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4.3 On displacement of the perihelion of planets

Draw an overview of available information on the subject under discussion.

"One of the reasons that originated doubts about the truth of Newton's law of gravitation, was anomalous precession of the perihelion of Mercury, discovered by the French astronomer Verrier in the middle of the XIX century. This phenomenon consists in the fact that the point of the elliptical orbit of the planet closest to the sun moves in the space in the forward direction, i.e., in the direction of motion of the planet, so that the entire orbit around the sun begins to rotate in the same direction. The explanation for this phenomenon Verrier tried to give, assuming that between the Sun and Mercury have some planetary material in the form of a small planet, which scientists later gave the name of Vulcan. In the future, this assumption has not been confirmed. Then it turned out that the perihelion occurs not only for Mercury but also that of other planets in the solar system, including the moon. We briefly discuss the main ideas proposed to explain the perihelion shift.

     As other material bodies that could influence the motion of Mercury, between it and the sun has not appeared, Le Verrier theorized that at perihelion may affect other planets.

However, the influence of the planets was impossible to explain the entire amount of perihelion displacement, which was more than the calculated value of 39 "per century. This discrepancy, Verrier tried to explain by introducing an additional force into the law of gravitation of Newton, which in this case took the following form (in vector form):

                                                                       

where: where G - gravitational constant, M - mass of the Sun, m - mass of the planet, r - distance from the planet to the Sun,  - the unit vector,  - an additional force. "

/§11. On displacement of the perihelion of planets

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"As is known from the literature, all of the planets' orbits evolve over time, including their ellipses as it rotated, but the most noticeable this effect only for Mercury. Observations show that in the 100 years of its perihelion turns to 5600 "(angular seconds), where 5025" it is the turn of the system of reference, and 575 "is a dynamic shift due to the influence of objects in the solar system. Again, as written in literature, 532 "due to the influence of solar system objects of classical mechanics, and 43" are explained by the relativistic mechanics. for example, Lavery found an increase in the longitude of the perihelion of Mercury Julian century, caused by the pull of the other planets, and Clemens has only recently (1947) made impact on the calculation of the perihelion advance not only the planets but the compression of the Sun 0.01, and even from the Mercury 0.025 (only as on itself can be affected by the Mercury I do not understand) .... By the way, Venus perihelion generally occurs in the opposite direction. According Brumberg Experimental data on Mercury and the Earth is 576 and 1179 seconds, and the value at offset 52 seconds of Venus can be entirely explained by the fact that the measurement error of the perihelion of Venus at its microscopic eccentricity 0.0068 can be very large and it is possible that the offset is actually a negative sign. 
/ The shift of the perihelion of Mercury and other planets Venus perihelion generally occurs in the opposite direction. According Brumberg Experimental data on Mercury and the Earth is 576 and 1179 seconds, and the value at offset 52 seconds of Venus can be entirely explained by the fact that the measurement error of the perihelion of Venus at its microscopic eccentricity 0.0068 can be very large and it is possible that the offset is actually a negative sign. / The shift of the perihelion of Mercury and other planets Venus perihelion generally occurs in the opposite direction. According Brumberg Experimental data on Mercury and the Earth is 576 and 1179 seconds, and the value at offset 52 seconds of Venus can be entirely explained by the fact that the measurement error of the perihelion of Venus at its microscopic eccentricity 0.0068 can be very large and it is possible that the offset is actually a negative sign. / The shift of the perihelion of Mercury and other planets that the offset is actually a negative sign. / The shift of the perihelion of Mercury and other planets

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"Attempts to improve Newton's law of universal gravitation undertaken since the mid XVIII century. The first attempt made in 1745, A. K. Klero to explain the anomaly in the motion of the moon. In his memoir "On top of the world system of the gravity" Claire suggested that instead of Newton's law:

the other, more general formula:

Here  — the force of gravity,  — the mass of bodies,  — the distance between the bodies,  — the gravitational constant "

"Article 1895 Saymon Nyukom explored the way to explain the anomalies associated with the modification of the law of universal gravitation. The simplest modification is the square of the distance is replaced by a slightly greater degree:

Then, during one revolution the perihelion will be equal to:
that is, an additional offset equal »

Some scientists (particularly Weber and Ritz) have expressed interest in this approach. Investigated and several more general version of the law of gravitation - adding in formula Newton expression is inversely proportional  or .

