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The Celestial Mechanics and centripetal acceleration of planet Mercury's orbit.
The anomalous perihelion precession of Mercury's orbit is also explained by a non-relativistic theory.
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'orbit is the most effective for its quantitative feature.
(Public domain image)
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 normally known as perihelion precession of Mercury'orbit, although in strict sense, the total precession is bigger due to the already explained precession.
By means of the tremendously complex field equations of relativistic 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. See the Web page of Mathpages about the anomalous precession of Mercury in General Relativity.
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.
Global Gravity Law
Let’s take a look now to see if the Laws of Global Gravity also explains the perihelion precession of Mercury'orbit and the physical principles that are derived from it.
The formula for the acceleration of gravity taken from the formula given by the Global Law of Gravity provides us with the desired results on angular deviation and the normal component of acceleration or centripetal acceleration.
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 *gg* should represent the centripetal acceleration due to the gravity force of Newton’s law as well as the gravity force added by the Laws of Global Gravity, due to the Merlin effect or second component of the atractis cause.
That is, *gg* will be the normal component of the acceleration or centripetal acceleration that will cause a complete revolution of the planet in the orbit in addition to the observed perihelion precession of Mercury'orbit 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 (even with de the mass increment due to velocity in the natural reference system), 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 centripetal acceleration or normal component of acceleration was shown to me by Sir Magicwick 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:
G = Universal gravitational constant = 6,67266 * 10-11 (m² N / kg²)
c = Speed of light = 2,99792458 * 108 (m/s)
M = Sun’s mass = 1,98892 * 1030 (Kg.)
r = Average radius of Mercury’s orbit = 57,9 * 106 (m)
T = Mercury’s orbit period = 7,60018 * 106 seconds = 414,9378 orbits in 100 years
v = Average speed of Mercury = 47948,31 (m/s)
For the empirical verification of the formula of the planet Mercury’s orbit dynamics, the following steps have been taken:
Circular planetary orbit
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.
Revolutions per period within Newton’s Law of Gravity
The formula for the Global Gravity Law can be written as its two components:
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 centripetal acceleration *an* we will be left with:
And recalling that the value of the orbital speed is the square root of *GM/r* we have to:
If we calculate normal component of acceleration *an* 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 2 π radians or 360 degrees, each degree has 60’ minutes and each minute has 60” arc seconds)
|Average radius||5,79000E+10||an= GM/r²||3,95876E-02|
|Average v||4,794831E+04||an / v = w||8,25631E-07|
|Revol. 100 years||4,149378E+02|
|Periode T||7,60018E+06||w * T = 2 π||6,27494E+00|
Revolutions per period due to the Merlin effect
Now then, what we are actually interested in is the second term of the Global Gravity Law, given that it will be centripetal acceleration caused by the second component of the atractis cause or Merlin effect (derived from the double attraction provoked by the kinetic energy). Such centripetal 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 *2 π*radians.
According to Mr. Magicwick, 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 *2 π*
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 centripetal acceleration is resolved without any problem; since so much speed, the centripetal 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 one.
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:
|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/revol.||6,283185307||ppm = 2π² GM / r c²||5,03415E-07|
|Revol./100 years||4,14938E+02||radians/100 years||2,08886E-04|
|Arc sec/radian||2,06265E+05||Arc sec/100 years||4,30858E+01|
* * *
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 Kriticism.
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 of Einstein gives a value of 3.8 arc seconds; the Global Dynamics, 4.018, and the value observed is is 3,85 arc seconds according the Web page of Mathpages cited above.
|Total radians||Precession arc second|
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.
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 the whole perihelion precession of Mercury's orbit obtained as a result of the Merlin effect or second component of the atractis cause in the interaction of the globine and bodies with mass.
In other words, the principle of equivalence between gravitational mass and inertial mass established by Newton and upheld by Einstein is correct, although if it would no longer be a principle, given that the behavior of physical mass in its interaction with globine is the same, whether studied with or without gravitational field. However, in the case of Global Dynamics it is not necessary to stretch time and space to explain the elliptical orbits of the planets.
In the section on Newton’s Second Law or the Law of Force from the online book of Global Dynamics the differences between the ideas of Newton, Einstein and Global Dynamics itself, due to intrinsic changes in mass and in the active forces, are given in more detail.
In conclusion, I want to point out than not once has the non-curved geometry of the Euclidean space been abandoned despite the curvature of the planet Mercury’s orbit, and that the equation used is supported by a physics model consistent with absolute time.
When Einsother finished the Web page,
he happily went to tell it to Prinspick, who said:
– Very good. And what did you do after that? –
Einsother, hesitating a pit, dit:
– I started to play with marbles
thinking about number π.
Then, a pish girl appeared,
she threw herself at my pheet,
and opened her pleegs
staring at my piballs. –
And Prinspick exclaimed:
– That’s picorny! –
Thanks very much for your visit,
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