1 FEEDBACK IN GRAVITATIONAL PROBLEM OF OLAR CYCLE AND PERIHELION PRECEION OF MERCURY by Jovan Djuic, etied UNM pofesso Balkanska 8, 11000 Belgade, ebia E-mail: olivedj@eunet.s PAC: 96.90.+c ; 96.60.qd ABTRACT Using the model with the two points, the cente of mass and the cente of self gavitation fo any mass object, with the consequential intinsic mass moment of that mass object, it is shown that the obvious feedback in the gavitational poblems logically explains the sola cycle and also the pecession of the peihelion of the planet Mecuy. INTRODUCTION Feedback is a vey familia concept in engineeing, paticulaly in electonic and contol engineeing. But it is inteesting to note that the concept of feedback is not pesent at all in physics, moe pecisely in gavitational poblems and astophysics. Namely, it is obvious that in the case of the planetay system, the gavitational foces acting between the un and the planets must poduce some modifications of the foms of the un and the planets, since those bodies ae not absolutely igid and ae subject to defomations by the mutual gavitational foces. This is paticulaly obvious fo the un, which as plasma must be defomed by the gavitational pulls of the planets. o, the question is aised how to take into account the athe obvious defomation of the un due to the planets, as well as the defomations of the planets themselves. Those defomations ae efeed to as the obvious feedback in the gavitational poblems. REPREENTATION OF PLANET AND UN The obits (tajectoies) of the planets aound the un ae calculated by appoximating the planets and the un as the mass points. uch a model excludes any possibility to take into account any possible defomations of the planets and the un due to thei mutual gavitational attactions. This autho found that anothe impotant point, which must exist fo any mass distibution, is the cente of self gavitation, i.e., the point at which the self gavitation is zeo, v. [1] and []. That point, the cente of self gavitation, is nomally within the mass distibutions, such as planets and stas, but it can be outside the mass distibutions in some vey unusual mass distibutions. The cente of self gavitation neve coincides with the cente of mass, except in the case of the absolute symmety of the obseved mass distibution, which can neve occu in natue due to the pesence of vaious extenal fields, paticulaly gavitational fields, which ae pesent eveywhee in natue.
The cente of self gavitation is not defined in the physics liteatue so fa to the best of knowledge of this autho, cf. [1] and []. That omission, not a simple eo, epesents a vey seious poblem in physics, which excluded the pope analysis and the pope undestanding of some vey impotant and vey inteesting poblems in physics. Thus, any mass object egadless of its size, and including all elementay paticles, must be epesented by the two points, its cente of mass and its cente of self gavitation. uch epesentation of the obseved mass object defines that mass object as a body of the finite dimensions, not a dimensionless mass point, which is vey impotant in the analysis of some poblems. The consequence of this epesentation of the mass object, i.e., mass distibution, by the two points, is that any mass object, and including any elementay paticle, must possess its mass and its intinsic mass moment, which is calculated with espect to its cente of self gavitation. That intinsic mass moment is zeo only in the case of the absolute symmety of any mass object, which neve occus in natue due to the inevitable pesence of vaious field foces, paticulaly gavitational fields. The intinsic mass moment of a mass distibution is an invaiant chaacteistics of the obseved mass object, but it changes if the mass distibution changes. OLAR CYCLE PROBLEM As the fist application of the inclusion of the cente of self gavitation in the analysis, let us conside the sola cycle. The un is epesented by its cente of mass and its cente of self gavitation fo this analysis. elf can be omitted fo bevity, unless it is vey impotant to be emphasized. The un attacts the planets fom its cente of gavitation, while the planets act upon the un at the cente of mass of the un, thus stetching the un. Note that the law of equality of action and eaction must emain valid, but its application is not so simple when the mass objects ae epesented by the two points. Anyway, it is obvious that the un, being plasma, must be somewhat stetched o bulged towads the