THE LAWS OF GRAVITY

II.2.b) Mercury’s orbit

If the prediction of the Theory of General Relativity about the light curve is the most striking and spectacular due to its way of verifying it with the observation of the eclipse of 1919, the explanation of perihelion precession of Mercury is the most effective for its quantitative feature.

Celestial Mechanics studies the orbit of the planets and other objects due to gravitational effects. Astronomers had observed a deviation unexplained by any known factor of 43.1” of arc in 100 years in the axis of the planet Mercury’s orbit, this deviation in the orbit is what is called perihelion precession of Mercury.

By means of the tremendously complicated field equations of relativist mechanics, Einstein arrived to a very close figure of 43” arc seconds of precession of the Mercury’s orbit, not explained by the Celestial Mechanics..

It is not surprising that in view of the adjustment of the planet Mercury’s orbit obtained by General Relativity that it would end up accepting relativity in its entirety to the detriment of other less risky alternatives. It is unquestionable that the field equations of General Relativity include some valid rules of nature’s behavior although they are masked in their mechanisms of conduct and calculation.

Of course, I imagine any other theory that explains the precession of Mercury’s orbit would have the same unquestionable nature.

Let’s take a look now to see if the Laws of Global Gravity also explains the perihelion precession of Mercury and the physics principles that are derived from it. According to the gravity laws proposed by the Theory of Global Equivalence the gravitational force of attraction will be proportional to the global mass, that is, the mass at rest plus the mass equivalent to kinetic energy.

Conceptually you would say that the mass equivalent to the total kinetic energy, or the kinetic mass, is equal to the kinetic energy [ ½ m₀v²] multiplied by [ 2π] to keep in mind the angular moment and divided by [ c²] accordingly to the famous mass-energy equivalence [ E = mc² ] and also included in the Theory of Global Equivalence but with other premises.

In order to become familiar with the total angular deviation in one revolution or Mercury’s orbit, the only thing we have to do is to substitute the variables for their values, keeping in mind that the total angular acceleration *g_g* should represent the centripetal acceleration due to the gravity force respective to Newton’s law as well as the gravity force added by the laws of global gravity.

That is, *g_g* will be the normal component of the acceleration or angular acceleration that will cause a complete revolution of the planet in the orbit in addition to the observed perihelion precession of Mercury or any other planet for the period *T*. This period *T*, by definition of its value in trigonometry, will cause exactly one complete revolution if it is exclusively considered Newton’s law of universal gravitation, given that we know that a perfectly elliptical orbit would be the result of the inverse-square law of the radius; since it is also observed in Kepler laws derived from the orbits of the planets of the Celestial mechanics.

The fast way for calculating the angular acceleration or normal component of acceleration was shown to me by MrCrackpot in a small experiment of intuitive mathematics. But before going on, I want to review the necessary information to carry out the calculations plus the unnecessary *v*, which are:

For the empirical verification of the formula of the planet Mercury’s dynamics, the following steps have been taken:

• The case of a circular orbit of the planet has been considered in order to simplify the calculations, because the play of gravity’s forces continues existing and the eccentricity of the planet Mercury’s orbit is rather low. Clearly it is sufficient for my purpose here.
  
  
• The formula for global gravity [4.b] can be written as:

   

  

  Where the first term on the right part is the gravity of Newton’s law or centripetal acceleration, the angular variation produced by it in a period should be, in principle, equal to a revolution or *2π* radians.

  So then, if we multiply or divide it by *v²*  and substitute *v²/r* for the normal component of acceleration or angular acceleration *a_n* we will be left with:

  

  And recalling that the value of the orbital speed is the square root of *GM/r* we have to:

  

  Since the normal component of acceleration *a_n* is the angular variation of speed or angular acceleration, if we calculate this angular acceleration by each *m/s* (dividing it by *v*) and we multiply it by the period *T* or the number of total seconds in one revolution, it will give us through trigonometry *2π* radians or one entire revolution of the planet’s orbit.

  Analytically, the previous reasoning would be:

  v T = 2πr w T = 2π v / r = w an / v = w an T / v = T (v²/r) (1/v) = T v/r = w T = 2π radianes q.e.d.