Seeliger and Neiman have offered one more modification of the law of universal gravitation:
In it the additional factor  it provides more rapid than that of Newton, gravity decrease with distance. Selection attenuation coefficient  also explains the perihelion of Mercury, but in this case the motion of Venus, Earth and Mars ceased to comply with the observations.

In 1897 the American astronomer William Ernest Brown published a very accurate tables of lunar motion.

At the same time (1896) Hugo Hans von Seeliger explored three options for modification of Newton's law, including the law of the Hall, and showed that they are not in agreement with the observations. In 1910, Newcomb also came to the conclusion that the gravitational field is described by the classic Newton's law. "

/ru.science.wikia.com > the wiki / Smeschenie_perigeliya ... /

In connection with the fitting results to justify the perihelion of Mercury, made by Einstein, A.K. Timiryazev wrote:

"... The formula which expresses this movement, which coincides with Einstein's, was put in another way, and Gerber was already published in Physics and Mathematics Journal [Zeitschrift fur Mathematik und Physik] in 1898, therefore 17 years before Einstein. But the most important thing is not the point. According to the formula of Einstein-Gerber is the following: the movement of the perihelion of a hundred years is 42 arc seconds (42 seconds of arc, ie 42/3600 of a degree - about one-hundredth of a degree). On the other hand, the processing of astronomical observations made by Le Verrier and Newcomb gives 42.2. "; Seemingly better match and can not be expected, however, and it is quite natural for a rigorous scientific work - have a number of scientists was the idea to double-check the findings Verrier and Newcomb, and what happened? it turned out that the calculations were not entirely accurate. E. Wiechert, carefully check the work of Le Verrier and Newcomb, I was not 42.2 "and 34". Grossman [Zeitschrift fur Physik, volume 5, p. 280. 1921 Astronom. Nachr. 214 p. 41 and 195. 1921] are also listed all astronomical observation, wherein it has allocated to a separate group of data received via the meridian circle. 29 observations obtained from this group, "and if you use all the observations, by Grossman turns 38". The results of these calculations has not been disproved. Thus, to talk about the agreement between theory and facts still early, but maybe later. ". /sceptic-ratio.narod.ru›fi/es13.htm/

Without going into an analysis of the conflicting experimental and calculated data, pay attention to the identified representation of data patterns.

Firstly, the state that no theory justifying the amendments to the law of universal gravitation, and the theory itself, explaining the essence of gravitational phenomena, according to Newton himself, so far no one has been presented. At the end of "Scholium generale" ( "general learning") Newton wrote: "So far we have explained the phenomenon of sea and the sky, resorting to the gravitational force, but we have not yet established gravity causes Obviously, this power comes from some cause that. It penetrates until the center of the sun and planets, without losing its ability; it operates in accordance with the particle surface area to be exposed (as is the case with mechanical reasons), and proportional to the amount of solid material which they contain and it applies to all sides over great distances, decreasing in ratio, reverse square of the distance. The attraction of the individual particles that make up the body of the Sun, the distance from the sun decreases in inverse proportion to the square of the distance up to the orbit of Saturn, as is clearly evident from the peace aphelia planets, and up until the last ... In truth, I have not yet managed to bring the cause of these properties of gravity hypothesis, I did not invent. "hypotheses, I did not invent. "hypotheses, I did not invent. "

That less, we must acknowledge that the law of gravity, yet is ingenious hypothesis of Isaac Newton.

Now back to the subject under discussion.

Studies 3.4 and 3.5 make it possible "to deduce the cause of those properties of gravity."

Indeed, when the sun interaction - source with planets - drains, in accordance with the equations 3.5.11 interaction force is reduced by the amount of the second term proportional to . And by reacting the Earth - Photo with the moon - the drain in accordance with the equations 3.5.14 interaction force is increased by the amount of the second term proportional to . Almost the same proportion to come Claireau selection method, Weber and Ritz - "in formula addition Newton expression is inversely proportional  or ».

Relative to the rotation of the perihelion of Venus in the opposite direction relative to the rotation of the perihelion of other planets, we should say that Venus, when the planet - source rotates as justified in the study 3.6 in the opposite direction than the other planets - drains.

According to the available observations anomalous value perihelion planets decreases with distance from the sun planets. But this is the result of the observed deviations from Newton's law of universal gravitation on relatively small distances confirmed by the investigation 3.4 with sufficient accuracy.

The study results prove the mechanical essence, both the law of universal gravitation, and the anomalous precession of the perihelion of the planets of the solar system.