planets in the plane of the obits (tajectoies) of the planets, i.e., the ecliptic plane If the oigin of the heliocentic coodinate system is placed at the cente of gavitation of the un, then its (un s) cente of mass is defined by the vecto, which must lie in the ecliptic plane, and whose absolute value is detemined by and is popotional to the gavitational pulls of the planets, which also detemine its instantaneous diection. The planet Jupite, which is by fa the lagest planet in ou planetay system, must obviously be the most influential planet in the detemination of that vecto, which obviously changes as the planets evolve aound the un. It is a fact that the poblem of the calculation of the obits (tajectoies) of the planets epesents a fomidable poblem, which can be solved only appoximately. But the intoduction of the obvious feedback makes this poblem even vey much moe fomidable. Howeve, some inteesting conclusions can be eached even without attempting to solve this poblem in its entiety. The fist obvious conclusion is that the vecto must evolve aound the coodinate oigin, which is mainly detemined by
3 the planet Jupite with the mino influences of the othe planets, i.e., appoximately aound 11 yeas as obseved, since 11.86 yeas is the peiod of evolution of Jupite aound the un, and this explains the sola cycle, as will be shown pesently. The ealy gavitational expeiments with the tiangulaly shaped gavitational needles made of wood o any non-feomagnetic mateial and pivoted to otate feely in the Eath s gavitational field and the new gavitational theoy of the oigin of the Eath s magnetic field by this autho ae pesented and descibed in his papes [3] and [4] which ae available on his Intenet ite. His futhe gavitational expeiments ae descibed in his othe papes, which ae submitted fo publication, but the papes [3] and [4] do contain the basic esults. Those expeimental esults show clealy that the intinsic mass moment of any mass object, i.e., mass distibution, is identified as its magnetic moment with a suitable constant of popotionality, which moment depends on the popety of the mateial of the mass object and its fom. Of couse, to epeat once moe, the intinsic mass moment of a mass object is calculated with espect to the cente of the self gavitation of that mass object, and is subject to vaiation if the mass distibution of the mass object vaies. INTRINIC MA MOMENT OF THE UN AND OLAR CYCLE As mentioned, the coodinate oigin of the heliocentic coodinate system is placed at the cente of self gavitation of the un. Thus, the intinsic mass moment of the un is by definition M = ρ dv = M, (1) whee V V ρ is the volume mass density of the un, and is its total mass. The vecto defines as stated ealie the cente of mass of the un in the defined heliocentic coodinate system. The coodinates of integation ae designated by pimes as customay. Note that that cente of mass depends only on and is caused stictly by the gavitational pulls of the planets, in whose assumed absence it must become appoximately zeo, since the un s self gavitation is spheically symmetical and its centifugal acceleation due to its athe iegula otation is axially symmetical, so its cente of mass must be on its axis of otation appoximately. The immediate consequence of the inevitable mass moment of the un due to the stetching o bulging of the un by the planets, i.e., due to the obvious feedback in that gavitational poblem, is that the gavitational potential of the un must contain beside its monopola tem also a dipola tem, so that U = + 3. () The vecto defines the position of the obsevation point fom the cente of the self gavitation of the un. G is the gavitational constant. The gavitational field of the un is, of couse 3G( M ) g = U = + 3 5. (3) 3 M
4 The pesence of the additional tems in the gavitational field of the un, which fall off as 3, is vey pobably quite inconsequential fo the distant planets, but it may be quite impotant fo the planets close to the un, paticulaly fo the closest planet Mecuy and the pecession of its peihelion. Note that the last tem in (3) has a cicula component, beside the adial component, and that cicula component appeas to be the main cause fo the pecession of the peihelion of the planet Mecuy, o at least the significant additional contibution to that effect. This was impossible to take into account so fa, since the cente of self gavitation was not defined o used so fa, and the obvious stetching o bulging