  The previous can be verified by carrying out calculations using the value of the average speed of the planet Mercury. (One entire revolution has 2π radians or 360 degrees, each degree has 60’ minutes and each minute has 60” arc seconds)

Angular acceleration and linear speed of Mercury

• Now then, what we are actually interested in is the second term of the formula [4.b.1] given that it will be the angular deviation of the angular speed or acceleration caused by the mass equivalent to kinetic energy or kinetic mass. Such angular acceleration will cause the perihelion precession of Mercury (ppm), or in any planet’s orbit, if we calculate it for the entire period considering how we have done it previously with *a(n)* to calculate the *2π*radians.  

  According to Mr. Crackpot, the intuitive integral of the differential equation not set out can be directly resolved if, once *v²/r* is substituted by *a(n) *, we place its value for a whole period which, as we have just discussed above in terms of trigonometry, will be *2π*

  In strict terms, it is enough to mention that the formal integral in relation to a whole period of time *T* or one revolution of the angular acceleration is resolved without any problem; since so much speed, the angular acceleration and the rest of the variables are constant or independent of time due to the simplification of a circular orbit of the planet Mercury. For this reason, it coincides with the basic calculations of trigonometry since the integral of *dt* is 1.

  So it remains that in:

  

  Therefore, the perihelion precession of Mercury in radians will be:

  

  The value of the Precession of the Perihelion of Mercury (ppm) obtained with the previous similarity, derived from the Theory of Global Equivalence (TGE) and the Laws of Global Gravity, is 43.08” arc seconds every 100 years as shown in the following graphs:

   

  Perihelion precession of Mercury

                                                                                                             

  G				6,67266E-11
  Sun’s mass	1,98892E+30		GM	1,32714E+20
  Average radius	5,79000E+10		an = GM/r	2,29212E+09
  c²	8,98755E+16		GM / r c²	2,55033E-08
  π	3,141592654		π GM / r c²	8,01210E-08
  2 π Radians/revolution	6,283185307		ppm = 2π² GM / r c²	5,03415E-07	radians/revolution
  Revolutions/100 years	4,14938E+02			2,08886E-04	radians/100 years
  Seconds/radian	2,06265E+05			4,30858E+01	seconds/100 years

We will recall that if in this formula we changed *2π* for *6* it would give us the formula obtained by Einstein in General Relativity regardless of the eccentricity, as mentioned in the book, the Theory of Relativity, Elements and Criticism.

The same formula used provides us with the perihelion precession of other planets and comets of the Solar System, always with previously indicated simplifications. For example; for Earth, general relativity gives a value of 3.8 arc seconds; the TGE, 4.02, and the value observed is 5 with a reliable interval of ± 1.2 arc seconds.

Precession of the planets of the Solar system
 according to the Theory of Global Equivalence

Although there is no doubt that both theories are two correct approaches or two forms of observing the same in relation to the orbit of the planet Mercury, it must be made clear that both are mutually incompatible, since it would doubly explain the same angular deviation.

Nonetheless, there are doubts as to where Einstein got the *6* since *2π* seems to come directly from the physics configuration of the Planck constant.  

 Moreover, they are based on different and contradictory principles; which will make it unnecessary to resort to the Occam razor, since there are other natural phenomena or physics experiments that will help to definitely tip the balance…

With the Laws of Global Gravity, we have verified that it is accurately explained that the perihelion precession of Mercury obtained as a result of the gravitational effect on the mass corresponding to the kinetic energy or kinetic mass, and likewise, the absence of inertia of the mass due to its different nature according to the mentioned gravitational laws.

In other words, the principle of equivalence between gravitational mass and inertial mass established by Newton and upheld by Einstein is incorrect as the perihelion precession of Mercury and the orbits of the planets in general seem to indicate. Maintaining such a principle requires, as done with the current paradigm of the relativist mechanics, to stretch space time in order to fit the elliptical orbits of the planets.

Another principle being that energy does not have mass is also affected in relation to that proposed by Global Mechanics, which is also reinforced with the explanation of the perihelion precession of Mercury by the Laws of Global Gravity.

In conclusion, I want to point out than not once has the non-curved geometry of the Euclidean space been abandoned despite of the planet Mercury’s orbit and that the equation used is supported by a physics model consistent with absolute time.