insert the constant G, which (in its dimensional content) includes time t (sec) or acceleration (m/sec²), while without time it could not this constant to express the phenomenon of motion and acceleration, that the force between of masses can causes. We can and insert the constant G, because it has been observed that the sizes (M, r, F and g) are increased or altered with the same rate and proportion. When we insert the constant G then the numerator in the fraction minimizes, after this is a quantity smaller than the unit (10^-11). Thus, for masses 1kg and distance 1m we have the result Fgrav=(6,6725 × 10^-11 ) × 1kg × 1kg / 1m² = 6,6725 × 10^-11 N

Even if the formula gives a result in force of attraction, still we observe in the denominator a distance r² that separates two (bodies) masses M that are attracted. This distance r² in the known formula is expressed as a straight line that links the centers of two masses, while the masses are considered spherical and we know that they attract from all the radius of their ball. That is to say, the gravitational force exists to each radius in the overall surface of masses and in opposite direction to the interior of bodies.

The straight line r² that links two overall masses constitutes the conceivable straight line that links only one from the radius of each ball with the second ball. We could consider that the gravitational force F in the Newton's formula is only one percentage of real gravitational force of each mass, the percentage that it corresponds in their one only radius and only in straight line. The constant G does expresses this percentage for the force of attraction in straight line distance? We could still think, that the force of attraction from the opposite directions of a same body possibly causes a distortion in its effect toward an other separate body. Also, we easily observe that we speak for one conceivable straight line that links the centres of two bodies, but this straight line does not coincide without fail with the straight line for the application of force or from the shortest length between bodies, after their attraction does not cause a rectilinear motion up to the conflict between of bodies.

With the units that are found in the dimensional content in the constant G, the result in the formulas is in agreement with physics very simply, without it needs we make more numerical calculations. Actually, we could not calculate this constant, if the phenomena of mass, gravitational force and distance they were not altered according to certain laws, so as the one depends from other in such way, that they do not force certain limits.

We will watch their relation with an example of mass M and radius r of our planet Earth. ¹.

We observe that the acceleration of gravity g increases depending on mass M (for the same radius).

When mass M increases in square M² then the acceleration g of the M increases on x M, that is to say g × M 

If mass M decreases in square root √M, then the radius r² should downsize in r² / √M so that results the same acceleration g.

Mass of Earth in the square root √ Μ₁ : 2,443972 ×10¹²

F = G √M₁ √M₁ / r² →

F = G (2,443972 ×10¹² ) (2,443972 ×10¹² ) / (6,3787 ×10⁶ )² = 39,8548 ×10¹³ / 40,6878 ×10¹² →

F = 9,795 Newton

g = G M₁ / r² → G × 5,973 ×10²⁴ / (6,3787 ×10⁶ )² = 9,795 m / sec²

The gravitational force F between two same spherical bodies is equal with gravitational accelerator g that cause the product of these two masses at the same radius r. Or the gravitational accelerator g is equal with force F where they would exert the 2 smaller masses  between them, but smaller in the square root of the initial mass √M but in the same distance r.

► From the equations resolved for the constant G and with the example of Sun - Earth 

still we observe :  

From the equation V²earth rers Mearth = M1 M2 G we can find mass of the Sun.

We find the same, from the equation V²earth Mearth / rers = F

Observe, how in one formula of equation the information is hidden, that us presents from the other formula : 

F rers / Mearth = G Msun / rers

►  The gravitational constant G in the Newton's formula shows, that the force between two spherical bodies in certain relation with their distance and mass can be altered, but with such proportion so as an immutable relation results from all together, that we determine it with the physical constant G. In the constant G is found already the answer that we ask. We do not make something else from dissolve the constant G mathematically in order to remains force F or the acceleration a.