of the un towads the planets due to the gavitational pulls of those planets emained unecognized. The analysis of all these poblems is outside of the intended scope of this pape. In view of the numeous gavitational expeiments of this autho, it follows that the intinsic mass moment of the un due to the gavitational pulls of the planets, paticulaly of the planet Jupite, is the magnetic moment of the un, which evolving aound the oigin of the defined heliocentic coodinate system is the cause of the sola cycle. The magnetic moment of the un was obseved to be in the ecliptic plane and nomal to the axis of otation of the un, v. [5]. The actual calculation of the intinsic mass moment of the un due to the gavitational pulls of the planets should be the subject fo anothe faily lage pape. It should be mentioned at the end of this pape that the papes and liteatue on the subject of the so called tides on the un due to the gavitational pulls of the planets epesent in the opinion of this autho the violation of logic. Namely, the tides on the planet Eath epesent the movement of the fluid wate with espect to the fim gound of the Eath due to the gavitational pulls of the Moon mainly, and of the un and the othe planets to a much lesse extent. But the un is only plasma, without any fim potions with espect to which such tides may be obseved and measued. Consequently, the wod tides should not be used in the case of the un, which obviously must be somehow stetched o bulged by the gavitational pulls of the planets, paticulaly Jupite. The only possible way to analyze coectly the obvious stetching o bulging of the un towads the planets due to the gavitational pulls of those planets is to calculate the intinsic mass moment of the un caused by the planets with the obligatoy stictly defined cente of self gavitation of the un as the coodinate oigin as poposed in this pape, but that calculation must be the subject fo anothe pape to epeat once moe. The so fa used coodinate system in the analysis of the un, whose oigin coincides with the cente of mass of the un, cannot be used fo the coect analysis of the stetching o bulging of the un, since in that coodinate system, the mass moment of the un is zeo by definition. But the bulging of the un by the gavitational pulls of the planets is coectly epesented only by the mass moment of the un, which must be zeo by definition in that coodinate system. uch analysis with that coodinate oigin leads inexoably to the logical impasse, even to some logical absudities. It is cetainly physically and logically absud to insist that the bulges of the un due to the gavitational pulls of the planets must occu on the both sides of the un, as such analysis does equie
5 in ode to etain zeo fo the un s mass moment, which is a must fo such analysis in that coodinate system!!?? It is to this logical impasse that the omission of the definition of the cente of self gavitation with the impope choice of the coodinate oigin of the coodinate system has bought physics theoy till today, and it will emain absudly thee until the cente of self gavitation is defined and used as the coodinate oigin of the coodinate system as poposed in this pape. ome physical and logical absudities in the theoy of the elementay paticles also occued due to the omission of the pope definition of the cente of self gavitation as shown by this autho in his othe papes. The pope choice of the coodinate oigin of the coodinate system of obsevation and/o analysis is of the paamount impotance. Remembe the huge poblem of the geocentic system vesus the heliocentic system. It is only the poblem of the pope choice of the coodinate system and its coodinate oigin. REFERENCE 1. Djuic, J. Cente of Mass and Cente of Gavitation, submitted fo publication.. Djuic, J. Poblem of Physics, submitted fo publication and pesented hee as APPENDIX. 3. Djuic, J. Magnetism as Manifestation of Gavitation, available in the pdf fomat on the Intenet ite http://jovandjuic.tipod.com 4. Djuic, J. Expeimental Connection of Magnetism with Gavitation, available in the pdf fomat on the Intenet ite http://jovandjuic.tipod.com 5. Wilcox, J. M. and Gonzalez, W., A Rotating ola Magnetic Dipole Obseved fom 196 to 1968, cience, Vol. 174, pp. 80-81, 1971. APPENDIX PROBLEM OF PHYIC by Jovan Djuic, etied UNM pofesso Balkanska 8, 11000 Belgade, ebia E-mail: olivedj@eunet.s PAC: 01.50.Zv ABTRACT The cente of mass and the cente of gavitation of a mass distibution ae defined. It is pointed out that, appaently, the cente of gavitation has not been defined o used in the published physics liteatue so fa. The cente of mass is defined in all physics textbooks as the point with espect to which the mass moment of the obseved mass distibution is zeo. On the othe hand, the cente of gavity is defined in some textbooks, but not mentioned at all in many othe textbooks. The cente of gavity in the textbooks whee it is mentioned and defined is shown to be in fact the cente of weight and identical to the cente of mass of the obseved mass distibution in the unifom extenal gavitational field. As such, the cente
