|Carlo Santagata theoretical physics|
Critics to the problem of two bodies
The advancement of Mercury's perihelion
Lunisolar precession and platonic years
the works [1, 2, 3] we examined and criticized the Problem of the two
bodies, fundamental argument of the Modern Celestial Mechanics. In
these works we posed in evidence the following salient points.
where m, M and R are respectively the masses of the grave, of the Earth and the terrestrial ray. So from the said formula we deduce that only when the relation m/M is completely negligible we obtain, as a case limit, Galileo’s fall law. On the terrestrial surface the relation m/M, for a ton grave, is of the order of 1x10-22, so the differences of acceleration among the various graves still escape to any experimental control, even if executed with the most refined modern instruments.
But this implied free fixity of the Sun that, in the specific case of Mercury, costs to C.M. a prevision error of just 44’’ a century, it shakes and strongly upsets it in the explanation of the grandiose phenomenon of the lunisolar precession, explanation in which, once more, it tries to attribute to the gyroscopic phenomenas only the relative motion of 50’’ a year recorded between the Sun and the point γ, to the sole motion of that one, this explanation, for other non-suspect aspects, already strongly contested at its time by scientists like Bernoulli, Eulero and d’Alambert, in ‘700. According to the quoted Authors, Newton’s explanation only would not succeed in justifying the whole observed phenomenon, but these researchers and illustrious scientists didn't advance other hypotheses or effects that would have been able to fill this deficiency that, according to the them, it would explain only about 30’’ a year and not a century. In addiction, the actual acquirements about the terrestrial geoid, constituted by a thin crust that floats on an incandescent magma, also sets in strong discussion the value of the moments of inactivity of the geoid itself, obviously attributed as ad hoc , so Newton’s explanation would go down to about ten seconds a year . To this big and unloadable deficiency of Newton’s justification, as shown in this script, can die the deceasing that instead the Sun suffers from all the various planets, motion unduly annulled by the Celestial Mechanics. So it’s finally found the law with which the move of the Sun toward the point γ should vary and it also succeeds in theoretically appraising the annual variation that suffers that one nowadays we commonly call lunisolar precession. The following graph gives the course of this phenomenon (Fig. 30)
On the abscissa the time is represented in years and on the ordinates the value of the move of the Sun toward the point γ given by the contribution of all the planets, included the negligible 44’’ a century, because of the recoil action of the Sun caused by Mercury. Theoretical variation amounts at ±0.00027 sessagesimal arch seconds a year. The experimental one, by Newcomb, at the beginning of last century it amounted at 0.000222. Instead this variation is totally incomprehensible and unjustifiable with the actual interpretation, absolutely gyroscopic.
So we have the impression, only because we want to avoid to say we’re certain, that if we remove the unbearable and inopportune theorist fixity of the Sun from C.M.’s perturbations theory, that also involves some substantial afterthoughts on the sidereal time, the theory of the insuperable Englishman will give again unexpected, positive and strong surprises.
 By now on, mind this number.
 For the system Earth-Moon it even climbs m/M=1.23x10-2!
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