6 of gavity is totally unnecessay and should not be even mentioned at all. It is obvious that gavity in the expession cente of gavity in the textbooks whee it is mentioned means nothing else but weight, i.e., identically as in the expession specific gavity. Howeve, the language is a living tool, and it changes in time. The wod gavity has assumed fo quite some time also the meaning of the gavitation o the gavitational field as evident, fo example, fom the name of a scientific jounal CLAICAL AND QUANTUM GRAVITY, whee GRAVITY obviously does not efe to WEGHT but cetainly to GRAVITATIONAL FIELD. The expessions wods gavity, gavitation and gavitational field ae fully intechangeable accoding to any college edition of the Webste dictionay, including also the Ameican Heitage Dictionay, electonic vesion. Thus, the expession cente of gavity may be misleading in some situations. o the textbooks, which omit altogethe that expession cente of gavity, ae cetainly justified. Hence, the expession cente of gavity may be sometimes intepeted eoneously as the cente of the gavitational field, o simply, the cente of gavitation. Howeve, it is inteesting to note that the cente of gavitation is not mentioned o defined o used in the published physics liteatue so fa to the best of knowledge of this autho. Consequently, the question is aised what is the meaning of the expession the cente of gavitation and how that tem should be defined?! The only logical definition is that the cente of gavitation (o self gavitation fo emphasis) is the point at which the gavitation, i.e., the gavitational field of the obseved mass distibution is zeo. It is easily concluded fom those definitions that the cente of mass and the cente of self gavitation ae the two distinctly diffeent points which coincide only in the case of the absolute symmety of the obseved mass distibution. Those two points ae the chaacteistic invaiants of the obseved mass distibution, which obviously vay if the obseved mass distibution changes. As an illustative example, conside the simplest mass distibution consisting of the two point masses and m at a distance d fom each othe. Let d designate m1 the distance of the cente of mass measued fom the mass point along the line connecting these two point masses, then m d m d, which yields ( m 1 d dm / m = + 1 / ) 1 ( ) = d d. On the othe hand, let designate the distance of the cente of gavitation measued fom the same point mass along the line connecting these two point masses, then applying the Newton s law of gavity we wite Gm / d = Gm ( d d ), which yields the expession = d m / m. 1 + m d ( G is, of couse, the univesal gavitational constant. Fo m 1 > m, it is easily poved that d > d. It is obvious fom the obtained expessions that these two centes coincide, if and only if those two point masses become equal, in which case that simplest mass distibution becomes symmetical evidently. m 1 m 1 1 )
7 It must be mentioned that the calculation of the cente of gavitation is not a simple task. In the geneal case when the mass distibution is defined by the volume mass density ρ m, the cente of gavitation is the solution of the integal equation ( ) ρ mdv g( ) = G = 0, (1) 3 whee the notation is customay. It is evident fom this equation that the poblem of calculating the cente of gavitation of a geneal mass distibution is fa fom simple, while the calculation of the cente of mass is elatively a simple task of the integations. That may be the explanation of the fact that the cente of gavitation was neve defined o used so fa in the published physics liteatue to the best of knowledge of this autho, to epeat once moe. Of couse, the cente of mass is in the geneal case defined by 1 ( ) dv ρ m = 0 i.e. = ( ρ mdv ) ρ mdv. () This obvious deficiency in the physics textbooks - liteatue should be eliminated.